SBNation.com User Blog: DoctorMyBrainHurts

Simulating Kovi

DoctorMyBrainHurts — Fri, 06 Aug 2010 01:15:46 -0000

I put together a series of simulations to see what spread of shooting production we might expect to see from average players and how the variability in that production compares to what we might expect from Kovi. In looking at the data over the last few years, it appears roughly 500 players have had greater than 20 even strength shots each season, with the maximum shots around 200. I used these as the basis for my models. I'm using a coin-flipping model, with every one of the 500 players other than Kovi having a known shooting percentage of 8.0%

Model 1

Each player takes 110 shots in a season. Data analyzed after 1 and 5 seasons.

Analysis	Average Std. Dev.	25% percentile	75^th percentile
1 year	2.58	2.52	2.63
5 years	1.16	1.13	1.18

For comparison, if each player takes 200 shots in a season

Analysis	Average Std. Dev.	25% percentile	75^th percentile
1 year	1.92	1.88	1.96
5 years	0.86	0.84	0.87

Model 2

Each player was assigned a random number of shots between 20 and 200. The number of shots was distributed uniformly. The same number of shots were taken by that player each season.

Analysis	Average Std. Dev.	25% percentile	75^th percentile
1 year	3.06	2.97	3.14
5 years	1.18	1.16	1.21

At one year, the standard deviations are about 20% greater. At 5 years, however, the standard deviations are only slightly greater than Model 1.

Model 3

Like Model 2, each player was randomly assigned a number of shots between 20 and 200. The player took this many shots in year 1. In the subsequent years, they took 1.2, 1.1, 0.9 and 0.8 times as many shots. Hence the player with 200 average shots took 200 shots in the first season, then 240, 220, 180, and finally 160 shots in the fifth season.

Analysis	Average Std. Dev.	25% percentile	75^th percentile
1 year	3.06	2.97	3.14
5 years	1.37	1.33	1.41

This obviously results in a substantial increase in the standard deviation of the 5 year estimate .

Kovi versus the models

In the first Model, the confidence interval of the average one year estimate of average runs from [2..94, 13.06]. At 5 years, it runs from [5.73 ,10.27] In Model 2, one year is [2.00,14.00] and 5 years is [5.69, 10.31]. In Model 3, one year is the same as model 2 and 5 year is [5.31, 10.69]. So in Model 1, at 5 years, he is at +1.69 SD. In Model 2, he is at +1.65 SD. In Model 3, he is at +1.42 SD.

Gabe had looked at this in an earlier post. He got a standard deviation of 0.44. Working with Model 1, I increased the number of shots in each season until the average standard deviation came down to 0.44. It took 750 shots per player per season for 5 seasons for the average standard deviation to reach this level. In Model 3, it takes about 1950 shots on average per player per season for 5 seasons to reach this level.

Conclusion

In these models, in the land of 8% shooters, the 10% shooter is less than 2 SD above the mean.

Save Percentage On Ice/Off Ice

DoctorMyBrainHurts — Sun, 01 Aug 2010 01:38:09 -0000

I opened another can of worms.

In an earlier post, Scott Reynolds pointed out the discrepancy between on ice save percentage and off ice save percentage for Smid, Fistric, Weaver, and Giordano. So I computed it, and sure enough, Smid's on ice save percentage falls outside the 95% CI established by his off ice save percentage. Same for Weaver. Same for Fistric. Same for Giordano. Uh-oh!

So I went through and calculated Z-statistics for everybody's on ice save percentage relative to their off ice number. Of the 879 players in the 2009 table, 61 had a Z-statistic above +2.0 and 89 had a Z-statistic below -2.0. This includes Fistric at +5.21 and 13 players at -4.0 or less. Jack Johnson is at -7.61. So if save percentages are the same on ice as off ice, there are some incredibly unlikely outcomes.

In 2008, same thing. 886 players. 55 above +2.0. 81 below -2.0 7 below -4.0 Marty Reasoner at +4.21 Alex Henry at -7.22.

2007 has 852 players. 67 above +2.0 86 below -2.0. 9 below -4.0 V. Kozlov at +4.51 Michael Nylander at -5.92.

Then I looked at whether players differ statistically over the 3 years.

LinearModel.1 <- lm(Z ~ NAME, data=zstat)

anova(LinearModel.1)

Analysis of Variance Table

Response: Z

Df Sum Sq Mean Sq F value Pr(>F)

NAME 1184 3336.8 2.8182 1.4486 1.368e-11 ***

Residuals 1406 2735.3 1.9455

52 players are significantly better than average, including Fistric, Weaver, and Smid, Giordano is close. 4 are worse than average: Jack Johnson, Brad Richards, Derek Smith, and Alex Henry. I put the table of coefficients at http://spreadsheets.google.com/ccc?key=0An-GS2MUpN1mdElOUVEyMldsNFdXUkdyZW8yQjhJTHc&hl=en&authkey=CI-h2I4D

So it looks like (I'm probably going to get hate mail for this) some players may well influence save percentage. The effect seems to persist over the 3 years for which I have data.

Defensive Contribution and QualComp/QualTeam

DoctorMyBrainHurts — Sat, 31 Jul 2010 16:17:01 -0000

I think it makes sense to incorporate QualComp and QualTeam into DGVA. It just doesn't make much difference.

I had been pondering whether it helped to utilize QualComp and QualTeam in computing DGVA from GAON and GAOFF. If I understand QualComp correctly, it is the average of (GFON/60 -GFOFF/60) – (GAON/60 – GAOFF/60) for all opponents faced. As such, it is in the same units as DGVA/60, and I think it makes sense to adjust GVA/60 accordingly. Presumably, I could scale DGVA/60 by multiplying by (1 + QC). It seems easier to add QC to DGVA/60. However, since QC is both offense and defense, and DGVA is just defense, I think adding 0.5*QC makes the most sense. Later, if/when I look at OGVA, I would add the other half.

QualTeam to me is a little less clear, since a player's performance influences the GAON/60 rates of his teammates. I'll think about whether there is a easy way to pull out the portion of QT independent of the player we are looking at. In the interim, from a symmetry standpoint if nothing else, we can subtract (to keep the signs and magnitudes correct) 0.5*QT from DGVA/60.

Looking at defensemen who had 20+ games last season, QC runs from +0.150 to -0.184. QT runs from +0.380 to -0..317. The ranges are greater than I would have guessed.

I reran the calculations using adjusted DGVA/60, and there really is not much change. The top 20 are basically the same. I listed them in Appendix A. Jack Johnson remain by far the worst, at -38.95 In looking at the differences between raw GVA and adjusted GVA, only 9 of 304 defensemen saw more than 2 goals difference. I listed the top 5 and bottom 5 in Appendix B. Zbynek Michalek goes up 3.95 due to QualTeam of -0.30. Conversely, Nicklas Lidstrom goes down 3.81 due to a QualTeam of +0.38

Appendix A

Top 20 Defensemen in Adjusted GVA

NAME	Minutes	QCOMP	QTEAM	RawGVA	AdjGVA
MARKFISTRIC	931.97	-0.09	-0.08	33.55	33.53
MARKGIORDANO	1280.84	-0.06	-0.08	20.71	21.00
MIKEWEAVER	971.74	-0.07	0.00	19.60	19.02
KEITHYANDLE	1289.86	-0.07	0.00	19.13	18.33
FRANCISBOUILLON	1296.81	-0.07	-0.01	18.80	18.22
MARCSTAAL	1474.36	0.14	0.06	16.96	17.96
TONILYDMAN	1049.89	-0.02	-0.02	17.15	17.18
ANDREWMACDONALD	751.64	0.02	0.08	17.41	17.06
JOSHGORGES	1332.50	0.01	-0.05	16.21	16.96
CHRISPRONGER	1437.46	0.10	0.18	16.77	15.85
SHELDONBROOKBANK	900.24	-0.07	-0.13	15.30	15.75
LADISLAVSMID	837.93	-0.07	0.02	16.06	15.42
KRISRUSSELL	1049.30	-0.08	-0.02	15.74	15.23
DENNISSEIDENBERG	1363.54	0.01	0.06	14.09	13.54
NICKBOYNTON	689.92	-0.03	0.03	13.80	13.43
SAMILEPISTO	1020.36	-0.05	0.03	13.60	12.93
DMITRYKULIKOV	969.68	-0.05	-0.07	12.61	12.82
RYANWILSON	874.13	-0.09	-0.09	12.38	12.37
JEFFSCHULTZ	1190.63	0.02	0.32	14.68	11.71

Appendix B

Biggest differences between Raw GVA and Adjusted GVA

NAME	Minutes	QCOMP	QTEAM	RawGVA	AdjGVA	Diff
ZBYNEKMICHALEK	1202.4	0.10	-0.30	-18.04	-14.09	3.95
DIONPHANEUF	1415.07	0.07	-0.10	-11.32	-9.29	2.03
RONHAINSEY	1299.2	0.09	-0.10	-3.03	-1.01	2.02
RYANSUTER	1482.56	0.03	-0.12	-8.15	-6.35	1.80
ROMANHAMRLIK	1336.5	0.06	0.30	-4.90	-7.67	-2.77
JEFFSCHULTZ	1190.63	0.02	0.32	14.68	11.71	-2.98
MIKEGREEN	1290	0.00	0.32	-7.96	-11.32	-3.36
BRIANRAFALSKI	1426.62	0.04	0.34	9.75	6.15	-3.60
NICKLASLIDSTROM	1434.18	0.06	0.38	5.26	1.45	-3.81

Defensive Contribution

DoctorMyBrainHurts — Sat, 31 Jul 2010 02:23:52 -0000

Having thoroughly messed up goaltender performance metrics, I lay awake a while last night pondering what to do next. I thought, "I'm a contrarian. Nobody looks at defensive contribution. Let's look at that."

One thing about defensive contribution puzzled me. While I'm no expert on Game Theory, hockey is obviously a zero-sum game. Team A scores a goal means Team B yields a goal. We all know that a goal prevented is as good as a goal scored, or at least that's what I tell my beer league team between periods. Given the zero-sum thing, I would think that the magnitude the value of defensive contribution would be similar to the magnitude the value of offensive contribution. But if you look at GVT in 2009-2010, Alex Ovechkin led the league in OGVT at 26.9, while Zdeno Chara and Chris Pronger led the league in DGVT at 8.9. The asymmetry bothers me.

I intend to sit down and figure out how to calculate DGVT at some point. For now, it looks like doing taxes. So I tried to figure out another method of getting at defensive contribution. A method where, ideally, somebody else does the hard work for me. An approach dawned on me that is probably too good to be true. If this works, somebody must have already described it, although I didn't find any links. If I'm stealing your idea, I apologize

I occurred to me that if I compare GAON/60 and GAOFF/60 the players essentially have done the math for me. The difference has to reflect the individual player's (plus possibly his partner's) contribution, with the team and goaltender effects averaged out. All we have to do is adjust the GAOFF/60 to the league average and we can easily calculate a defensive GVA for the player.

First we compute average GA/60. For NHL defensemen I get 9495 goals against in 232572.47 minutes played. That works out to GA/60 = 2.45 .

How to adjust GAOFF/60? Well, we can add/subtract or multiply/divide. I looked at both. The results tend to be pretty close.

Add/Subtract example

For these examples, I'm looking at 5v5 data. Chris Pronger played 1437.46 minutes at even strength. His GAON/60 was 1.96 and his GAOFF/60 was 2.66. The difference 2.66 – 1.96 gives his GVA/60 of +0.70. His GVA computes to +0.70*1437.46/60 or +16.77.

Multiply/Divide example

Again for Pronger. His ratio of GAON/60 to GAOFF/60 is 1.96/2.66 or 0.7368. This times 2.45 gives his adjusted GAON/60 or 1.80. GVA/60 computed this way is 2.45 – 1.80 or +0.65. GVA is +0.65*1437.46/60 or +15.45

Appendix A contains 5v5 GVA computed both ways for the top 20 defensemen in 2009-2010. The full table is at http://spreadsheets.google.com/ccc?key=0An-GS2MUpN1mdFNkZWYyMlFsb0dUUmUxaDJ5UFFya0E&hl=en&authkey=CKrE1o4D. The differences are generally small. Computationally, add/subtract is easier. Also, if GAOFF/60 is 0, multiply/divide blows up. Using the add method, Mark Fistric led the league at 33.5. Jack Johnson finished last at -37.44. Using the multiply method, Mark Fistric again led the league at 25.77. Jack Johnson again was last at -56.98 From a symmetry standpoint, add/subtract looks more appealing.

Issues

I can see where this method would tend to inflate the value of a good defenseman on an otherwise poor team or inflate the lack of value of a poor defenseman on an otherwise good team (cough, Jack Johnson). Conversely, a good defenseman on a good team is going to have his value somewhat understated. Potentially, you could use QualComp and QualTeam to fine tune GVA, although I'd have to sit down and think about whether this is helpful.

Appendix A

add GVA Defensive GVA calculated by the add/subtract methodology

mult GVA Defensive GVA calculated by the multiply/divide methodology

NAME	TEAM	Minutes	GAON/60	GAOFF/60	addGVA	multGVA
MARKFISTRIC	DAL	931.97	1.03	3.19	33.55	25.77
MARKGIORDANO	CGY	1280.84	1.55	2.52	20.71	20.13
MIKEWEAVER	STL	971.74	1.67	2.88	19.60	16.67
KEITHYANDLE	PHX	1289.86	1.54	2.43	19.13	19.29
FRANCISBOUILLON	NSH	1296.81	1.67	2.54	18.80	18.14
ANDREWMACDONALD	NYI	751.64	2.00	3.39	17.41	12.58
TONILYDMAN	BUF	1049.89	1.83	2.81	17.15	14.95
MARCSTAAL	NYR	1474.36	1.87	2.56	16.96	16.23
CHRISPRONGER	PHI	1437.46	1.96	2.66	16.77	15.45
JOSHGORGES	MTL	1332.50	1.80	2.53	16.21	15.70
LADISLAVSMID	EDM	837.93	2.22	3.37	16.06	11.68
KRISRUSSELL	CBJ	1049.30	1.94	2.84	15.74	13.58
SHELDONBROOKBANK	ANA	900.24	1.93	2.95	15.30	12.71
JEFFSCHULTZ	WSH	1190.63	1.61	2.35	14.68	15.31
DENNISSEIDENBERG	BOS	1363.54	1.89	2.51	14.09	13.75
NICKBOYNTON	CHI	689.92	1.91	3.11	13.80	10.87
SAMILEPISTO	PHX	1020.36	1.53	2.33	13.60	14.31
DMITRYKULIKOV	FLA	969.68	2.04	2.82	12.61	10.95
RYANWILSON	COL	874.13	1.79	2.64	12.38	11.49

Replacement Level Goaltenders

DoctorMyBrainHurts — Fri, 30 Jul 2010 02:59:31 -0000

Replacement goaltenders are not the same as threshold goaltenders.

In baseball, VORP, or Value Over Replacement Player, is one metric used to assess the value of players. Keith Woolner, the creator of VORP, says if a team has to replace a starting player "the team may be stuck playing a utility bench player, bringing up a AAA player, or finding some other journeyman to fill the gap." Woolner continues "Replacement level is the *expected* (his emphasis) level of performance the average team can obtain if it needs to replace a starting player at minimal cost."

I looked for replacement goaltenders by pulling out all goalies who played in 5 games or fewer in a single season.

	Number	Even Strength	Penalty Kill	Power Play	Overall
1 game	78	0.897	0.821	0.900	0.884
1-2 games	120	0.897	0.840	0.864	0.885
1-3 games	155	0.895	0.852	0.878	0.887
1-4 games	181	0.897	0.852	0.880	0.887
1-5 games	207	0.898	0.851	0.858	0.887

These values probably represent a slight overestimate of true replacement level performance, as this includes some injured starters (Khabibulin, Fernandez), and some top prospects (Bernier, Schneider), as well as some "one-hit wonders" (the locally famous Richard Shulmistra, among others).

By comparison, NHL average and threshold values are:

	Even Strength	Penalty Kill	Power Play	Overall
NHL Average	0.917	0.868	0.914	0.909
Calculated Threshold	0.914	0.863	0.911	0.905

Obviously, the value you pick for threshold makes a tremendous difference in calculated GVT. The average NHL team in 2009 faced 2478 shots, 1971 at even strength, 437 on the penalty kill, and 70 on the power play. If a hypothetical starter played 2/3 of his teams minutes, I calculate the goaltender portion of GVT (GGVT) of 4.16 using the threshold numbers and 24.40 using my replacement numbers (As always, I am not attempting to calculate puck handling or shootout, so I am not calculating total GVT). Similarly for Ryan Miller and Vesa Toskala.

Name	GGVT threshold values	GGVT replacement values
Ryan Miller	35.3	61.52
Vesa Toskala	-14.06	-4.65
NHL Average	4.16	24.4

Toskala remains minus even with my values because he remains -7.50 on the penalty kill. Given my other data showing a lack of goalie effect on the PK, I'm not sure it is fair to attribute PK success or failure to individual goaltenders. If you take out the PK, Toskala is a +2.85 in the other situations.

Conclusion

Relative to observed replacement goaltender performance, the standard method of calculating threshold save percentage severely overestimates the ability of a replacement level goaltender to stop the puck at even strength, on the power play, and overall. Since GVT values depend on this threshold performance, GVT values calculated this way will greatly underestimate the magnitude of goaltender contribution relative to replacement level goaltenders.

Acknowledgments

Again, I want to thank Sunny Mehta for his very helpful correspondence. I also want to thank Tom Awad for his patient and thoughtful discussions of GVT.

Comparing GGVT to GVA

DoctorMyBrainHurts — Mon, 26 Jul 2010 04:17:08 -0000

For goaltenders, GGVT is the same as GVA.

I've been looking at simulating goaltender performance and calculating GVA and GVT. Here, I look at actual GGVT compared to actual GVA and the simulation data for GVA. For example, in 2009 Roberto Luongo had a observed GGVT of 11.1 and an observed GVA of 9.03. Simulating his workload, I found that GVA had standard deviation of 12.58 at that workload. Thus a 95% confidence interval for his GVA is [33.68, -15.62]. Since Luongo's GGVT falls in this interval, it is statistically the same as his GVA.

I compared actual GGVT to the calculated confidence intervals for GVA for all 434 goaltenders who played at least 1 game from 2005 to present. The 2009-2010 data is presented in full in Appendix A below. The data for all seasons is here http://spreadsheets.google.com/ccc?key=0An-GS2MUpN1mdFJsZE1veTU4a1o3cjRwTlEtMW43a3c&hl=en&authkey=CP7-uq8F Every single one of the 434 actual GGVT values observed fell within the corresponding 95% confidence interval for GVA.

In most cases, the differences between actual GGVT and GVA are small. There are 30 goalies for whom the difference is greater than 10. 28 of them are from 2005 and 2006. The other 2 are from 2008. For example, Martin Gerber in 2005 has the greatest difference. His actual GGVT was 11.8 but his GVA was -10.4 for a difference of 22.2. I calculate a GGVT* of -3.64, which is a lot closer to his GVA. I have listed the 30 goaltenders, their actual GGVT, GVA, and calculated GGVT* in Appendix B. I am unable to explain why 28 of the 30 most extreme discrepancies occur in those 2 years.

If you compare observed GGVT to the distribution of GVA generated by average goalies, observed GGVT looks more like GVA than GVA itself. Of the 434 observed GGVT values, 31 fell above the average goalie 95% CI, 8 fell below the average goalie 95% CI, and 405 fell within the average goalie 95% CI. For GVA, the numbers were 24 above, 41 below, and 369 within. Thus more of the actual GGVT values fell into the average goalie GVA confidence interval than did actual GVA values.

55 goaltenders have a GVA > actual GGVT. 2 goaltenders, Bryzgalov in 2009 and Halak in 2009 had a GVA that was above the average goalie CI while their actual GGVT was within the average goalie CI.

Why is GGVT the same as GVA? GGVT is defined relative to threshold save percentages while GVA is defined relative to average save percentages. Comparing the values:

	Even Strength	Penalty Kill	Power Play	Overall
NHL Average	0.917	0.868	0.914	0.909
Calculated Threshold	0.914	0.863	0.911	0.905
Required Shots 80% Power	134930	73094	139262	82757

Sample sizes for binomial distribution testing are reasonably easy to calculate. For a given pair of probabilities we can calculate the number of trials needed to see a difference in the two probabilities. Imagine we had a group of "average" goalies and a group of "threshold" goalies. For p1=0.917 and p2=0.914, to have an 80% probability of seeing a difference, the required number of shots each group would need to face calculates as 134930. The table above shows the results for the other pairs of probabilities.

Conclusion

GGVT is statistically indistinguishable from GVA. The threshold save percentages used to calculate GVT are statistically indistinguishable from the average save percentages used to calculate GVA.

Acknowledgments

Again, I want to thank Sunny Mehta for his very helpful correspondence. I also want to thank Tom Awad again for his patient and thoughtful discussions of GVT.

Appendix A

GGVT: GGVT from Tom's tables

GVA: GVA calculated as before

StdDev: standard deviation of GVA derived from the simulations

Upper CI: Upper limit of the 95% CI for GVA

Lower CI: Lower limit of the 95% CI for GVA

Year	Name	GGVT	GVA	StdDev	Upper CI	Lower CI
2009	AndersonCraig	18.50	19.36	13.73	46.27	-7.55
2009	AuldAlex	-5.60	-8.99	7.11	4.94	-22.92
2009	BacklundJohan	0.20	0.14	1.39	2.87	-2.59
2009	BackstromNiklas	-3.50	-9.75	11.65	13.09	-32.59
2009	BernierJonathan	3.90	4.55	2.77	9.98	-0.88
2009	BironMartin	-7.20	-8.81	8.41	7.68	-25.30
2009	BoucherBrian	-3.40	-7.57	8.09	8.29	-23.43
2009	BrodeurMartin	13.70	11.51	12.92	36.84	-13.82
2009	BrodeurMike	4.20	5.20	2.70	10.48	-0.08
2009	BryzgalovIlya	23.60	25.44	12.81	50.55	0.33
2009	BudajPeter	3.30	2.76	5.63	13.80	-8.28
2009	ClemmensenScott	2.40	1.43	7.41	15.96	-13.10
2009	ClimieMatt	-1.20	-1.74	1.71	1.62	-5.10
2009	ConklinTy	10.00	11.26	8.03	27.01	-4.49
2009	CrawfordCorey	0.20	0.15	1.69	3.47	-3.17
2009	CurryJohn	-3.00	-2.92	0.99	-0.97	-4.87
2009	DanisYann	2.50	2.58	4.12	10.65	-5.49
2009	DeslauriersJeff	-7.50	-12.20	11.21	9.77	-34.17
2009	DipietroRick	-0.80	-2.37	4.01	5.48	-10.22
2009	DubielewiczWade	-1.40	-1.73	1.72	1.64	-5.10
2009	DubnykDevan	-8.10	-10.38	6.87	3.09	-23.85
2009	DuchesneJeremy	-0.50	-0.62	0.59	0.53	-1.77
2009	ElliottBrian	3.70	2.12	10.86	23.41	-19.17
2009	EllisDan	1.10	0.00	8.35	16.36	-16.36
2009	EmeryRay	0.40	-1.83	8.10	14.05	-17.71
2009	EnrothJhonas	-0.50	-0.67	1.77	2.80	-4.14
2009	ErsbergErik	0.10	-0.01	4.48	8.77	-8.79
2009	FleuryMarc-Andre	0.00	-4.12	12.22	19.83	-28.07
2009	GaronMathieu	-1.40	-3.62	8.45	12.94	-20.18
2009	GiguereJean-Sebastien	0.50	-0.36	9.24	17.75	-18.47
2009	GreissThomas	2.10	1.33	5.74	12.59	-9.93
2009	GustavssonJonas	-4.10	-7.24	9.81	11.99	-26.47
2009	HalakJaroslav	20.20	21.08	10.70	42.06	0.10
2009	HardingJosh	-1.10	-3.05	7.56	11.76	-17.86
2009	HedbergJohan	10.10	10.36	10.53	31.00	-10.28
2009	HillerJonas	18.30	18.48	12.33	42.64	-5.68
2009	HowardJimmy	24.70	27.12	12.27	51.17	3.07
2009	HuetCristobal	-10.20	-14.60	9.40	3.82	-33.02
2009	JohnsonBrent	0.10	-1.49	6.63	11.51	-14.49
2009	JohnsonChad	1.40	1.20	3.32	7.71	-5.31
2009	KhabibulinNikolai	1.00	0.10	7.09	14.00	-13.80
2009	KhudobinAnton	2.80	3.58	2.02	7.54	-0.38
2009	KiprusoffMiikka	23.00	25.08	12.97	50.50	-0.34
2009	LaBarberaJason	8.30	9.65	6.30	22.00	-2.70
2009	LalimePatrick	0.20	0.13	5.98	11.85	-11.59
2009	LeclairePascal	-12.50	-15.85	8.37	0.55	-32.25
2009	LegaceManny	0.90	-1.35	7.83	14.00	-16.70
2009	LehtonenKari	1.30	1.26	5.38	11.81	-9.29
2009	LeightonMichael	0.10	-2.48	8.67	14.51	-19.47
2009	LundqvistHenrik	25.70	24.55	13.05	50.13	-1.03
2009	LuongoRoberto	11.10	9.03	12.58	33.68	-15.62
2009	MacDonaldJoey	-1.90	-2.43	3.64	4.71	-9.57
2009	MasonChris	11.00	9.60	11.92	32.97	-13.77
2009	MasonSteve	-5.60	-10.88	11.91	12.46	-34.22
2009	McElhinneyCurtis	-1.50	-1.98	6.61	10.99	-14.95
2009	MillerRyan	36.70	40.12	13.10	65.80	14.44
2009	NabokovEvgeni	27.90	30.38	13.64	57.11	3.65
2009	NeuvirthMichal	2.90	2.10	6.11	14.08	-9.88
2009	NiemiAntti	4.30	4.03	8.88	21.44	-13.38
2009	NiittymakiAntero	3.30	3.34	10.80	24.51	-17.83
2009	OsgoodChris	-8.70	-12.33	6.83	1.06	-25.72
2009	PavelecOndrej	-0.50	-2.10	10.65	18.77	-22.97
2009	PechurskiAlexander	0.20	0.23	1.05	2.29	-1.83
2009	PetersJustin	-0.20	-1.21	4.41	7.42	-9.84
2009	PriceCarey	6.10	4.99	10.31	25.21	-15.23
2009	QuickJonathan	1.30	-2.89	12.81	22.22	-28.00
2009	RaskTuukka	24.10	26.92	10.02	46.57	7.27
2009	RaycroftAndrew	2.00	1.18	5.92	12.78	-10.42
2009	RinnePekka	4.70	2.33	11.23	24.35	-19.69
2009	RolosonDwayne	0.00	-3.19	11.37	19.10	-25.48
2009	SalakAlexander	-1.90	-2.03	1.87	1.64	-5.70
2009	SchneiderCory	0.40	0.25	2.20	4.55	-4.05
2009	SmithMike	-5.60	-10.64	9.76	8.50	-29.78
2009	TheodoreJose	4.80	3.98	10.80	25.14	-17.18
2009	ThomasTim	7.50	7.10	9.94	26.58	-12.38
2009	TokarskiDustin	-1.20	-1.62	1.11	0.56	-3.80
2009	ToskalaVesa	-16.90	-21.37	8.08	-5.54	-37.20
2009	TurcoMarty	7.60	7.93	11.51	30.48	-14.62
2009	ValiquetteSteve	-5.60	-7.05	3.28	-0.62	-13.48
2009	VarlamovSemyon	2.30	0.08	7.70	15.16	-15.00
2009	VokounTomas	29.30	32.15	13.14	57.90	6.40
2009	WardCam	10.80	11.49	10.85	32.75	-9.77
2009	ZabaMatt	-0.40	-0.38	1.22	2.00	-2.76

Appendix B

GGVT: GGVT from Tom's tables

GVA: GVA calculated as before

GGVT*: GGVT calculated as before

Defference: GGVT - GVA

Year	Name	GGVT	GVA	GGVT*	Difference
2005	GerberMartin	11.80	-10.40	-3.64	22.20
2005	KhabibulinNikolai	-7.40	-26.29	-16.15	18.89
2005	GaronMathieu	-2.20	-19.80	-10.31	17.60
2005	TheodoreJose	-11.80	-28.17	-18.13	16.37
2005	GrahameJohn	-9.60	-24.79	-14.91	15.19
2005	AuldAlex	11.40	-3.41	2.55	14.81
2005	TurcoMarty	5.10	-8.91	-2.35	14.01
2005	DipietroRick	5.50	-8.37	-1.58	13.87
2006	ThomasTim	8.70	-4.96	1.30	13.66
2005	DenisMarc	5.70	-7.09	-1.35	12.79
2005	AebischerDavid	2.60	-9.91	-3.61	12.51
2006	RaycroftAndrew	-7.60	-20.08	-10.02	12.48
2005	MarkkanenJussi	-9.80	-22.27	-14.42	12.47
2005	FleuryMarc-Andre	3.60	-8.70	-2.60	12.30
2005	LuongoRoberto	35.00	22.76	23.57	12.24
2005	NabokovEvgeni	-10.60	-22.39	-13.78	11.79
2006	WardCam	-3.00	-14.79	-6.95	11.79
2005	JosephCurtis	9.20	-2.47	2.62	11.67
2006	BelfourEd	4.60	-7.04	-1.30	11.64
2008	TurcoMarty	-7.80	-19.33	-9.46	11.53
2005	KolzigOlie	2.80	-8.43	-0.92	11.23
2006	FleuryMarc-Andre	10.00	-1.22	4.10	11.22
2006	NiittymakiAntero	-6.70	-17.90	-9.35	11.20
2005	BelfourEd	-3.20	-14.38	-6.83	11.18
2005	NiittymakiAntero	-0.70	-11.74	-5.47	11.04
2006	DenisMarc	-16.10	-26.84	-17.47	10.74
2006	JosephCurtis	-7.30	-17.90	-9.60	10.60
2005	RaycroftAndrew	-10.40	-20.91	-13.57	10.51
2008	ToskalaVesa	-16.10	-26.37	-15.95	10.27

Simulating GGVT

DoctorMyBrainHurts — Fri, 23 Jul 2010 23:48:33 -0000

In a previous post, I looked at simulating GVA. Here I simulate goaltender performance and calculate the goaltender portion of GVT.

In a previous post, I looked at simulating goaltender performance and calculating GVA. I found that observed values of GVA could be obtained from an average goaltender and random factors. I also found that GVA is fairly imprecise with a relatively large standard deviation and wide confidence interval. I would think GVT would perform similarly to GVA. To explore this, I ran some simulations using a pseudo-random number generator. For these simulations I used ES threshold save percentage of 0.914, PK threshold save percentage of 0.863, and PP threshold save percentage of 0.911. I used the results to calculate the goaltender portion of GVT (GGVT). For these simulations, I did not attempt to calculate puck handling or shoot out contributions. As I found in my last post, the GGVT value I calculated is not quite what Gabe's tables show. As such, I call my statistic GGVT*.

Theoretical Average Goaltender Average Workload

The average NHL team in 2009 faced 2478 shots, 1971 at even strength, 437 on the penalty kill, and 70 on the power play. If a hypothetical starter played 2/3 of his teams minutes, he faced 1314 shots at ES, 291 on the PK, and 47 on the PP. The average goaltender had ES save percentage of 0.917, PK 0.868 and PP 0.914. Running 10,000 simulated seasons gives:

GGVT*

Min. :-34.459

1st Qu.: -1.460

Median : 4.540

Mean : 4.157

3rd Qu.: 9.790

Max. : 39.791

Std. Dev. 8.798131

Thus a 95% CI for GGVT at this workload is [21.401, -13.087]

I ran simulations for each actual goaltender workload. The data for this is in the appendix below. Ryan Miller and Tuukka Rask had GVT values that are above the 95% confidence interval and Vesa Toskala and John Curry had GVT values that are below the 95% confidence interval.

Conclusion

The range of GGVT* seen in a single season can be duplicated by an average goaltender and random factors. Extreme values of GGVT* do lie outside the 95% CI for average GGVT*.

As an estimate of goaltender performance, GGVT* is subject to estimation error. This simulation data suggests that observed GGVT*, like GVA, is a fairly imprecise estimate, with a large standard deviation and a large confidence interval.

Acknowledgments

Again, I want to thank Sunny Mehta for his very helpful correspondence. I also want to thank Tom Awad for his patient and thoughtful discussions of GVT.

Appendix

GVTact : actual GGVT from the 2009-2010 season

Max : maximum GGVT* seen in the simulation at this workload

Min : minimum GGVT* seen in the simulation at this workload

Mean : average GGVT* seen in the simulation at this workload

StdDev : standard deviation of GGVT* seen in the simulation at this workload

Upper CI : upper limit of the 95% confidence interval

Lower CI : lower limit of the 95% confidence interval

Name	GGVTact	Max	Min	Mean	StdDev	Upper CI	Lower CI
MillerRyan	38.5	52.06	-37.94	7.06	13.1	32.74	-18.63
VokounTomas	31.5	53.05	-49.95	6.79	13.14	32.54	-18.95
NabokovEvgeni	30.5	56.71	-52.29	7.37	13.64	34.1	-19.35
HowardJimmy	26.8	49.26	-37.74	5.86	12.27	29.92	-18.19
RaskTuukka	24.9	42.97	-32.03	4.21	10.02	23.86	-15.44
BryzgalovIlya	26	56.08	-49.92	6.86	12.81	31.97	-18.25
KiprusoffMiikka	25.7	53.96	-40.04	6.96	12.97	32.38	-18.46
LundqvistHenrik	28.3	56.54	-44.46	6.76	13.05	32.34	-18.82
HalakJaroslav	21.7	43.68	-43.32	4.58	10.7	25.56	-16.4
AndersonCraig	21.9	60.86	-44.14	7.42	13.73	34.33	-19.49
HillerJonas	20.9	52.71	-42.29	6.26	12.33	30.42	-17.9
BrodeurMartin	17.1	55.06	-38.94	6.63	12.92	31.96	-18.7
WardCam	13.1	46.27	-39.73	4.8	10.85	26.05	-16.46
ConklinTy	10.9	30.87	-33.13	2.59	8.03	18.34	-13.16
HedbergJohan	12.3	44.94	-40.06	4.73	10.53	25.37	-15.91
LaBarberaJason	8.7	22.21	-23.79	1.57	6.3	13.92	-10.79
MasonChris	13.8	51.37	-47.63	5.77	11.92	29.14	-17.6
LuongoRoberto	14.5	55.47	-55.54	6.47	12.58	31.12	-18.18
TurcoMarty	10.6	61.34	-38.66	5.41	11.51	27.96	-17.14
ThomasTim	9.6	39.16	-33.84	4.21	9.94	23.69	-15.28
BrodeurMike	4.1	8.5	-10.5	0.33	2.7	5.62	-4.95
PriceCarey	8.4	41.16	-43.84	4.21	10.31	24.42	-16.01
BernierJonathan	3.8	8.86	-10.14	0.3	2.77	5.72	-5.13
NiemiAntti	6	34.18	-30.82	3.12	8.88	20.52	-14.29
TheodoreJose	7.4	40.55	-40.45	4.52	10.8	25.68	-16.64
KhudobinAnton	2.7	4.75	-8.25	0.2	2.02	4.16	-3.77
NiittymakiAntero	6.1	45.11	-38.89	4.89	10.8	26.06	-16.28
BudajPeter	3.9	22.03	-23.98	1.31	5.63	12.35	-9.72
DanisYann	2.8	14.25	-16.75	0.74	4.12	8.81	-7.34
RinnePekka	7.7	47.41	-35.59	5.1	11.23	27.12	-16.92
ElliottBrian	6.6	46.96	-40.04	4.85	10.86	26.14	-16.44
NeuvirthMichal	3.6	21.63	-23.37	1.62	6.11	13.6	-10.36
ClemmensenScott	3.7	26.64	-28.36	2.15	7.41	16.68	-12.38
GreissThomas	2.8	21.66	-24.34	1.29	5.74	12.55	-9.96
LehtonenKari	1.9	19.44	-21.56	1.26	5.38	11.81	-9.29
JohnsonChad	1.6	11.65	-14.35	0.42	3.32	6.93	-6.1
RaycroftAndrew	2.9	23.64	-23.36	1.41	5.92	13.01	-10.19
SchneiderCory	0.5	5.44	-8.56	0.18	2.2	4.49	-4.12
PechurskiAlexander	0.2	1.27	-5.73	0.04	1.05	2.1	-2.02
CrawfordCorey	0.2	3.27	-6.73	0.11	1.69	3.43	-3.2
BacklundJohan	0.2	2.22	-6.78	0.07	1.39	2.79	-2.66
LalimePatrick	1.1	22.6	-21.41	1.53	5.98	13.25	-10.2
KhabibulinNikolai	2.2	27.11	-23.89	1.93	7.09	15.83	-11.98
VarlamovSemyon	3.7	31.46	-27.54	2.57	7.7	17.66	-12.51
EllisDan	2.9	34.81	-29.19	2.86	8.35	19.23	-13.5
ErsbergErik	0.6	16.8	-19.2	0.79	4.48	9.57	-7.99
GiguereJean-Sebastien	2.8	36.14	-30.86	3.49	9.24	21.6	-14.62
ZabaMatt	-0.3	1.69	-6.32	0.05	1.22	2.43	-2.34
DuchesneJeremy	-0.4	0.4	-2.61	0.01	0.59	1.16	-1.14
EnrothJhonas	-0.4	3.46	-7.55	0.09	1.77	3.56	-3.37
PetersJustin	0.3	16.59	-15.41	0.83	4.41	9.46	-7.8
LegaceManny	2.5	29.12	-28.88	2.49	7.83	17.84	-12.86
JohnsonBrent	1.3	26.32	-26.68	1.77	6.63	14.78	-11.23
TokarskiDustin	-1.1	1.43	-4.57	0.05	1.11	2.23	-2.13
DubielewiczWade	-1.2	3.39	-6.61	0.13	1.72	3.51	-3.24
ClimieMatt	-1	3.38	-8.62	0.11	1.71	3.46	-3.25
EmeryRay	2.1	34.81	-28.19	2.63	8.1	18.52	-13.25
McElhinneyCurtis	-0.2	24.82	-23.18	1.71	6.61	14.67	-11.26
SalakAlexander	-1.6	4.12	-7.88	0.12	1.87	3.8	-3.55
PavelecOndrej	2.5	40.47	-36.54	4.65	10.65	25.52	-16.22
DipietroRick	-0.3	13.27	-15.73	0.62	4.01	8.47	-7.23
MacDonaldJoey	-1.4	12.1	-16.9	0.51	3.64	7.65	-6.64
LeightonMichael	2	35.54	-33.46	3.08	8.67	20.07	-13.91
QuickJonathan	5.5	60.58	-41.42	6.47	12.81	31.57	-18.64
CurryJohn	-2.7	1.12	-4.88	0.05	0.99	2	-1.9
HardingJosh	0.5	28.25	-30.75	2.17	7.56	16.98	-12.65
RolosonDwayne	3.4	41.99	-39.01	5.17	11.37	27.46	-17.12
GaronMathieu	0.6	33.28	-33.72	2.94	8.45	19.5	-13.62
FleuryMarc-Andre	3.9	49.88	-41.12	6.14	12.22	30.09	-17.81
ValiquetteSteve	-4.8	11.39	-13.61	0.42	3.28	6.85	-6.01
GustavssonJonas	-1.2	38.59	-32.41	3.81	9.81	23.04	-15.43
BoucherBrian	-1.4	31.08	-30.92	2.63	8.09	18.49	-13.23
BironMartin	-4.7	35.13	-25.87	2.98	8.41	19.47	-13.51
AuldAlex	-3.8	23.01	-24.99	2.02	7.11	15.95	-11.91
BackstromNiklas	0.4	52.66	-39.34	5.54	11.65	28.38	-17.3
DubnykDevan	-6.2	28.58	-27.42	1.94	6.87	15.41	-11.53
SmithMike	-2.6	45.24	-36.76	4	9.76	23.14	-15.13
MasonSteve	-1.5	46.69	-39.31	5.57	11.91	28.91	-17.76
DeslauriersJeff	-3.6	44.91	-39.09	5.3	11.21	27.27	-16.67
OsgoodChris	-6.8	25.52	-24.48	1.87	6.83	15.26	-11.52
HuetCristobal	-7	42.03	-32.97	3.65	9.4	22.07	-14.77
LeclairePascal	-9.7	32.98	-28.02	2.92	8.37	19.32	-13.48
ToskalaVesa	-13.8	33.25	-34.75	2.66	8.08	18.49	-13.17

Calculating GVT

DoctorMyBrainHurts — Fri, 23 Jul 2010 23:38:42 -0000

Turns out it's harder than you think.

In a previous post, I looked at simulating GVA. Up next, I plan to look at GVT. First, though, I needed to see if I can accurately calculate GVT. Tom Awad outlines how to calculate GVT in his "Understanding GVT" series. In Part 3, http://www.puckprospectus.com/article.php?articleid=236, he explains how to calculate goaltender GVT (GGVT).

Threshold save percentage (Spt) is defined in terms of average save percentage. There is a typo in the equation in the article at this point. Let me define Yield (Y) as Y = 1 – SP. Threshold yield Yt is defined as 4% more than average yield, or Yt = Ya * 1.04. Thus, SPt = SPa - GTV * (1 - SPa)

Save Percentage	ES	PK	PP	Total
Average	0.917	0.868	0.914	0.909
Threshold	0.914	0.863	0.911	0.904

Expected goals are calculated as shots faced times save percentage. Expected goals minus actual goals gives GGVTraw. This is then multiplied by 0.75 to get GGVT. Two additional components, for puck-handling and shootout are added to GGVT to get total GVT. I'm not going to calculate these, but they are small relative to GGVT. Seems easy enough, but I'm not getting the same values Gabe has in his tables. I calculated a piece of GGVTraw at ES, another on PK, and a third on PP. These are added up. For example, for Ryan Miller, I get expected goals against as 197.06, GGVTraw of 47.06, and GGVT as 35.3. Gabe's tables have it as 38.5. Similarly, for Vesa Toskala I get GGVTraw as -18.75 and GGVT as -14.1. Gabe's tables have him at -13.8. In fact, my calculated GGVT values average 1.12 less than Gabe's tables. The appendix has the calculated GGVT values for 2009.

I then calculated GGVT based on total shots and total save percentage. Miller 38.56, Toskala -14.1. Still not quite right. These values are low by 0.51 on average. The appendix also has these values.

I'm going to declare victory and move on. I'm going to calculate GGVT a piece at a time, ES plus PK plus PP. I'll call what I calculate GGVT* to make it clear that what I am calculating is not quite GGVT, although the difference is small, much smaller than the standard deviation we saw with GVA. I suspect the difference in GGVT and GGVT* reflects a difference in calculating shot mix.

Acknowledgment

I want to thank Tom Awad for his patient and very helpful correspondence about GVT.

Appendix

GVTcalc : the GVT calculated from ES + PK + PP

GVTact : GVT from Gabe's tables

Diff1 : difference between GVTcalc and GVTact

GVTtot: the GVT calculated from total shots

Diff2 : the difference between GVTtot and GVTact

Name	GVTcalc	GVTact	Diff1	GVTtot	Diff2
MillerRyan	35.30	38.50	-3.20	38.56	0.06
VokounTomas	29.29	31.50	-2.21	32.08	0.58
NabokovEvgeni	28.28	30.50	-2.22	28.60	-1.90
HowardJimmy	24.95	26.80	-1.85	27.38	0.58
BryzgalovIlya	24.06	26.00	-1.94	24.91	-1.09
KiprusoffMiikka	23.97	25.70	-1.73	24.19	-1.51
LundqvistHenrik	23.66	28.30	-4.64	24.27	-4.03
RaskTuukka	23.23	24.90	-1.67	26.60	1.70
AndersonCraig	20.15	21.90	-1.75	21.04	-0.86
HalakJaroslav	19.26	21.70	-2.44	21.28	-0.42
HillerJonas	18.53	20.90	-2.37	19.92	-0.98
BrodeurMartin	13.54	17.10	-3.56	18.29	1.19
WardCam	12.20	13.10	-0.90	12.20	-0.90
LuongoRoberto	11.60	14.50	-2.90	10.01	-4.49
MasonChris	11.53	13.80	-2.27	11.31	-2.49
HedbergJohan	11.21	12.30	-1.09	8.30	-4.00
ConklinTy	10.40	10.90	-0.50	11.33	0.43
TurcoMarty	10.00	10.60	-0.60	12.63	2.03
LaBarberaJason	8.41	8.70	-0.29	10.56	1.86
ThomasTim	8.37	9.60	-1.23	9.91	0.31
PriceCarey	6.87	8.40	-1.53	4.01	-4.39
TheodoreJose	6.41	7.40	-0.99	7.82	0.42
NiittymakiAntero	6.08	6.10	-0.02	3.77	-2.33
RinnePekka	5.56	7.70	-2.14	5.89	-1.81
NiemiAntti	5.38	6.00	-0.62	6.59	0.59
ElliottBrian	5.22	6.60	-1.38	2.71	-3.89
BrodeurMike	4.13	4.10	0.03	4.69	0.59
BernierJonathan	3.64	3.80	-0.16	3.79	-0.01
BudajPeter	3.02	3.90	-0.88	2.90	-1.00
KhudobinAnton	2.81	2.70	0.11	8.20	5.50
ClemmensenScott	2.73	3.70	-0.97	5.03	1.33
NeuvirthMichal	2.72	3.60	-0.88	3.41	-0.19
QuickJonathan	2.69	5.50	-2.81	3.85	-1.65
DanisYann	2.44	2.80	-0.36	2.48	-0.32
GiguereJean-Sebastien	2.36	2.80	-0.44	1.95	-0.85
EllisDan	2.11	2.90	-0.79	1.47	-1.43
GreissThomas	1.99	2.80	-0.81	2.29	-0.51
RaycroftAndrew	1.98	2.90	-0.92	0.50	-2.40
PavelecOndrej	1.85	2.50	-0.65	0.19	-2.31
VarlamovSemyon	1.84	3.70	-1.86	0.27	-3.43
LehtonenKari	1.83	1.90	-0.07	0.23	-1.67
KhabibulinNikolai	1.58	2.20	-0.62	1.10	-1.10
RolosonDwayne	1.49	3.40	-1.91	2.09	-1.31
FleuryMarc-Andre	1.41	3.90	-2.49	2.95	-0.95
JohnsonChad	1.24	1.60	-0.36	3.31	1.71
LalimePatrick	1.20	1.10	0.10	0.35	-0.75
LegaceManny	0.84	2.50	-1.66	2.23	-0.27
EmeryRay	0.61	2.10	-1.49	-0.35	-2.45
ErsbergErik	0.60	0.60	0.00	-0.46	-1.06
LeightonMichael	0.40	2.00	-1.60	-0.34	-2.34
SchneiderCory	0.33	0.50	-0.17	0.10	-0.40
JohnsonBrent	0.24	1.30	-1.06	1.89	0.59
CrawfordCorey	0.20	0.20	0.00	0.70	0.50
PechurskiAlexander	0.20	0.20	0.00	-1.10	-1.30
BacklundJohan	0.17	0.20	-0.03	-1.30	-1.50
McElhinneyCurtis	-0.13	2.90	-3.03	-1.01	-3.91
ZabaMatt	-0.24	-0.30	0.06	0.88	1.18
PetersJustin	-0.31	0.30	-0.61	-0.59	-0.89
EnrothJhonas	-0.41	-0.40	-0.01	-1.62	-1.22
DuchesneJeremy	-0.45	-0.40	-0.05	2.17	2.57
GaronMathieu	-0.54	0.60	-1.14	-0.53	-1.13
HardingJosh	-0.56	0.50	-1.06	-1.45	-1.95
TokarskiDustin	-1.18	-1.10	-0.08	0.98	2.08
DubielewiczWade	-1.21	-1.20	-0.01	3.74	4.94
ClimieMatt	-1.22	-1.00	-0.22	-2.06	-1.06
DipietroRick	-1.30	-0.30	-1.00	0.32	0.62
SalakAlexander	-1.41	-1.60	0.19	3.21	4.81
MacDonaldJoey	-1.42	-1.40	-0.02	-0.47	0.93
CurryJohn	-2.16	-2.70	0.54	1.58	4.28
GustavssonJonas	-2.56	-1.20	-1.36	-5.03	-3.83
BackstromNiklas	-3.26	0.40	-3.66	-1.49	-1.89
BoucherBrian	-3.69	-1.40	-2.29	-2.69	-1.29
MasonSteve	-3.99	-1.50	-2.49	-4.90	-3.40
BironMartin	-4.40	-4.70	0.30	-4.08	0.62
ValiquetteSteve	-4.96	-4.80	-0.16	-1.00	3.80
SmithMike	-5.07	-2.60	-2.47	-6.31	-3.71
AuldAlex	-5.24	-3.80	-1.44	-3.87	-0.07
DeslauriersJeff	-5.32	-3.60	-1.72	-3.23	0.37
DubnykDevan	-6.31	-6.20	-0.11	-3.91	2.29
OsgoodChris	-7.86	-6.80	-1.06	-6.86	-0.06
HuetCristobal	-8.23	-7.00	-1.23	-7.52	-0.52
LeclairePascal	-9.77	-9.70	-0.07	-10.57	-0.87
ToskalaVesa	-14.06	-13.80	-0.26	-14.09	-0.29
Average Difference			-1.12		-0.51

Simulation of GVA and the estimation error of GVA

DoctorMyBrainHurts — Tue, 20 Jul 2010 01:11:28 -0000

Sunny Mehta recently suggested that the observed range of goaltender save percentages over the course of a single season could essentially be duplicated by an average goalie and random factors. It dawned on me that, if this were true, that observed goaltender performance metrics ought to similarly be indistinguishable from metrics derived from an average goaltender plus random factors. To explore this, I ran some simulations using a pseudo-random number generator. For these simulations I used an ES save percentage of 0.917, PK save percentage of 0.868, and PP save percentage of 0.914

The range of GVA seen in a single season can be duplicated by an average goaltender and random factors. GVA is a fairly imprecise estimate, with a large standard error and a large confidence interval.

Theoretical Average Goaltender Average Workload
The average NHL team in 2009 faced 2478 shots, 1971 at even strength, 437 on the penalty kill, and 70 on the power play. If a hypothetical starter played 2/3 of his teams minutes, he faced 1314 shots at ES, 291 on the PK, and 47 on the PP. Running 10,000 simulated seasons gives:

      GVA
Min.   :-45.4900
1st Qu.: -7.4900
Median : 0.5100
Mean   : 0.0952
3rd Qu.: 8.5100
Max.   : 47.5100

Std. Dev. 11.57677

Thus a 95% CI for GVA is [22.69, -22.69]

Average Goaltender Ryan Miller workload
Miller led the league in GVT. He faced 1690 ES shots, 321 PK shots, and 87 PP shots. 10,000 simulated seasons with an average goaltender facing that workload:

      GVA
Min.   :-46.8800
1st Qu.: -8.8800
Median : 0.1200
Mean   : 0.1159
3rd Qu.: 9.1200
Max.   : 48.1200

Std. Dev. 13.10482

Thus a 95% CI for GVA at this workload is [25.69, -25.69]. Miller's GVA was 40.12, which is outside the CI, but within the range generated.

Average Goaltender Vesa Toskala workload
Toskala, on the other hand, had the worst GVT in the league. He faced 540 ES shots, 151 PK shots, and 23 PP shots. 10,000 simulated seasons with an average goaltender facing that workload:

      GVA
Min.   :-37.3700
1st Qu.: -5.3700
Median : 0.6300
Mean   : 0.0421
3rd Qu.: 5.6300
Max.   : 30.6300

Std. Dev. 8.026439

Thus a 95% CI for GVA at this workload is [15.73, -15.73]. Toskala's GVA was -21.37, which is outside the CI, but again within the range generated.

Conclusion
The range of GVA seen in a single season can be duplicated by an average goaltender and random factors. Extreme values of GVA do lie outside the 95% CI for average GVA.

As an estimate of goaltender performance, GVA is subject to estimation error. This simulation data suggests that observed GVA is a fairly imprecise estimate, with a large standard error and a large confidence interval.

Acknowledgment

I want to thank Sunny Mehta for his very helpful correspondence.

Addendum

Ryan Miller at Ryan Miller workload

      GVA
Min.   : 0.1200
1st Qu.: 32.1200
Median : 40.1200
Mean   : 39.6262
3rd Qu.: 47.3700
Max.   : 83.1200

Std. Dev. 11.79438
95% CI [63.24, 17.00]

Vesa Toskala at Vesa Toskala workload

      GVA
Min.   :-61.3700
1st Qu.: -27.3700
Median : -20.3700
Mean   : -20.0783
3rd Qu.: -14.3700
Max.   : 13.6300

Std. Dev. 8.950644
95% CI [-2.54, -37.62]

Shootout Save Percentage

DoctorMyBrainHurts — Thu, 08 Jul 2010 12:51:26 -0000

The final chapter.

I finish my look at save percentages to shootout data. Once again I calculated logits from the save percentages. In my other analyses, I removed goalies with logits that were infinity or undefined. In this analysis, I ran the data two ways. First, the usual way, removing these goalies. I was concerned that removing them would introduce bias given the much smaller samples sizes and smaller number of shots so I ran the data a second time estimating a logit for these goalies. A save percentage of 1.000 gives a logit of infinity. I assumed the next shot faced would be a goal, calculated the resulting logit, and then multiplied by 2. Hence, for a goalie who is 10 for 10, I assigned a logit of LN(10/1)*2 or 4.605. Similarly, a save percentage of 0.000 gives a logit that is undefined. I assumed the next shot faced would be a save, calculated the resulting logit, and then multiplied by 2. For a goalie who is 0 for 4 (Looking at you, Brian Boucher of 2006), I assigned a logit of LN(1/4)*2 or -2.773. Fortunately, the two methods gave essentially the same results. Since I use shots faced as a weighting factor, and all of these goalies had faced only a handful of shots, the difference in the two approaches was minimal.

Team Effect

Taken by itself, there is no Team effect.

> LinearModel.41 <- lm(ASOLogit ~ Team, data=SOData, weights=TotalSA)

> anova(LinearModel.41)


Analysis of Variance Table

Response: ASOLogit

           Df  Sum Sq Mean Sq F value Pr(>F)

Team       29  214.69  7.4030   1.116 0.3164

Residuals 283 1877.31  6.6336

Year Effect

Taken by itself, there is no Year effect.

> LinearModel.42 <- lm(ASOLogit ~ Year, data=SOData, weights=TotalSA)

> anova(LinearModel.42)


Analysis of Variance Table

Response: ASOLogit

           Df  Sum Sq Mean Sq F value Pr(>F)

Year        1    0.65  0.6539  0.0972 0.7554

Residuals 311 2091.34  6.7246

Goalie Effect

Taken by itself, there is a significant goaltender effect.

> LinearModel.43 <- lm(ASOLogit ~ LastFirst, data=SOData, weights=TotalSA)

> anova(LinearModel.43)

Analysis of Variance Table

Response: ASOLogit

           Df Sum Sq Mean Sq F value   Pr(>F)

LastFirst 108  989.7  9.1639  1.6959 0.000641 ***

Residuals 204 1102.3  5.4034

For the coefficients of the final model, see the Appendix below.

Conclusions

Not surprisingly, shootout save percentage is best predicted by goaltender. Team and Year do not add resolving power to the model. The model predicts about 47% of the total variability seen in the data.

Appendix

Coefficients:	Estimate	Std.Error	tvalue	Pr(>\|t\|)
LastFirst[T.KolesnikVitaly]	3.20E+000	1.04E+000	3.088	0.002
LastFirst[T.BernierJonathan]	2.89E+000	1.10E+000	2.636	0.009
LastFirst[T.GreissThomas]	2.89E+000	1.10E+000	2.636	0.009
LastFirst[T.HolmqvistJohan]	1.29E+000	6.81E-001	1.891	0.060
LastFirst[T.DenisMarc]	1.09E+000	6.57E-001	1.655	0.099
LastFirst[T.HedbergJohan]	7.82E-001	6.05E-001	1.293	0.197
LastFirst[T.PrusekMartin]	1.25E+000	9.88E-001	1.267	0.207
LastFirst[T.GaronMathieu]	7.64E-001	6.04E-001	1.265	0.207
LastFirst[T.NiemiAntti]	7.68E-001	6.85E-001	1.121	0.263
LastFirst[T.JohnsonBrent]	6.72E-001	6.57E-001	1.022	0.308
LastFirst[T.RinnePekka]	5.08E-001	6.15E-001	0.825	0.410
LastFirst[T.LehtonenKari]	4.83E-001	5.98E-001	0.808	0.420
LastFirst[T.TheodoreJose]	4.64E-001	6.13E-001	0.758	0.450
LastFirst[T.DubielewiczWade]	5.35E-001	7.25E-001	0.738	0.461
LastFirst[T.LundqvistHenrik]	4.16E-001	5.73E-001	0.726	0.469
LastFirst[T.SabourinDany]	4.35E-001	6.48E-001	0.671	0.503
LastFirst[T.JosephCurtis]	4.12E-001	6.53E-001	0.631	0.529
LastFirst[T.ThomasTim]	3.64E-001	5.79E-001	0.629	0.530
LastFirst[T.ClemmensenScott]	3.97E-001	6.62E-001	0.599	0.550
LastFirst[T.DiPietroRick]	3.52E-001	5.90E-001	0.596	0.552
LastFirst[T.BrustBarry]	6.91E-001	1.18E+000	0.588	0.557
LastFirst[T.HalakJaroslav]	3.75E-001	6.62E-001	0.566	0.572
LastFirst[T.FernandezManny]	3.19E-001	6.21E-001	0.513	0.608
LastFirst[T.FleuryMarc-Andre]	3.06E-001	5.99E-001	0.510	0.610
LastFirst[T.HillerJonas]	2.99E-001	6.14E-001	0.486	0.627
LastFirst[T.MillerRyan]	2.50E-001	5.77E-001	0.434	0.665
LastFirst[T.VarlamovSemyon]	2.84E-001	6.81E-001	0.417	0.677
LastFirst[T.DeslauriersJeff]	2.67E-001	6.60E-001	0.405	0.686
LastFirst[T.BrodeurMartin]	2.29E-001	5.74E-001	0.399	0.690
LastFirst[T.LaBarberaJason]	2.45E-001	6.55E-001	0.374	0.709
LastFirst[T.HardingJosh]	2.47E-001	6.85E-001	0.361	0.719
LastFirst[T.LuongoRoberto]	2.02E-001	5.79E-001	0.349	0.728
LastFirst[T.PriceCarey]	2.03E-001	6.11E-001	0.332	0.740
LastFirst[T.TellqvistMikael]	2.39E-001	7.47E-001	0.320	0.749
LastFirst[T.DubnykDevan]	2.84E-001	8.90E-001	0.319	0.750
LastFirst[T.NiittymakiAntero]	1.91E-001	6.00E-001	0.318	0.751
LastFirst[T.LegaceManny]	1.89E-001	6.01E-001	0.315	0.753
LastFirst[T.SchaeferNolan]	4.04E-001	1.29E+000	0.314	0.754
LastFirst[T.RolosonDwayne]	1.84E-001	5.87E-001	0.313	0.754
LastFirst[T.MasonChris]	1.73E-001	6.04E-001	0.286	0.775
LastFirst[T.TurcoMarty]	1.60E-001	5.73E-001	0.280	0.780
LastFirst[T.ValiquetteSteve]	1.92E-001	7.07E-001	0.272	0.786
LastFirst[T.GerberMartin]	1.29E-001	6.26E-001	0.206	0.837
LastFirst[T.RaskTuukka]	1.38E-001	6.81E-001	0.203	0.840
LastFirst[T.BacashihuaJason]	1.62E-001	9.17E-001	0.176	0.860
LastFirst[T.HowardJimmy]	8.20E-002	6.33E-001	0.130	0.897
LastFirst[T.QuickJonathan]	4.74E-002	6.19E-001	0.077	0.939
LastFirst[T.ThibaultJocelyn]	3.22E-002	7.07E-001	0.045	0.964
LastFirst[T.LeneveuDavid]	5.97E-016	1.45E+000	0.000	1.000
LastFirst[T.EllisDan]	-2.25E-003	6.60E-001	-0.003	0.997
LastFirst[T.ToivonenHannu]	-3.06E-002	7.55E-001	-0.040	0.968
LastFirst[T.BryzgalovIlya]	-3.85E-002	5.98E-001	-0.064	0.949
LastFirst[T.AubinJean-Sebastien]	-5.53E-002	7.55E-001	-0.073	0.942
LastFirst[T.VokounTomas]	-6.23E-002	5.81E-001	-0.107	0.915
LastFirst[T.GiguereJean-Sebastien]	-6.50E-002	5.90E-001	-0.110	0.912
LastFirst[T.ElliottBrian]	-7.96E-002	6.68E-001	-0.119	0.905
LastFirst[T.MasonSteve]	-8.90E-002	6.26E-001	-0.142	0.887
LastFirst[T.LeclairePascal]	-9.15E-002	6.15E-001	-0.149	0.882
LastFirst[T.KhabibulinNikolai]	-1.44E-001	5.96E-001	-0.242	0.809
LastFirst[T.JohnsonChad]	-2.90E-001	1.18E+000	-0.247	0.805
LastFirst[T.KolzigOlie]	-1.48E-001	5.98E-001	-0.247	0.805
LastFirst[T.NabokovEvgeni]	-1.50E-001	5.81E-001	-0.259	0.796
LastFirst[T.RaycroftAndrew]	-1.63E-001	6.25E-001	-0.261	0.795
LastFirst[T.ErsbergErik]	-1.76E-001	6.48E-001	-0.271	0.787
LastFirst[T.NorrenaFredrik]	-2.15E-001	6.78E-001	-0.317	0.752
LastFirst[T.HasekDominik]	-2.10E-001	6.50E-001	-0.322	0.748
LastFirst[T.GrahameJohn]	-2.42E-001	7.19E-001	-0.337	0.737
LastFirst[T.BelfourEd]	-2.24E-001	6.62E-001	-0.338	0.736
LastFirst[T.OsgoodChris]	-2.17E-001	6.17E-001	-0.352	0.725
LastFirst[T.MacDonaldJoey]	-2.90E-001	8.13E-001	-0.357	0.722
LastFirst[T.CloutierDan]	-4.24E-001	1.10E+000	-0.387	0.699
LastFirst[T.GustavssonJonas]	-4.09E-001	1.04E+000	-0.395	0.693
LastFirst[T.ShieldsSteve]	-6.95E-001	1.73E+000	-0.401	0.689
LastFirst[T.LalimePatrick]	-2.64E-001	6.48E-001	-0.407	0.684
LastFirst[T.WeekesKevin]	-3.21E-001	7.39E-001	-0.434	0.665
LastFirst[T.HuetCristobal]	-2.69E-001	6.12E-001	-0.439	0.661
LastFirst[T.AndersonCraig]	-2.72E-001	6.13E-001	-0.443	0.658
LastFirst[T.AuldAlex]	-2.88E-001	6.31E-001	-0.457	0.648
LastFirst[T.BackstromNiklas]	-3.11E-001	5.90E-001	-0.528	0.598
LastFirst[T.BishopBen]	-6.95E-001	1.29E+000	-0.541	0.589
LastFirst[T.McLennanJamie]	-6.95E-001	1.29E+000	-0.541	0.589
LastFirst[T.MunroAdam]	-6.95E-001	1.29E+000	-0.541	0.589
LastFirst[T.RamoKarri]	-4.74E-001	8.13E-001	-0.584	0.560
LastFirst[T.BudajPeter]	-3.69E-001	6.00E-001	-0.615	0.540
LastFirst[T.BoucherBrian]	-5.28E-001	8.46E-001	-0.624	0.533
LastFirst[T.EmeryRay]	-4.37E-001	6.62E-001	-0.660	0.510
LastFirst[T.WardCam]	-4.14E-001	6.25E-001	-0.663	0.508
LastFirst[T.ConklinTy]	-4.52E-001	6.60E-001	-0.685	0.494
LastFirst[T.GarnettMichael]	-6.95E-001	9.88E-001	-0.704	0.482
LastFirst[T.KiprusoffMiikka]	-4.43E-001	5.97E-001	-0.743	0.458
LastFirst[T.SmithMike]	-4.96E-001	6.50E-001	-0.763	0.446
LastFirst[T.BironMartin]	-5.09E-001	6.29E-001	-0.809	0.419
LastFirst[T.DunhamMike]	-7.21E-001	8.66E-001	-0.832	0.406
LastFirst[T.BurkeSean]	-6.33E-001	6.81E-001	-0.930	0.354
LastFirst[T.LeightonMichael]	-1.10E+000	1.18E+000	-0.936	0.350
LastFirst[T.ClimieMatt]	-1.39E+000	1.45E+000	-0.959	0.339
LastFirst[T.CrawfordCorey]	-1.39E+000	1.45E+000	-0.959	0.339
LastFirst[T.DivisReinhard]	-1.39E+000	1.45E+000	-0.959	0.339
LastFirst[T.ToskalaVesa]	-6.02E-001	6.26E-001	-0.962	0.337
LastFirst[T.PavelecOndrej]	-8.80E-001	8.90E-001	-0.989	0.324
LastFirst[T.SanfordCurtis]	-6.81E-001	6.74E-001	-1.010	0.314
LastFirst[T.MarkkanenJussi]	-8.05E-001	7.65E-001	-1.053	0.294
LastFirst[T.EscheRobert]	-9.72E-001	9.17E-001	-1.060	0.290
LastFirst[T.CaronSebastien]	-1.10E+000	9.17E-001	-1.200	0.232
LastFirst[T.PoggeJustin]	-2.08E+000	1.73E+000	-1.201	0.231
LastFirst[T.CassiviFrederic]	-1.39E+000	1.10E+000	-1.268	0.206
LastFirst[T.DanisYann]	-1.77E+000	9.88E-001	-1.794	0.074
LastFirst[T.SchneiderCory]	-2.89E+000	1.45E+000	-1.995	0.047

Power Play Save Percentage

DoctorMyBrainHurts — Wed, 07 Jul 2010 02:25:55 -0000

I expanded my look at save percentages to power play data. Once again I calculated logits from the save percentages. I removed goalies with logits that were infinity or undefined. Power play save percentage looks a lot like the even strength data. Goalies differ, teams don't. Only here, some goalies are better than average.

Power Play versus Even Strength

There is a small correlation between even strength save percentage and power play save percentage. Power play save percentage is converted to "PPLogit" and even strength save percentage is converted to "RawLogit".

>LinearModel.1 <- lm(PPLogit ~ RawLogit, data=PPData, weights=PPSA)

>anova(LinearModel.1)Analysis of Variance Table
Response:PPLogit

                           Df Sum Sq Mean Sq F value  Pr(>F)

RawLogit    1   70.9  70.922  6.0878 0.01386 *

Residuals 676 7875.3  11.650

While the effect is statistically significant, the effect is of little practical significance.

Year Effect

Unlike even strength, there does not seem to be a year effect.

>LinearModel.3 <- lm(PPLogit ~ Year, data=PPData, weights=PPSA)

>anova(LinearModel.3)

Analysis of Variance Table

Response: PPLogit

               Df Sum Sq Mean Sq F value Pr(>F)

Year        1    1.9  1.8913  0.1609 0.6884

Residuals 676 7944.4 11.7520

Team Effect

Taken by itself, there is no team effect.

>LinearModel.4 <- lm(PPLogit ~ Team, data=PPData, weights=PPSA)

>anova(LinearModel.4)

Analysis of Variance Table

Response: PPLogit

           Df Sum Sq Mean Sq F value Pr(>F)

Team       29  428.6  14.779  1.2739 0.1548

Residuals 648 7517.6  11.601

Goalie Effect

Taken by itself, there is a significant goalie effect.

>LinearModel.2 <- lm(PPLogit ~ lastfirst, data=PPData, weights=PPSA)

>anova(LinearModel.2)

Analysis of Variance Table

Response: PPLogit

               Df Sum Sq Mean Sq F value   Pr(>F)

lastfirst 180 2641.1  14.673  1.3746 0.003857 **

Residuals 497 5305.1  10.674

Multiple Effects

Looking at Team, Year, and Goalie.

>LinearModel.5 <- lm(PPLogit ~ lastfirst+Team+Year, data=PPData, weights=PPSA)

>anova(LinearModel.5)

Analysis of Variance Table

Response: PPLogit

               Df Sum Sq Mean Sq F value   Pr(>F)

lastfirst 180 2641.1 14.6728  1.3640 0.005051 **

Team       29  275.7  9.5067  0.8837 0.643386

Year        1    5.7  5.7223  0.5319 0.466157

Residuals 467 5023.7 10.7574

Since Team and Year don't seem to add anything, let's take them out and compare the resulting model.

>LinearModel.6 <- lm(PPLogit ~ lastfirst, data=PPData, weights=PPSA)

>anova(LinearModel.6)
Analysis of Variance Table

Response: PPLogit

           Df Sum Sq Mean Sq F value   Pr(>F)

lastfirst 180 2641.1  14.673  1.3746 0.003857 **

Residuals 497 5305.1  10.674

>anova(LinearModel.5, LinearModel.6)

Analysis of Variance Table

Model 1: PPLogit ~ lastfirst + Team + Year

Model 2: PPLogit ~ lastfirst

  Res.Df RSS  Df Sum of Sq     F Pr(>F)

1  467 5023.7

2  497 5305.1 -30   -281.42 0.872 0.6644

Comparing the two models shows we have not lost anything. For the coefficients of the final model, see the Appendix below.

Conclusions

Power play save percentage is best predicted by goaltender. Team and Year do not add resolving power to the model. The model predicts about 35% of the total variability seen in the data.

Appendix

Coefficients:	Estimate	Std.Error	tvalue	Pr(>\|t\|)
(Intercept)	2.167	0.282	7.676	0.000
lastfirst[T.HuetCristobal]	1.108	0.365	3.035	0.003
lastfirst[T.HowardJimmy]	1.519	0.527	2.884	0.004
lastfirst[T.RaskTuukka]	1.498	0.589	2.544	0.011
lastfirst[T.DafoeByron]	0.845	0.340	2.488	0.013
lastfirst[T.ThibaultJocelyn]	0.800	0.328	2.440	0.015
lastfirst[T.LeclairePascal]	0.929	0.388	2.393	0.017
lastfirst[T.ElliottBrian]	1.007	0.473	2.127	0.034
lastfirst[T.KiddTrevor]	0.738	0.350	2.112	0.035
lastfirst[T.BudajPeter]	0.777	0.380	2.046	0.041
lastfirst[T.VernonMichael]	0.755	0.385	1.963	0.050
lastfirst[T.TheodoreJose]	0.605	0.326	1.857	0.064
lastfirst[T.GiguereJean-Sebastien]	0.595	0.321	1.854	0.064
lastfirst[T.KhabibulinNikolai]	0.538	0.313	1.718	0.086
lastfirst[T.VokounTomas]	0.509	0.314	1.624	0.105
lastfirst[T.ShieldsSteve]	0.576	0.357	1.615	0.107
lastfirst[T.NoronenMika]	0.944	0.607	1.556	0.120
lastfirst[T.MarkkanenJussi]	0.786	0.514	1.531	0.126
lastfirst[T.NorrenaFredrik]	0.721	0.473	1.524	0.128
lastfirst[T.DanisYann]	0.866	0.607	1.427	0.154
lastfirst[T.BryzgalovIlya]	0.513	0.372	1.377	0.169
lastfirst[T.MillerRyan]	0.424	0.324	1.308	0.192
lastfirst[T.HasekDominik]	0.394	0.317	1.244	0.214
lastfirst[T.CloutierDan]	0.401	0.343	1.169	0.243
lastfirst[T.SmithMike]	0.479	0.415	1.154	0.249
lastfirst[T.JosephCurtis]	0.360	0.315	1.142	0.254
lastfirst[T.BurkeSean]	0.390	0.345	1.129	0.260
lastfirst[T.KiprusoffMiikka]	0.362	0.323	1.122	0.263
lastfirst[T.LehtonenKari]	0.384	0.344	1.115	0.265
lastfirst[T.HnilickaMilan]	0.472	0.425	1.112	0.267
lastfirst[T.GerberMartin]	0.394	0.356	1.107	0.269
lastfirst[T.HealyGlenn]	0.598	0.541	1.104	0.270
lastfirst[T.LalimePatrick]	0.364	0.330	1.100	0.272
lastfirst[T.PriceCarey]	0.444	0.405	1.096	0.274
lastfirst[T.IrbeArturs]	0.356	0.326	1.090	0.276
lastfirst[T.CechmanekRoman]	0.409	0.376	1.088	0.277
lastfirst[T.NiemiAntti]	0.830	0.767	1.082	0.280
lastfirst[T.WaiteJimmy]	0.830	0.767	1.082	0.280
lastfirst[T.GrahameJohn]	0.410	0.387	1.062	0.289
lastfirst[T.SaloTommy]	0.351	0.331	1.060	0.290
lastfirst[T.BelfourEd]	0.330	0.314	1.052	0.293
lastfirst[T.RolosonDwayne]	0.337	0.328	1.026	0.305
lastfirst[T.RanfordBill]	0.634	0.627	1.011	0.313
lastfirst[T.ToivonenHannu]	0.427	0.471	0.906	0.366
lastfirst[T.KolzigOlie]	0.282	0.316	0.894	0.372
lastfirst[T.TurcoMarty]	0.281	0.321	0.878	0.381
lastfirst[T.DipietroRick]	0.303	0.346	0.875	0.382
lastfirst[T.BacashihuaJason]	0.542	0.643	0.842	0.400
lastfirst[T.TurekRoman]	0.299	0.356	0.839	0.402
lastfirst[T.HackettJeff]	0.324	0.406	0.798	0.425
lastfirst[T.NabokovEvgeni]	0.248	0.312	0.795	0.427
lastfirst[T.BrathwaiteFred]	0.261	0.352	0.742	0.458
lastfirst[T.ToskalaVesa]	0.258	0.349	0.738	0.461
lastfirst[T.DenisMarc]	0.239	0.325	0.735	0.462
lastfirst[T.BironMartin]	0.231	0.326	0.710	0.478
lastfirst[T.LegaceManny]	0.230	0.333	0.692	0.489
lastfirst[T.NiittymakiAntero]	0.252	0.367	0.689	0.491
lastfirst[T.HedbergJohan]	0.234	0.345	0.677	0.499
lastfirst[T.RamoKarri]	0.416	0.620	0.671	0.502
lastfirst[T.FitzpatrickMark]	0.484	0.737	0.656	0.512
lastfirst[T.MasonChris]	0.238	0.366	0.651	0.515
lastfirst[T.ThomasTim]	0.218	0.341	0.640	0.522
lastfirst[T.RoyPatrick]	0.206	0.325	0.633	0.527
lastfirst[T.VarlamovSemyon]	0.542	0.864	0.627	0.531
lastfirst[T.NurminenPasi]	0.231	0.381	0.606	0.545
lastfirst[T.HebertGuy]	0.212	0.369	0.574	0.566
lastfirst[T.LaBarberaJason]	0.236	0.433	0.545	0.586
lastfirst[T.OsgoodChris]	0.172	0.319	0.540	0.589
lastfirst[T.SabourinDany]	0.473	0.890	0.531	0.596
lastfirst[T.BrodeurMartin]	0.163	0.310	0.528	0.598
lastfirst[T.AubinJean-Sebastien]	0.189	0.370	0.510	0.610
lastfirst[T.WardCam]	0.171	0.336	0.509	0.611
lastfirst[T.FernandezManny]	0.173	0.340	0.508	0.612
lastfirst[T.LuongoRoberto]	0.157	0.310	0.506	0.613
lastfirst[T.RichterMike]	0.165	0.336	0.492	0.623
lastfirst[T.PuppaDaren]	0.245	0.550	0.446	0.656
lastfirst[T.QuickJonathan]	0.181	0.462	0.393	0.694
lastfirst[T.EscheRobert]	0.164	0.433	0.380	0.704
lastfirst[T.ConklinTy]	0.158	0.425	0.373	0.710
lastfirst[T.McLeanKirk]	0.187	0.517	0.361	0.718
lastfirst[T.GaronMathieu]	0.125	0.363	0.345	0.730
lastfirst[T.VanbiesbrouckJohn]	0.124	0.364	0.340	0.734
lastfirst[T.SanfordCurtis]	0.150	0.450	0.334	0.738
lastfirst[T.TugnuttRon]	0.115	0.364	0.315	0.753
lastfirst[T.RhodesDamian]	0.109	0.363	0.299	0.765
lastfirst[T.LeightonMichael]	0.137	0.475	0.289	0.773
lastfirst[T.BarrassoTom]	0.113	0.403	0.279	0.780
lastfirst[T.PavelecOndrej]	0.169	0.627	0.269	0.788
lastfirst[T.FleuryMarc-Andre]	0.085	0.327	0.259	0.795
lastfirst[T.SnowGarth]	0.093	0.362	0.256	0.798
lastfirst[T.FuhrGrant]	0.099	0.438	0.227	0.821
lastfirst[T.DunhamMike]	0.068	0.333	0.203	0.839
lastfirst[T.AuldAlex]	0.067	0.400	0.168	0.867
lastfirst[T.ShtalenkovMikhail]	0.075	0.534	0.140	0.889
lastfirst[T.HrudeyKelly]	0.085	0.767	0.110	0.912
lastfirst[T.EllisDan]	0.048	0.462	0.104	0.917
lastfirst[T.AndersonCraig]	0.041	0.402	0.102	0.919
lastfirst[T.EssensaBob]	0.039	0.385	0.101	0.920
lastfirst[T.BoucherBrian]	0.035	0.355	0.097	0.922
lastfirst[T.DeslauriersJeff]	0.047	0.594	0.079	0.937
lastfirst[T.ErsbergErik]	0.041	0.660	0.063	0.950
lastfirst[T.MacDonaldJoey]	0.031	0.589	0.052	0.959
lastfirst[T.WeekesKevin]	0.017	0.342	0.049	0.961
lastfirst[T.BerkhoelAdam]	0.031	1.071	0.028	0.977
lastfirst[T.ChiodoAndy]	0.031	1.071	0.028	0.977
lastfirst[T.FisetStephane]	0.011	0.385	0.028	0.977
lastfirst[T.HirschCorey]	0.031	1.071	0.028	0.977
lastfirst[T.McElhinneyCurtis]	0.031	1.071	0.028	0.977
lastfirst[T.ClemmensenScott]	0.003	0.523	0.005	0.996
lastfirst[T.MasonSteve]	-0.004	0.450	-0.010	0.992
lastfirst[T.HardingJosh]	-0.015	0.475	-0.031	0.975
lastfirst[T.LeneveuDavid]	-0.056	0.607	-0.093	0.926
lastfirst[T.LundqvistHenrik]	-0.033	0.337	-0.096	0.923
lastfirst[T.GarnettMichael]	-0.088	0.820	-0.107	0.915
lastfirst[T.TerreriChris]	-0.073	0.660	-0.111	0.911
lastfirst[T.HurmeJani]	-0.062	0.558	-0.112	0.911
lastfirst[T.OuelletMaxime]	-0.110	0.890	-0.123	0.902
lastfirst[T.StorrJamie]	-0.060	0.373	-0.160	0.873
lastfirst[T.LangkowScott]	-0.221	1.189	-0.185	0.853
lastfirst[T.PetersJustin]	-0.221	1.189	-0.185	0.853
lastfirst[T.ReeseJeff]	-0.221	1.189	-0.185	0.853
lastfirst[T.FankhouserScott]	-0.168	0.712	-0.236	0.814
lastfirst[T.MoogAndy]	-0.152	0.627	-0.241	0.809
lastfirst[T.RaycroftAndrew]	-0.097	0.344	-0.283	0.777
lastfirst[T.JohnsonBrent]	-0.106	0.372	-0.284	0.777
lastfirst[T.CousineauMarcel]	-0.375	1.267	-0.296	0.768
lastfirst[T.PotvinFelix]	-0.118	0.383	-0.308	0.758
lastfirst[T.CharpentierSebastien]	-0.295	0.890	-0.331	0.741
lastfirst[T.RousselDominic]	-0.295	0.890	-0.331	0.741
lastfirst[T.BackstromNiklas]	-0.145	0.372	-0.389	0.698
lastfirst[T.PassmoreSteve]	-0.206	0.527	-0.391	0.696
lastfirst[T.FichaudEric]	-0.260	0.660	-0.394	0.694
lastfirst[T.RinnePekka]	-0.183	0.458	-0.399	0.690
lastfirst[T.BrochuMartin]	-0.558	1.363	-0.409	0.683
lastfirst[T.SkudraPeter]	-0.170	0.413	-0.411	0.681
lastfirst[T.HextallRon]	-0.207	0.502	-0.413	0.680
lastfirst[T.TellqvistMikael]	-0.201	0.473	-0.425	0.671
lastfirst[T.EmeryRay]	-0.196	0.378	-0.519	0.604
lastfirst[T.GarnerTyrone]	-0.781	1.488	-0.524	0.600
lastfirst[T.SalakAlexander]	-0.781	1.488	-0.524	0.600
lastfirst[T.WhitmoreKay]	-0.781	1.488	-0.524	0.600
lastfirst[T.HodsonKevin]	-0.432	0.783	-0.551	0.582
lastfirst[T.McKennaMike]	-0.432	0.783	-0.551	0.582
lastfirst[T.HillerJonas]	-0.249	0.441	-0.564	0.573
lastfirst[T.BlackburnDan]	-0.302	0.534	-0.565	0.572
lastfirst[T.ValiquetteSteve]	-0.558	0.984	-0.566	0.571
lastfirst[T.DivisReinhard]	-0.489	0.712	-0.687	0.492
lastfirst[T.HolmqvistJohan]	-0.403	0.583	-0.690	0.490
lastfirst[T.TabaracciRichard]	-0.383	0.523	-0.733	0.464
lastfirst[T.PrusekMartin]	-0.538	0.724	-0.742	0.458
lastfirst[T.ColemanGerald]	-1.474	1.907	-0.773	0.440
lastfirst[T.GageJoaquin]	-1.474	1.907	-0.773	0.440
lastfirst[T.GustafsonDerek]	-1.474	1.907	-0.773	0.440
lastfirst[T.HauserAdam]	-1.474	1.907	-0.773	0.440
lastfirst[T.KochanDieter]	-1.474	1.907	-0.773	0.440
lastfirst[T.MorrisonMichael]	-1.474	1.907	-0.773	0.440
lastfirst[T.TrefilovAndrei]	-1.474	1.907	-0.773	0.440
lastfirst[T.WilkinsonDerek]	-1.474	1.907	-0.773	0.440
lastfirst[T.MaracleNorm]	-0.424	0.538	-0.789	0.430
lastfirst[T.TallasRobbie]	-0.481	0.568	-0.848	0.397
lastfirst[T.LabbeJean-Francois]	-1.068	1.189	-0.898	0.370
lastfirst[T.HalakJaroslav]	-0.452	0.477	-0.946	0.345
lastfirst[T.DubielewiczWade]	-0.499	0.527	-0.948	0.344
lastfirst[T.ParentRich]	-1.242	1.267	-0.980	0.328
lastfirst[T.MunroAdam]	-1.251	1.267	-0.987	0.324
lastfirst[T.YeremeyevVitali]	-1.251	1.267	-0.987	0.324
lastfirst[T.McLennanJamie]	-0.476	0.434	-1.096	0.273
lastfirst[T.CassiviFrederic]	-1.159	1.025	-1.131	0.259
lastfirst[T.CaronSebastien]	-0.499	0.432	-1.155	0.249
lastfirst[T.BillingtonCraig]	-0.556	0.465	-1.196	0.232
lastfirst[T.WreggetKen]	-0.886	0.737	-1.201	0.230
lastfirst[T.NeuvirthMichal]	-0.837	0.689	-1.215	0.225
lastfirst[T.MossTyler]	-1.317	1.071	-1.230	0.219
lastfirst[T.BierkZac]	-0.733	0.583	-1.257	0.209
lastfirst[T.SchwabCorey]	-0.621	0.477	-1.301	0.194
lastfirst[T.GreissThomas]	-1.474	1.125	-1.310	0.191
lastfirst[T.FlahertyWade]	-1.065	0.724	-1.470	0.142
lastfirst[T.LamotheMarc]	-2.860	1.907	-1.499	0.134
lastfirst[T.LarocqueMichel]	-2.860	1.907	-1.499	0.134
lastfirst[T.SauvePhilippe]	-1.474	0.890	-1.656	0.098
lastfirst[T.JablonskiPat]	-2.572	1.488	-1.728	0.085

Penalty Kill Save Percentage

DoctorMyBrainHurts — Wed, 07 Jul 2010 01:29:35 -0000

I expanded my look at save percentages to penalty kill data. Once again I calculated logits from the save percentages. I removed goalies with logits that were infinity or undefined. Compared to even strength, the penalty kill data is a real muddle. The best model explains only about 13% of the variability seen. About 87% of the variability remains unexplained.

Penalty Kill versus Even Strength

There is a small correlation between even strength save percentage and penalty kill save percentage. Penalty kill save percentage is converted to "PKLogit" and even strength save percentage is converted to "RawLogit".

> cor.test(RawLogit, PKLogit, alternative="two.sided", method="pearson")

Pearson's product-moment correlation
data: RawLogit and PKLogit

t = 7.4081, df = 868, p-value = 3.035e-13

alternative hypothesis: true correlation is not equal to 0

95 percent confidence interval:
0.1803148  0.3053741

sample estimates:

      cor
0.2438580

> LinearModel.10 <- lm(PKLogit ~
RawLogit, Data=PKxxx, weights=PKSA)

> anova(LinearModel.10)

Analysis of Variance Table

Response: PKLogit

                Df Sum Sq Mean Sq F value    Pr(>F)

RawLogit    1  497.5  497.54  48.466 6.629e-12 ***

Residuals 868 8910.7   10.27

Year Effect

Unlike even strength, there does not seem to be a year effect. The dotted line is the mean. The solid line is the least squares best fit.

> LinearModel.11 <- lm(PKLogit ~ Year, Data=PKxxx, weights=PKSA)

> anova(LinearModel.11)

Analysis of Variance Table

Response: PKLogit

             Df Sum Sq Mean Sq F value Pr(>F)

Year         1    9.2  9.1984  0.8495 0.3570

Residuals  868 9399.1 10.8284

Team Effect

Taken by itself, there is a small team effect.

> LinearModel.12 <- lm(PKLogit ~ Team, Data=PKxxx, weights=PKSA)

> anova(LinearModel.12)

Analysis of Variance Table

Response: PKLogit

            Df Sum Sq Mean Sq F value   Pr(>F)

Team        29  566.1  19.521  1.8545 0.004252 **

Residuals  840 8842.1  10.526

Goalie Effect

Taken by itself, there does not seem to be a goalie effect.

> LinearModel.13 <- lm(PKLogit ~ GoalieName, Data=PKxxx, weights=PKSA)

> anova(LinearModel.13)

Analysis of Variance Table

Response: PKLogit

                 Df Sum Sq Mean Sq F value Pr(>F)

GoalieName      220 2535.4  11.525  1.0883 0.2148

Residuals       649 6872.8  10.590

Multiple Effects

Looking at Team, Year, and Goalie.

> LinearModel.16 <- lm(PKLogit ~ Year + Team + lastfirst, data=PKData, weights=PKSA)

> anova(LinearModel.16)

Analysis of Variance Table

Response: PKLogit

           Df Sum Sq Mean Sq F value   Pr(>F)

Year        1    9.2  9.1984  0.9051 0.341786

Team       29  566.3 19.5272  1.9215 0.002828 **

lastfirst 220 2542.1 11.5548  1.1370 0.118023

Residuals 619 6290.7 10.1627

Since goalie doesn't add to the model, let's take it out.

Looking at Team and Year.

> LinearModel.14 <- lm(PKLogit ~ Year+Team, data=PKData, weights=PKSA)

> anova(LinearModel.14)

Analysis of Variance Table

Response: PKLogit

           Df Sum Sq Mean Sq F value   Pr(>F)

Year        1    9.2  9.1984  0.8737 0.350194

Team       29  566.3 19.5272  1.8548 0.004243 **

Residuals 839 8832.8 10.5277

Finally, looking at Team, Year, and Team*Year interaction.

> LinearModel.15 <- lm(PKLogit ~ Year*Team, data=PKData, weights=PKSA)

> anova(LinearModel.15)

Analysis of Variance Table

Response: PKLogit

           Df Sum Sq Mean Sq F value    Pr(>F)

Year        1    9.2  9.1984  0.9124 0.3397687

Team       29  566.3 19.5272  1.9369 0.0023447 **

Year:Team  29  666.6 22.9845  2.2798 0.0001598 ***

Residuals 810 8166.2 10.0817

For the coefficients of this model, see the Appendix below.

Comparing the two models shows we have not lost anything.

> anova(LinearModel.15,LinearModel.16)

Analysis of Variance Table

Model 1: PKLogit ~ Year * Team

Model 2: PKLogit ~ Year + Team + lastfirst
    Res.Df    RSS  Df Sum of Sq      F Pr(>F)

1    810 8166.2

2    590 5870.4 220    2295.8 1.0488 0.3283

Conclusions

Penalty kill save percentage is best predicted by Team and a Team*Year interaction term. Goaltenders do not seem to differ significantly and do not add resolving power to the model. The model predicts only about 13% of the total variability seen in the data.

Appendix

> summary(LinearModel.15)

Call:

lm(formula = PKData$PKLogit ~ Year * Team, data = PKData, weights = PKSA)

Residuals:

Min      1Q  Median      3Q     Max

-8.0952 -2.3457 -0.5473  1.7953  9.7120

Coefficients:

Estimate Std. Error t value Pr(>|t|)

(Intercept)      -23.986591  22.206924  -1.080  0.28040

Year               0.012944   0.011086   1.168  0.24329

Team[T.ATL]      -10.523932  35.026909  -0.300  0.76391

Team[T.BOS]       14.805245  32.815465   0.451  0.65199

Team[T.BUF]       27.982456  31.241862   0.896  0.37069

Team[T.CAR]       71.411711  32.527856   2.195  0.02842 *

Team[T.CBJ]       29.715859  39.199665   0.758  0.44863

Team[T.CGY]      -11.023374  30.860942  -0.357  0.72104

Team[T.CHI]        6.342364  32.909471   0.193  0.84723

Team[T.COL]       83.106082  31.357718   2.650  0.00820 **

Team[T.DAL]       77.805340  33.163387   2.346  0.01921 *

Team[T.DET]       78.066731  32.214720   2.423  0.01560 *

Team[T.EDM]       23.276299  31.503776   0.739  0.46022

Team[T.FLA]       -5.228478  31.574171  -0.166  0.86852

Team[T.LAK]       75.850056  31.358441   2.419  0.01579 *

Team[T.MIN]      -31.303930  40.540374  -0.772  0.44024

Team[T.MTL]       20.734570  32.961644   0.629  0.52949

Team[T.NJD]       11.933600  33.733418   0.354  0.72361

Team[T.NSH]       25.535574  34.270177   0.745  0.45641

Team[T.NYI]       49.159100  33.088931   1.486  0.13776

Team[T.NYR]      -21.016443  32.208480  -0.653  0.51426

Team[T.OTT]       33.700302  32.921507   1.024  0.30630

Team[T.PHI]       39.878339  33.149079   1.203  0.22933

Team[T.PHX]       20.381213  33.090162   0.616  0.53811

Team[T.PIT]       24.266255  31.996114   0.758  0.44842

Team[T.SJS]      -14.503204  32.040726  -0.453  0.65092

Team[T.STL]      -15.382665  32.119666  -0.479  0.63213

Team[T.TBL]       35.760341  32.690079   1.094  0.27432

Team[T.TOR]       98.249645  32.546095   3.019  0.00262 **

Team[T.VAN]       29.383455  32.439625   0.906  0.36532

Team[T.WSH]       89.971782  30.869225   2.915  0.00366 **

Year:Team[T.ATL]   0.005163   0.017480   0.295  0.76781

Year:Team[T.BOS]  -0.007405   0.016381  -0.452  0.65137

Year:Team[T.BUF]  -0.013926   0.015597  -0.893  0.37221

Year:Team[T.CAR]  -0.035679   0.016237  -2.197  0.02828 *

Year:Team[T.CBJ]  -0.014835   0.019559  -0.758  0.44839

Year:Team[T.CGY]   0.005478   0.015407   0.356  0.72227

Year:Team[T.CHI]  -0.003197   0.016428  -0.195  0.84574

Year:Team[T.COL]  -0.041499   0.015656  -2.651  0.00819 **

Year:Team[T.DAL]  -0.038867   0.016556  -2.348  0.01913 *

Year:Team[T.DET]  -0.038944   0.016083  -2.421  0.01568 *

Year:Team[T.EDM]  -0.011641   0.015727  -0.740  0.45939

Year:Team[T.FLA]   0.002624   0.015761   0.166  0.86783

Year:Team[T.LAK]  -0.037921   0.015655  -2.422  0.01564 *

Year:Team[T.MIN]   0.015664   0.020228   0.774  0.43893

Year:Team[T.MTL]  -0.010338   0.016453  -0.628  0.52996

Year:Team[T.NJD]  -0.005968   0.016839  -0.354  0.72311

Year:Team[T.NSH]  -0.012764   0.017106  -0.746  0.45579

Year:Team[T.NYI]  -0.024568   0.016514  -1.488  0.13722

Year:Team[T.NYR]   0.010468   0.016079   0.651  0.51519

Year:Team[T.OTT]  -0.016838   0.016433  -1.025  0.30583

Year:Team[T.PHI]  -0.019930   0.016547  -1.204  0.22877

Year:Team[T.PHX]  -0.010213   0.016520  -0.618  0.53662

Year:Team[T.PIT]  -0.012158   0.015972  -0.761  0.44673

Year:Team[T.SJS]   0.007222   0.015995   0.452  0.65175

Year:Team[T.STL]   0.007655   0.016033   0.477  0.63319

Year:Team[T.TBL]  -0.017942   0.016318  -1.100  0.27186

Year:Team[T.TOR]  -0.049103   0.016249  -3.022  0.00259 **

Year:Team[T.VAN]  -0.014681   0.016193  -0.907  0.36487

Year:Team[T.WSH]  -0.044899   0.015410  -2.914  0.00367 **

Beating Save Percentage to Death: The Theory Of Everything

DoctorMyBrainHurts — Tue, 06 Jul 2010 02:04:41 -0000

The Big TOE. The big fella, the Lizard King. Godzilla.

Goalie matters. Hasek was better than Fuhr. Who knew? However, it looks like goalie matters in a perverse sort of way. If you look at the coefficients, only Hasek pops out as better than average. A lot of goalies are worse than average. Somebody has to finish last. Fuhr finished his career with an 0.863 in Calgary in 1999. That will get you there.

Year matters (a little). Average save percentage has gone up from 0.914 in 1997 to 0.920 in 2009. It is reasonable to correct for this effect. I think this effect will vanish in the next few years as I do not expect save percentage to continue to climb much above current levels. Looking at the sum of squares, Year only accounts for something like 0.4% of the total variability.

Age matters (some). Again I expect that this effect is going to diminish over the next couple years. Most of the goalies with a significant upward trend are currently active. I don't think they can continue to go up. Cam Ward has gone from 0.898 to 0.926. He is not going to be at 0.950 in another 5 years. (If he is, Jim Rutherford goes back to being a genius.) Johnathan Bernier was 0.867 in 2007 and 0.961 in 2009. Niittymaki has gone from 0.910 to 0.919. Halak has gone from 0.906 to 0.933. Clemmensen has gone from 0.883 to 0.912. Greiss went from 0.788 (seriously) in 2007 to 0.923 in 2009. Miller has gone from 0.901 to 0.928.

Team doesn't matter at all. Which is good. These are even strength save percentages, and the assumption is that the quality of scoring chances yielded at even strength by all teams should be about the same. This data supports that notion.

>LinearModel.5 <- lm(RawLogit ~ lastfirst/Age+Year+Team,
data=Dataset, weights=ESA)

>anova(LinearModel.5)

Analysis of Variance Table
Response: RawLogit

                      Df Sum Sq Mean Sq F value    Pr(>F)

lastfirst     230 6263.1  27.231  1.9890 1.650e-10 ***

Year            1   63.3  63.340  4.6264   0.03198 *

Team           29  473.7  16.335  1.1932   0.22689

lastfirst:Age 172 2825.5  16.428  1.1999   0.06790 .

Residuals     486 6653.7  13.691

>summary(LinearModel.5)

Call:lm(formula = RawLogit ~ lastfirst/Age + Year + Team, data = Dataset,

    weights = ESA)

Residuals:

       Min           1Q     Median         3Q        Max

-9.993e+00  -1.684e+00 -1.593e-16  1.269e+00  1.055e+01

TeamCoefficients:	Estimate	StdError	tvalue	Pvalue
Team[T.OTT]	0.136	0.148	0.919	0.359
Team[T.NJD]	0.119	0.165	0.721	0.471
Team[T.MIN]	0.038	0.131	0.286	0.775
Team[T.PHI]	0.010	0.131	0.077	0.939
Team[T.CAR]	-0.009	0.124	-0.071	0.943
Team[T.NSH]	-0.013	0.140	-0.095	0.925
Team[T.MTL]	-0.026	0.141	-0.185	0.854
Team[T.VAN]	-0.024	0.128	-0.189	0.850
Team[T.PHX]	-0.025	0.125	-0.198	0.843
Team[T.CGY]	-0.026	0.123	-0.211	0.833
Team[T.BOS]	-0.036	0.134	-0.268	0.789
Team[T.FLA]	-0.052	0.123	-0.420	0.675
Team[T.WSH]	-0.083	0.153	-0.545	0.586
Team[T.STL]	-0.083	0.125	-0.666	0.505
Team[T.PIT]	-0.097	0.139	-0.697	0.486
Team[T.TOR]	-0.094	0.125	-0.754	0.451
Team[T.TBL]	-0.113	0.125	-0.900	0.369
Team[T.ATL]	-0.145	0.153	-0.946	0.345
Team[T.CBJ]	-0.133	0.140	-0.950	0.343
Team[T.DET]	-0.120	0.126	-0.950	0.343
Team[T.CHI]	-0.133	0.136	-0.978	0.328
Team[T.BUF]	-0.137	0.137	-1.000	0.318
Team[T.COL]	-0.146	0.142	-1.027	0.305
Team[T.NYR]	-0.158	0.146	-1.078	0.282
Team[T.NYI]	-0.175	0.133	-1.320	0.187
Team[T.EDM]	-0.192	0.133	-1.446	0.149
Team[T.SJS]	-0.190	0.130	-1.461	0.145
Team[T.LAK]	-0.211	0.132	-1.595	0.111
Team[T.DAL]	-0.256	0.143	-1.795	0.073

AgeCoefficients:	Estimate	StdError	tvalue	Pvalue
WardCam:Age	0.208	0.081	2.567	0.011
BernierJonathan:Age	0.763	0.309	2.466	0.014
NiittymakiAntero:Age	0.195	0.082	2.369	0.018
HalakJaroslav:Age	0.217	0.101	2.145	0.032
ClemmensenScott:Age	0.218	0.102	2.138	0.033
HurmeJani:Age	0.307	0.144	2.124	0.034
GreissThomas:Age	0.690	0.345	1.996	0.046
MillerRyan:Age	0.149	0.075	1.977	0.049
BierkZac:Age	0.184	0.095	1.947	0.052
HebertGuy:Age	0.201	0.104	1.944	0.053
EmeryRay:Age	0.167	0.087	1.921	0.055
VokounTomas:Age	0.137	0.072	1.897	0.058
PotvinFelix:Age	0.145	0.077	1.879	0.061
CechmanekRoman:Age	0.172	0.092	1.878	0.061
LamotheMarc:Age	0.379	0.206	1.838	0.067
TugnuttRon:Age	0.148	0.081	1.830	0.068
RoyPatrick:Age	0.137	0.075	1.826	0.068
SnowGarth:Age	0.140	0.077	1.823	0.069
DipietroRick:Age	0.136	0.075	1.816	0.070
AndersonCraig:Age	0.143	0.079	1.809	0.071
LaBarberaJason:Age	0.163	0.092	1.767	0.078
RolosonDwayne:Age	0.125	0.072	1.734	0.084
BryzgalovIlya:Age	0.153	0.089	1.730	0.084
SabourinDany:Age	0.225	0.131	1.712	0.088
BoucherBrian:Age	0.120	0.073	1.641	0.101
LalimePatrick:Age	0.119	0.073	1.625	0.105
HedbergJohan:Age	0.120	0.075	1.607	0.109
BrodeurMartin:Age	0.114	0.071	1.603	0.110
KhabibulinNikolai:Age	0.115	0.072	1.596	0.111
FleuryMarc-Andre:Age	0.120	0.076	1.581	0.114
McLennanJamie:Age	0.119	0.076	1.569	0.117
WeekesKevin:Age	0.116	0.074	1.556	0.120
CousineauMarcel:Age	1.004	0.658	1.527	0.127
PrusekMartin:Age	0.224	0.148	1.515	0.130
TheodoreJose:Age	0.112	0.074	1.510	0.132
GiguereJean-Sebastien:Age	0.106	0.072	1.457	0.146
RhodesDamian:Age	0.137	0.095	1.451	0.147
BurkeSean:Age	0.107	0.074	1.445	0.149
BudajPeter:Age	0.123	0.085	1.440	0.150
ThomasTim:Age	0.113	0.079	1.436	0.152
TellqvistMikael:Age	0.142	0.100	1.412	0.159
KolzigOlie:Age	0.101	0.072	1.411	0.159
LuongoRoberto:Age	0.101	0.072	1.400	0.162
OuelletMaxime:Age	0.253	0.182	1.389	0.166
SchwabCorey:Age	0.123	0.088	1.388	0.166
GaronMathieu:Age	0.106	0.077	1.381	0.168
RichterMike:Age	0.106	0.077	1.377	0.169
DunhamMike:Age	0.102	0.075	1.362	0.174
JohnsonBrent:Age	0.101	0.074	1.361	0.174
HolmqvistJohan:Age	0.153	0.113	1.354	0.176
ThibaultJocelyn:Age	0.100	0.074	1.351	0.177
SaloTommy:Age	0.103	0.077	1.335	0.182
FernandezManny:Age	0.097	0.073	1.331	0.184
MasonChris:Age	0.104	0.079	1.324	0.186
SchneiderCory:Age	0.818	0.621	1.318	0.188
HowardJimmy:Age	0.161	0.123	1.310	0.191
OsgoodChris:Age	0.094	0.072	1.305	0.192
NabokovEvgeni:Age	0.094	0.072	1.304	0.193
CloutierDan:Age	0.096	0.075	1.287	0.199
GrahameJohn:Age	0.096	0.076	1.264	0.207
AubinJean-Sebastien:Age	0.092	0.075	1.226	0.221
LangkowScott:Age	0.332	0.281	1.180	0.239
LundqvistHenrik:Age	0.090	0.078	1.159	0.247
SkudraPeter:Age	0.101	0.088	1.153	0.250
BironMartin:Age	0.083	0.073	1.142	0.254
LegaceManny:Age	0.081	0.073	1.120	0.263
LeightonMichael:Age	0.094	0.084	1.118	0.264
DanisYann:Age	0.144	0.133	1.079	0.281
NiemiAntti:Age	0.623	0.578	1.077	0.282
EscheRobert:Age	0.083	0.078	1.072	0.284
RinnePekka:Age	0.149	0.142	1.053	0.293
KiprusoffMiikka:Age	0.077	0.074	1.048	0.295
DenisMarc:Age	0.077	0.074	1.043	0.298
BrathwaiteFred:Age	0.087	0.083	1.042	0.298
JosephCurtis:Age	0.073	0.072	1.008	0.314
TabaracciRichard:Age	0.272	0.271	1.004	0.316
HasekDominik:Age	0.073	0.073	0.998	0.319
TurcoMarty:Age	0.071	0.072	0.982	0.327
ParentRich:Age	0.236	0.245	0.963	0.336
FisetStephane:Age	0.048	0.051	0.933	0.351
TurekRoman:Age	0.074	0.081	0.917	0.360
ConklinTy:Age	0.071	0.078	0.914	0.361
LehtonenKari:Age	0.076	0.083	0.910	0.363
RaskTuukka:Age	0.221	0.249	0.888	0.375
RaycroftAndrew:Age	0.066	0.076	0.867	0.386
BelfourEd:Age	0.063	0.073	0.854	0.393
HuetCristobal:Age	0.065	0.076	0.848	0.397
CrawfordCorey:Age	0.214	0.253	0.846	0.398
KiddTrevor:Age	0.065	0.079	0.819	0.413
MunroAdam:Age	0.173	0.216	0.797	0.426
BlackburnDan:Age	0.165	0.212	0.780	0.436
HnilickaMilan:Age	0.091	0.122	0.747	0.455
DafoeByron:Age	0.057	0.077	0.744	0.457
HealyGlenn:Age	0.088	0.119	0.738	0.461
FinleyBrian:Age	0.257	0.354	0.725	0.469
IrbeArturs:Age	0.055	0.077	0.714	0.476
BacashihuaJason:Age	0.202	0.287	0.705	0.481
RamoKarri:Age	0.155	0.221	0.704	0.482
VarlamovSemyon:Age	0.248	0.374	0.664	0.507
PelletierJean-Marc:Age	0.127	0.194	0.657	0.512
McLeanKirk:Age	0.095	0.145	0.654	0.514
AebischerDavid:Age	0.051	0.080	0.645	0.519
HardingJosh:Age	0.074	0.114	0.644	0.520
HillerJonas:Age	0.076	0.120	0.636	0.525
SanfordCurtis:Age	0.059	0.095	0.626	0.531
RanfordBill:Age	0.103	0.166	0.621	0.535
PassmoreSteve:Age	0.057	0.094	0.613	0.540
HirschCorey:Age	0.110	0.189	0.582	0.561
KochanDieter:Age	0.131	0.232	0.565	0.573
NurminenPasi:Age	0.075	0.133	0.565	0.572
LasakJan:Age	0.454	0.819	0.555	0.579
EllisDan:Age	0.058	0.106	0.545	0.586
WhitmoreKay:Age	0.555	1.020	0.544	0.587
NoronenMika:Age	0.078	0.150	0.519	0.604
StorrJamie:Age	0.040	0.079	0.510	0.610
HackettJeff:Age	0.040	0.079	0.505	0.614
GerberMartin:Age	0.039	0.086	0.460	0.646
QuickJonathan:Age	0.072	0.157	0.460	0.646
PriceCarey:Age	0.048	0.110	0.436	0.663
VanbiesbrouckJohn:Age	0.042	0.102	0.415	0.678
PuppaDaren:Age	0.079	0.196	0.405	0.685
WreggetKen:Age	0.062	0.166	0.372	0.710
MaracleNorm:Age	0.058	0.158	0.366	0.714
VernonMichael:Age	0.033	0.092	0.362	0.718
CaronSebastien:Age	0.037	0.103	0.359	0.720
NeuvirthMichal:Age	0.163	0.479	0.340	0.734
FankhouserScott:Age	0.132	0.390	0.339	0.735
AuldAlex:Age	0.027	0.085	0.316	0.752
HodsonKevin:Age	0.035	0.114	0.303	0.762
McElhinneyCurtis:Age	0.193	0.675	0.286	0.775
LabbeJean-Francois:Age	0.083	0.297	0.279	0.780
MarkkanenJussi:Age	0.019	0.085	0.221	0.825
LeneveuDavid:Age	0.089	0.438	0.203	0.839
BrochuMartin:Age	0.027	0.199	0.136	0.892
BackstromNiklas:Age	0.009	0.087	0.104	0.917
WilkinsonDerek:Age	0.050	0.517	0.097	0.923
FountainMichael:Age	0.031	0.347	0.089	0.929
DeslauriersJeff:Age	0.022	0.277	0.080	0.937
ChabotFrederic:Age	0.015	0.401	0.038	0.969
ToskalaVesa:Age	0.000	0.080	0.005	0.996
FlahertyWade:Age	0.000	0.128	-0.003	0.998
PavelecOndrej:Age	-0.001	0.163	-0.007	0.994
BarrassoTom:Age	-0.009	0.105	-0.087	0.931
LittleNeil:Age	-0.127	0.811	-0.156	0.876
ShieldsSteve:Age	-0.013	0.080	-0.159	0.874
SmithMike:Age	-0.023	0.108	-0.216	0.829
BillingtonCraig:Age	-0.022	0.097	-0.221	0.825
DubielewiczWade:Age	-0.030	0.129	-0.233	0.816
EssensaBob:Age	-0.031	0.106	-0.291	0.771
LeclairePascal:Age	-0.025	0.086	-0.291	0.771
MacDonaldJoey:Age	-0.094	0.300	-0.313	0.754
FuhrGrant:Age	-0.051	0.133	-0.384	0.701
MossTyler:Age	-0.068	0.151	-0.450	0.653
ValiquetteSteve:Age	-0.093	0.195	-0.478	0.633
ElliottBrian:Age	-0.097	0.187	-0.521	0.603
ToivonenHannu:Age	-0.081	0.155	-0.525	0.600
MasonSteve:Age	-0.088	0.162	-0.543	0.588
ClimieMatt:Age	-0.447	0.777	-0.576	0.565
CareyJim:Age	-0.337	0.571	-0.590	0.555
CassiviFrederic:Age	-0.085	0.137	-0.623	0.533
SauvePhilippe:Age	-0.189	0.302	-0.628	0.530
NorrenaFredrik:Age	-0.104	0.160	-0.649	0.517
RousselDominic:Age	-0.186	0.282	-0.660	0.510
HextallRon:Age	-0.168	0.247	-0.679	0.497
FitzpatrickMark:Age	-0.362	0.511	-0.709	0.479
FichaudEric:Age	-0.139	0.171	-0.811	0.418
TallasRobbie:Age	-0.103	0.127	-0.811	0.418
WaiteJimmy:Age	-0.267	0.328	-0.815	0.415
CharpentierSebastien:Age	-0.232	0.282	-0.822	0.412
ErsbergErik:Age	-0.165	0.179	-0.919	0.359
TerreriChris:Age	-0.180	0.182	-0.990	0.322
DivisReinhard:Age	-0.270	0.207	-1.306	0.192

GoalieCoefficients:	Estimate	StdError	tvalue	Pvalue
Hasek Dominik	0.143	0.079	1.820	0.069
Shulmistra Richard	0.780	0.764	1.022	0.307
Brodeur Mike	0.488	0.479	1.021	0.308
Rask Tuukka	0.119	0.137	0.864	0.388
Lacosta Daniel	0.377	0.505	0.747	0.455
Cechmanek Roman	0.060	0.091	0.665	0.507
Jablonski Pat	0.239	0.434	0.552	0.581
Roy Patrick	0.042	0.081	0.524	0.600
Barrasso Tom	0.056	0.108	0.513	0.608
Crawford Corey	0.153	0.336	0.454	0.650
Hiller Jonas	0.041	0.100	0.409	0.682
Schwarz Marek	0.357	0.892	0.401	0.689
Cousineau Marcel	0.100	0.327	0.305	0.760
Luongo Roberto	0.018	0.075	0.240	0.810
Schaefer Nolan	0.067	0.373	0.181	0.856
Vokoun Tomas	0.009	0.075	0.122	0.903
Burke Sean	0.008	0.085	0.097	0.923
Coleman Gerald	0.067	1.039	0.065	0.948
Montoya Al	0.020	0.394	0.052	0.959
Curry John	0.020	0.518	0.039	0.969
Dubielewicz Wade	0.000	0.150	0.002	0.998
Thomas Tim	-0.006	0.083	-0.078	0.938
Bernier Jonathan	-0.027	0.323	-0.084	0.933
Enroth Jhonas	-0.083	0.764	-0.108	0.914
Varlamov Semyon	-0.020	0.160	-0.125	0.900
Giguere Jean-Sebastien	-0.011	0.078	-0.134	0.893
Danis Yann	-0.024	0.140	-0.171	0.864
Anderson Craig	-0.019	0.094	-0.206	0.837
Peters Justin	-0.069	0.284	-0.241	0.810
Ouellet Maxime	-0.062	0.250	-0.247	0.805
Lundqvist Henrik	-0.025	0.081	-0.304	0.761
Gustafson Derek	-0.138	0.436	-0.315	0.753
Salak Alexander	-0.266	0.830	-0.320	0.749
Eklund Brian	-0.445	1.295	-0.343	0.731
Lehtonen Kari	-0.033	0.087	-0.380	0.704
Prusek Martin	-0.054	0.141	-0.382	0.702
Ersberg Erik	-0.054	0.137	-0.392	0.695
Halak Jaroslav	-0.041	0.103	-0.396	0.693
Fernandez Manny	-0.033	0.082	-0.404	0.686
Wall Michael	-0.241	0.589	-0.409	0.683
Hebert Guy	-0.038	0.091	-0.417	0.677
Backlund Johan	-0.370	0.870	-0.425	0.671
Flaherty Wade	-0.066	0.154	-0.430	0.667
Johnson Chad	-0.165	0.378	-0.436	0.663
Chiodo Andy	-0.125	0.285	-0.437	0.662
Minard Mike	-0.325	0.723	-0.449	0.654
Climie Matt	-0.178	0.386	-0.462	0.644
Cassivi Frederic	-0.118	0.248	-0.478	0.633
Kiprusoff Miikka	-0.038	0.078	-0.481	0.631
Lamothe Marc	-0.198	0.404	-0.491	0.623
Rinne Pekka	-0.052	0.103	-0.511	0.610
Neuvirth Michal	-0.106	0.196	-0.540	0.590
Little Neil	-0.408	0.736	-0.555	0.579
Tugnutt Ron	-0.051	0.090	-0.569	0.570
MacIntyre Drew	-0.565	0.943	-0.599	0.550
Konstantinov Evgeny	-0.953	1.585	-0.601	0.548
Beckford-Tseu Chris	-0.967	1.585	-0.610	0.542
Howard Jimmy	-0.071	0.116	-0.614	0.539
Underhill Matt	-0.476	0.736	-0.646	0.518
Roussel Dominic	-0.104	0.158	-0.657	0.512
Conklin Ty	-0.063	0.096	-0.658	0.511
Mannino Peter	-0.336	0.497	-0.675	0.500
Damphousse Jean-Francois	-0.278	0.404	-0.688	0.492
Tokarski Dustin	-0.692	1.004	-0.689	0.491
Emery Ray	-0.066	0.095	-0.695	0.487
Harding Josh	-0.084	0.117	-0.716	0.474
Nabokov Evgeni	-0.055	0.077	-0.721	0.471
Leneveu David	-0.163	0.216	-0.755	0.451
Brochu Martin	-0.265	0.343	-0.771	0.441
Fukufuji Yutaka	-0.536	0.669	-0.801	0.423
Hauser Adam	-0.931	1.122	-0.830	0.407
Brodeur Martin	-0.063	0.074	-0.855	0.393
Ellis Dan	-0.092	0.104	-0.879	0.380
Price Carey	-0.085	0.097	-0.883	0.378
Brathwaite Fred	-0.080	0.091	-0.886	0.376
Greiss Thomas	-0.191	0.216	-0.886	0.376
Turco Marty	-0.070	0.078	-0.892	0.373
Terreri Chris	-0.131	0.146	-0.900	0.369
Fitzpatrick Mark	-0.157	0.173	-0.908	0.364
Morrison Michael	-0.639	0.700	-0.912	0.362
Charpentier Sebastien	-0.172	0.188	-0.917	0.360
Bierk Zac	-0.137	0.149	-0.925	0.355
Fichaud Eric	-0.150	0.159	-0.940	0.348
Sauve Philippe	-0.200	0.210	-0.954	0.340
Brust Barry	-0.278	0.288	-0.964	0.335
Gerber Martin	-0.087	0.091	-0.964	0.336
Taylor Daniel	-1.187	1.228	-0.966	0.334
Larocque Michel	-0.546	0.558	-0.977	0.329
Tellqvist Mikael	-0.128	0.130	-0.983	0.326
Hackett Jeff	-0.092	0.093	-0.984	0.326
Michaud Alfie	-0.909	0.917	-0.991	0.322
Storr Jamie	-0.092	0.093	-0.996	0.320
Centomo Sebastien	-1.295	1.295	-1.000	0.318
Backstrom Niklas	-0.088	0.087	-1.016	0.310
Miller Ryan	-0.082	0.081	-1.017	0.310
Biron Martin	-0.081	0.079	-1.024	0.306
Quick Jonathan	-0.111	0.103	-1.076	0.282
Shields Steve	-0.098	0.088	-1.109	0.268
McKenna Mike	-0.266	0.239	-1.113	0.266
Belfour Ed	-0.088	0.077	-1.134	0.257
Smith Mike	-0.120	0.106	-1.136	0.256
Kolesnik Vitaly	-0.392	0.344	-1.138	0.256
Labbe Jean-Francois	-0.298	0.260	-1.146	0.252
Bryzgalov Ilya	-0.104	0.090	-1.152	0.250
Patzold Dimitri	-1.187	1.004	-1.182	0.238
Gage Joaquin	-0.476	0.402	-1.184	0.237
Schneider Cory	-0.363	0.293	-1.240	0.215
Billington Craig	-0.150	0.119	-1.253	0.211
Fankhouser Scott	-0.241	0.191	-1.260	0.208
Trefilov Andrei	-0.445	0.352	-1.263	0.207
Fiset Stephane	-0.121	0.095	-1.264	0.207
Tordjman Josh	-0.684	0.537	-1.273	0.203
Maracle Norm	-0.162	0.126	-1.283	0.200
Mason Chris	-0.111	0.086	-1.293	0.197
Bishop Ben	-0.555	0.426	-1.302	0.193
Moog Andy	-0.204	0.156	-1.305	0.192
Theodore Jose	-0.102	0.077	-1.326	0.185
Munro Adam	-0.298	0.224	-1.328	0.185
Shtalenkov Mikhail	-0.216	0.162	-1.333	0.183
Sanford Curtis	-0.149	0.112	-1.336	0.182
Puppa Daren	-0.205	0.151	-1.353	0.176
Clemmensen Scott	-0.154	0.113	-1.369	0.171
Askey Tom	-0.575	0.417	-1.379	0.168
Waite Jimmy	-0.249	0.180	-1.386	0.166
Salo Tommy	-0.114	0.082	-1.388	0.166
Wilkinson Derek	-0.390	0.277	-1.411	0.159
Hextall Ron	-0.188	0.133	-1.414	0.158
Hrudey Kelly	-0.278	0.195	-1.422	0.155
Legace Manny	-0.117	0.082	-1.432	0.153
Yeats Matthew	-0.555	0.386	-1.436	0.152
Bacashihua Jason	-0.230	0.160	-1.440	0.150
Stana Rastislav	-0.630	0.436	-1.443	0.149
Reese Jeff	-0.938	0.650	-1.443	0.150
LaBarbera Jason	-0.161	0.111	-1.449	0.148
Bach Ryan	-0.768	0.527	-1.456	0.146
Auld Alex	-0.142	0.097	-1.460	0.145
Mason Steve	-0.149	0.102	-1.465	0.143
McLean Kirk	-0.178	0.121	-1.473	0.141
Chabot Frederic	-0.312	0.211	-1.477	0.140
Tabaracci Richard	-0.195	0.131	-1.486	0.138
Khabibulin Nikolai	-0.114	0.076	-1.496	0.135
Vanbiesbrouck John	-0.144	0.096	-1.504	0.133
Niemi Antti	-0.232	0.154	-1.513	0.131
Divis Reinhard	-0.323	0.212	-1.521	0.129
Stephan Tobias	-0.476	0.310	-1.533	0.126
Yeremeyev Vitali	-0.718	0.465	-1.542	0.123
Valiquette Steve	-0.250	0.161	-1.560	0.119
Roloson Dwayne	-0.122	0.078	-1.561	0.119
Joseph Curtis	-0.121	0.077	-1.581	0.114
McElhinney Curtis	-0.417	0.264	-1.581	0.114
Garnett Michael	-0.313	0.198	-1.581	0.114
Naumenko Gregg	-1.313	0.830	-1.582	0.114
Lasak Jan	-0.635	0.394	-1.613	0.107
Garon Mathieu	-0.143	0.089	-1.614	0.107
Dunham Mike	-0.134	0.082	-1.632	0.103
Finley Brian	-0.787	0.479	-1.644	0.101
Esche Robert	-0.157	0.094	-1.667	0.096
Norrena Fredrik	-0.190	0.113	-1.673	0.095
Huet Cristobal	-0.153	0.090	-1.708	0.088
Dafoe Byron	-0.142	0.083	-1.713	0.087
Toskala Vesa	-0.151	0.088	-1.720	0.086
Dipietro Rick	-0.145	0.084	-1.726	0.085
Fountain Michael	-0.863	0.493	-1.749	0.081
Gustavsson Jonas	-0.253	0.144	-1.749	0.081
Weekes Kevin	-0.151	0.086	-1.762	0.078
Wregget Ken	-0.231	0.129	-1.789	0.074
Blackburn Dan	-0.222	0.124	-1.790	0.074
Dubnyk Devan	-0.347	0.193	-1.793	0.073
Johnson Brent	-0.158	0.088	-1.794	0.073
Irbe Arturs	-0.149	0.082	-1.819	0.069
Berkhoel Adam	-0.555	0.303	-1.828	0.068
Skudra Peter	-0.204	0.111	-1.838	0.066
Fleury Marc-Andre	-0.154	0.083	-1.856	0.064
Garner Tyrone	-1.030	0.553	-1.863	0.063
Essensa Bob	-0.198	0.106	-1.877	0.061
Elliott Brian	-0.220	0.115	-1.915	0.056
MacDonald Joey	-0.237	0.123	-1.923	0.055
Turek Roman	-0.162	0.084	-1.928	0.054
Desrochers Patrick	-0.871	0.450	-1.935	0.053
Budaj Peter	-0.179	0.091	-1.967	0.050
Richter Mike	-0.161	0.082	-1.969	0.049
Ranford Bill	-0.312	0.158	-1.972	0.049
Raycroft Andrew	-0.172	0.087	-1.985	0.048
Moss Tyler	-0.355	0.179	-1.987	0.047
Kolzig Olie	-0.151	0.075	-2.007	0.045
Whitmore Kay	-0.884	0.439	-2.014	0.044
Potvin Felix	-0.185	0.091	-2.029	0.043
Thibault Jocelyn	-0.167	0.081	-2.063	0.040
Hurme Jani	-0.254	0.122	-2.073	0.039
McLennan Jamie	-0.205	0.099	-2.074	0.038
Leighton Michael	-0.258	0.123	-2.090	0.037
Pelletier Jean-Marc	-0.906	0.434	-2.091	0.037
Ward Cam	-0.177	0.084	-2.094	0.037
Holmqvist Johan	-0.298	0.141	-2.106	0.036
Sabourin Dany	-0.297	0.139	-2.135	0.033
Pavelec Ondrej	-0.263	0.122	-2.161	0.031
Leclaire Pascal	-0.214	0.097	-2.209	0.027
Osgood Chris	-0.171	0.077	-2.211	0.027
Markkanen Jussi	-0.257	0.116	-2.213	0.027
Hnilicka Milan	-0.219	0.099	-2.214	0.027
Ramo Karri	-0.300	0.135	-2.226	0.026
Kochan Dieter	-0.503	0.226	-2.228	0.026
Boucher Brian	-0.195	0.087	-2.232	0.026
Caron Sebastien	-0.245	0.110	-2.237	0.026
Parent Rich	-0.415	0.182	-2.282	0.023
Nurminen Pasi	-0.229	0.100	-2.287	0.022
Lalime Patrick	-0.189	0.080	-2.349	0.019
Snow Garth	-0.204	0.087	-2.354	0.019
Kidd Trevor	-0.214	0.090	-2.374	0.018
Niittymaki Antero	-0.215	0.090	-2.394	0.017
Hirsch Corey	-0.530	0.219	-2.420	0.016
Rhodes Damian	-0.228	0.094	-2.437	0.015
Pogge Justin	-0.809	0.331	-2.441	0.015
Deslauriers Jeff	-0.300	0.122	-2.460	0.014
Aubin Jean-Sebastien	-0.223	0.090	-2.475	0.014
Noronen Mika	-0.328	0.132	-2.486	0.013
Passmore Steve	-0.312	0.124	-2.529	0.012
Carey Jim	-0.680	0.267	-2.546	0.011
Tallas Robbie	-0.324	0.126	-2.571	0.010
Healy Glenn	-0.342	0.130	-2.632	0.009
Vernon Michael	-0.262	0.098	-2.677	0.008
Hedberg Johan	-0.229	0.084	-2.740	0.006
Schwab Corey	-0.305	0.110	-2.772	0.006
Hodson Kevin	-0.474	0.165	-2.866	0.004
Grahame John	-0.271	0.094	-2.897	0.004
Denis Marc	-0.235	0.081	-2.918	0.004
Cloutier Dan	-0.250	0.084	-2.967	0.003
Toivonen Hannu	-0.396	0.131	-3.018	0.003
Langkow Scott	-0.643	0.209	-3.083	0.002
Fuhr Grant	-0.379	0.109	-3.482	0.001

Simulating Rink Bias

DoctorMyBrainHurts — Wed, 19 May 2010 00:00:35 -0000

I ran some simulations to see if rink bias really matters. It does not seem to make much difference.

Baseline Model

Typical goalie with a save percentage of 0.920 facing 1500 shots in a season. I ran 10,000 seasons.

Goals allowed was determined using a pseudo-random number generator.

Mean 1380 Minimum 1335 Maximum 1417

90% confidence interval is 1363 to 1397 Save percentage 90% CI is 0.908666 to 0.931333

95% confidence interval is 1360 to 1401 Save percentage 95% CI is 0.906666 to 0.934000

Rink Bias Model

Once again, a goalie with a save percentage of 0.920 faces 1500 shots. The number of goals determined by using a pseudo-random number generator. However, the number of shots at home was assumed to be undercounted or overcounted by 5% or 10%. (750 shots at home adjusted up or down by 37 or 75.) Saves were then computed from shots minus goals. Save percentages were computed, and compared to the confidence intervals above. I ran 50,000 seasons for each of the 4 possibilities.

Scenario	# < 0.906666	# < 0.908666	# > 0.931333	# > 0.934000
5% over	663	1297	4119	1910
5% under	2955	4923	1559	626
10% over	251	663	6749	2812
10% under	3923	6818	786	341
Control	1304	2461	2911	1260

In the 5% over scenario 94.854% of the computed save percentages fell in the 95% CI. 89.168% of the computed save percentages fell in the 90% CI.

In the 5% under scenario 92.838% of the computed save percentages fell in the 95% CI. 87.036% of the computed save percentages fell in the 90% CI.

In the 10% over scenario 93.874% of the computed save percentages fell in the 95% CI. 85.176% of the computed save percentages fell in the 90% CI.

In the 10% under scenario 91.472% of the computed save percentages fell in the 95% CI. 84.792% of the computed save percentages fell in the 90% CI.

In the validation control 94.872% of the computed save percentages fell in the 95% CI. 89.256% of the computed save percentages fell in the 90% CI.

In this simulation of rink bias, despite a systematic miscounting of shots of 5% or even 10%, the vast majority of observed save percentages fall within the range you would see if there were no rink bias.

Beating save percentage to death: Teams

DoctorMyBrainHurts — Sat, 15 May 2010 19:04:14 -0000

I used my Even Strength Save Data to look at the effect of Teams. There is not much there.

Using the dense data, I constructed the logits (ln(p/(1-p)) myself. I first corrected the observed save percentages for year.

> LinearModel.2 <- lm(CalcLogit ~ Team, data=Dataset, weights=ESA)

> anova(LinearModel.2)

Analysis of Variance Table

Response: CalcLogit

Df Sum Sq Mean Sq F value Pr(>F)

Team 29 1871.2 64.524 3.8031 1.240e-10 ***

Residuals 895 15184.5 16.966

At a first glance, that looks promising. However, the sum of squares is less than 1/3 the sum of squares we saw for goalies. And we know that teams and individual goalies are highly confounded.

Looking at teams and goalies (with no interaction term)

> LinearModel.4 <- lm(CalcLogit ~ last.first+Team, data=Dataset, weights=ESA)

> anova(LinearModel.4)

Analysis of Variance Table

Response: CalcLogit

Df Sum Sq Mean Sq F value Pr(>F)

last.first 231 6041.3 26.153 1.6677 4.121e-07 ***

Team 29 601.9 20.755 1.3236 0.1209

Residuals 664 10412.6 15.682

Adding in goalies, the significance of the team effect goes away.

Looking at teams and goalies (with interaction)

> LinearModel.4 <- lm(CalcLogit ~ last.first*Team, data=Dataset, weights=ESA)

> anova(LinearModel.3)

Analysis of Variance Table

Response: CalcLogit

Df Sum Sq Mean Sq F value Pr(>F)

last.first 231 6041.3 26.153 1.6835 9.678e-07 ***

Team 29 601.9 20.755 1.3361 0.1156

last.first:Team 168 2707.5 16.116 1.0375 0.3772

Residuals 496 7705.0 15.534

So the effect of goaltenders remains highly significant. The team effect is not significant, and in magnitude is only about 1/10 that of the goaltenders. Finally, we can compare the models directly, to see if adding in team and the team*goalie interaction adds significance to the model.

> anova (LinearModel.1, LinearModel.3, test="F")

Analysis of Variance Table

Model 1: CalcLogit ~ last.first

Model 2: CalcLogit ~ last.first * Team

Res.Df RSS Df Sum of Sq F Pr(>F)

1 693 11014

2 496 7705 197 3309.5 1.0814 0.249

And it does not.

Conclusion

Using weighted logistic regression, there is not a statistically significant differences between NHL teams in even strength save percentages over the period 1997-2010 if you control for the effect of individual goaltenders.

Beating save percentage to death: Logistic Regression.

DoctorMyBrainHurts — Sat, 15 May 2010 15:42:57 -0000

I reran my Even Strength Save Data using logistic regression. The results again show a significant difference between goalies.

First, I converted the data to sparse format (each line is a single observation). There are over 600k shots in the database. When I tried to run a logistic regression on the sparse data R politely coughed up a hairball and died. Unable to allocate a 1.6Gb data vector? Weak!

So I went back to the dense data and constructed the logits (ln(p/(1-p)) myself. I first corrected the observed save percentages for year.

> LinearModel.1 <- lm(CalcLogit ~ last.first, data=Dataset, weights=ESA)

> anova(LinearModel.1)

Analysis of Variance Table

Response: CalcLogit

Df Sum Sq Mean Sq F value Pr(>F)

last.first 231 6041.3 26.153 1.6455 6.833e-07 ***

Residuals 693 11014.5 15.894

Even with the inherent selection bias, the weighted analysis shows a difference that is highly statistically significant. The difference in goalies accounts for about 35% of the variability seen in the calculated logits.

One problem with logistic regression is the difficulty in translating regression results into effects sizes. Beyond that is the question of practical significance in the differences.

Conclusion

Using weighted logistic regression, there is a statistically significant differences between NHL goalies in even strength save percentages over the period 1997-2010.

Beating save percentage to death: Simulation

DoctorMyBrainHurts — Mon, 10 May 2010 18:10:45 -0000

Using a psuedo-random number generator, I simulated up to 5 seasons of goalie save data. Results after the jump.

Each season has 30 goalies. In the first scenario, I specified that all 30 goalies have an intrinsic save percentage (ISP) of 0.920. In the second scenario, I specified that 3 goalies have an ISP of 0.940, 7 have an ISP of 0.930, 10 have an ISP of 0.920, 7 have an ISP of 0.910, and 3 have an ISP of 0.900. In the third scenario I specified that 5 goalies have an ISP of 0.930, 5 have an ISP of 0.925, 10 have an ISP of 0.920, 5 have an ISP of 0.915, and 5 have an ISP of 0.910 For each scenario, I simulated 10,000 seasons. I ran a series of one-way ANOVAs testing for a difference in number of saves between goalies. I tested after 2 seasons, 3 seasons, 4 seasons, and all 5 seasons

Scenario 1 – Equal Goalies 1000 shots per season

Seasons	F cutoff	# > F	Minimum F	Maximum F
2	1.85	480	0.2206	3.6850
3	1.66	463	0.2491	3.0979
4	1.59	531	0.2272	3.0312
5	1.56	538	0.2675	2.4660

500 shots per season

Seasons	F cutoff	# > F	Minimum F	Maximum F
2	1.85	488	0.2357	3.6358
3	1.66	480	0.2789	3.0623
4	1.59	509	0.2632	2.7501
5	1.56	518	0.3115	2.6902

I chose an alpha of 0.05. Appropriately, about 5% of the test statistics exceeded the cutoff. None exceeded it by much, and the maximum calculated F goes down as I add subsequent seasons.

Scenario 2 – Unequal Goalies 1000 shots per season

Seasons	F cutoff	# > F	Minimum F	Maximum F
2	1.85	9990	1.3799	14.7428
3	1.66	10000	2.8665	15.1415
4	1.59	10000	4.0280	21.2827
5	1.56	10000	4.8464	19.0096

500 shots per season

Seasons	F cutoff	# > F	Minimum F	Maximum F
2	1.85	8994	0.8113	11.5604
3	1.66	9986	1.3541	11.3162
4	1.59	10000	1.9170	10.1930
5	1.56	10000	2.2067	12.8249

In the second scenario, with 1000 shots, essentially all the test statistics exceed the cutoff. Compared to scenario 1, there is little overlap by 3 seasons and none by 4 seasons. Even with only 500 shots in a season, essentially all the test statistics still exceed the cutoff. There is little overlap by 3 seasons, although complete separation is not reached by 5 seasons. Opposite to what we saw in scenario 1, as we add seasons the magnitude of the test statistics tends to go up.

Scenario 3 – Unequal Goalies 1000 shots per season

Seasons	F cutoff	# > F	Minimum F	Maximum F
2	1.85	6825	0.4595	7.6507
3	1.66	9619	0.9553	8.3440
4	1.59	9980	1.1465	9.6530
5	1.56	9998	1.3629	8.5005

500 shots per season

Seasons	F cutoff	# > F	Minimum F	Maximum F
2	1.85	3266	0.3604	6.2699
3	1.66	6576	0.6075	6.8692
4	1.59	8635	0.7319	5.3931
5	1.56	9561	0.8393	6.7881

In the third scenario, with 1000 shots, it takes 3 seasons of analysis before essentially all the test statistics exceed the cutoff. With only 500 shots in a season, it takes 5 seasons of analysis before essentially all the test statistics still exceed the cutoff. Complete separation from scenario 1 is not reached by 5 seasons. Compared to scenario 2, as we add seasons the trend in the magnitude of the test statistics is less apparent.

Conclusions

Obviously, more data is better. More shots per season and more seasons allow better discrimination of a goalie effect. The real world data has 267 goalie seasons with at least 1000 even strength shots, and 514 with at least 500 shots. Effects of the magnitude that I built into the models ought to be detectable in the real world data, but it might take 3-5 years of data.

Beating Save Percentage to Death Part 3: Goaltenders

DoctorMyBrainHurts — Sun, 02 May 2010 20:35:38 -0000

Goalie differences

Do goalies differ? As a fan of the Quebec Nordiques, my answer is an emphatic "Yes!" I would bet fans of the pre-lockout Ottawa Senators would wholeheartedly agree.

Not everybody does. Sunny Mehta recently said "No one has conclusively shown a meaningful difference in skill between NHL goaltenders. I'm not saying it doesn't exist, I'm just saying no one's really proved it, and that all signs point to goaltending differences being far less important than everyone thinks."

Let's look at even strength save percentages for all goalies from 1998-2010. First, looking at the raw data.

> AnovaModel.1 <- aov(ESVPCT ~ last.first, data=Dataset)

> summary(AnovaModel.1)

Df Sum Sq Mean Sq F value Pr(>F)

last.first 249 0.70705 0.00283956 3.9338 < 2.2e-16 ***

Residuals 785 0.56665 0.00072185

So goaltenders do differ significantly. The differences between goalies accounts for about 56% of the total variability seen in the raw data.

Correcting for year

I have already shown average even strength save percentage has a small but significant increase over the time period we are looking at. So I have recalculated the model using adjusted even strength save percentages. It always makes me a little nervous when people say they are adjusting the data without describing what they did. On a theoretical level, I have converted the observed save percentage to a standard normal Z-statistic using the observed mean for the year as the mean and the observed standard deviation over the 12 year period as the standard error. I have then rescaled the Z-statistics to the 2009-2010 mean save percentage of 0.919. From a practical standpoint, this amounts to adding or subtracting a small constant to each observation. For example, in 1997 the observed average save percentage was 0.915. To make the adjustment, I added 0.004 to each observation from 1997. The results:

> AnovaModel.2 <- aov(ADJESSVP ~ last.first, data=Dataset)

> summary(AnovaModel.2)

Df Sum Sq Mean Sq F value Pr(>F)

last.first 249 0.69835 0.00280463 3.8826 < 2.2e-16

Residuals 785 0.56705 0.00072236

So basically the same. Goaltenders do differ significantly. The differences between goalies accounts for about 55% of the total variability seen in the adjusted data.

Regular Goalies

Finally, I removed all goalies who had played less than 10 games in a season from the data.

> AnovaModel.1 <- aov(ADJESSVP ~ last.first, data=Dataset2)

> summary(AnovaModel.1)

Df Sum Sq Mean Sq F value Pr(>F)

last.first 165 0.046939 0.00028448 1.6446 1.344e-05

Residuals 595 0.102922 0.00017298

A little less dramatic, but regular goaltenders do differ significantly. The differences between regular goalies accounts for about 31% of the total variability seen in the adjusted data.

Conclusion

The difference in goalies over the period 1997-2010 is statistically significant. The difference in goalies who played more than 10 games in a season over the period 1997-2010 is also statistically significant.

Beating Save Percentage to Death Part 2: Year

DoctorMyBrainHurts — Sat, 01 May 2010 01:28:00 -0000

I've looked at even strength save percentage for all goalies from 1997-2010. The data for 1997-1998 for special teams on the NHL.com web site has been fixed and I am now including it. In part 1 I looked at goalie age and even strength save percentage. In part 2, I look at the trend of even strength save percentage over time.

Unweighted

A first look at the relationship comes from unweighted data. Each goalie is one data point, whether he played 1 game or 80. Here is the scatter plot:

via 2.bp.blogspot.com

Model Summary

	R	R Square	Adjusted R Square	Std. Error of the Estimate
	.03	.00	.00	.04

ANOVA

	Sum of Squares	df	Mean Square	F	Significance
Regression	.00	1	.00	1.09	.30
Residual	1.27	1033	.00
Total	1.27	1034

Coefficients

	B	Std. Error	Beta	t	Significance
(Constant)	.31	.57	.00	.54	.68
Year	.00	.00	.03	1.04	.30

Not a lot there.

Weighted

We can rerun the regression, using shots faced as a weighting factor. The scatter plot of the means does look promising:

via 2.bp.blogspot.com

And there is a significant relationship.

Model Summary

	R	R Square	Adjusted R Square	Std. Error of the Estimate
	.61	.38	.38	.00

ANOVA

	Sum of Squares	df	Mean Square	F	Significance
Regression	0.0000	1.0000	0.0000	6.0317	0.0339
Residual	0.0001	10.0000	0.0000
Total	0.0001	11.0000

Coefficients

	B	Std. Error	Beta	t	Significance
(Constant)	0.06538	0.35000	0.00000	0.19000	0.88000
Year	0.00043	0.00020	0.61340	2.45600	0.03390

So not a huge effect from year to year, but over the 12 years the predicted average even strength save percentage does go from 0.914 to 0.919. As an aside, the 1997-1998 data put this over the hump in terms of statistical significance. Looking at the trend in overall save percentage, I suspect that, if we go back further, the trend continues. If anyone has the data from the years before 1997 and would like to make it available to me I would be deeply appreciative. If not, I can see if I can construct it myself.

Conclusion

There is a statistically significant relationship between year and even strength save percentage.

Unweighted

A first look at the relationship comes from unweighted data. Each goalie is one data point, whether he played 1 game or 80. Here is the scatter plot:

via 2.bp.blogspot.com

Model Summary

	R	R Square	Adjusted R Square	Std. Error of the Estimate
	.03	.00	.00	.04

ANOVA

	Sum of Squares	df	Mean Square	F	Significance
Regression	.00	1	.00	1.09	.30
Residual	1.27	1033	.00
Total	1.27	1034

Coefficients

	B	Std. Error	Beta	t	Significance
(Constant)	.31	.57	.00	.54	.68
Year	.00	.00	.03	1.04	.30

Not a lot there.

Weighted

We can rerun the regression, using shots faced as a weighting factor. The scatter plot of the means does look promising:

via 2.bp.blogspot.com

And there is a significant relationship.

Model Summary

	R	R Square	Adjusted R Square	Std. Error of the Estimate
	.61	.38	.38	.00

ANOVA

	Sum of Squares	df	Mean Square	F	Significance
Regression	0.0000	1.0000	0.0000	6.0317	0.0339
Residual	0.0001	10.0000	0.0000
Total	0.0001	11.0000

Coefficients

	B	Std. Error	Beta	t	Significance
(Constant)	0.06538	0.35000	0.00000	0.19000	0.88000
Year	0.00043	0.00020	0.61340	2.45600	0.03390

Conclusion

There is a statistically significant relationship between year and even strength save percentage.

Beating Save Percentage to Death Part 1B: Young Goalies

DoctorMyBrainHurts — Wed, 28 Apr 2010 19:23:26 -0000

The following goalies made their debut at 19 or 20, and had at least 3 years of data. The first four made their debut at 19, the remainder at 20.

Backstrom

Dipietro

Fleury

Ouellet

Auld

Emery

Esche

Fiset

Labarbara

Lehtonen

Luongo

Pavelec

Pelletier

Price

Ramo

Rask

Raycroft

Schwarz

One-Sample Statistics

	N	Mean	Std. Deviation	S.E. Mean
slope	18	0.005	0.016	.00

One-Sample Test

	Test Value = 0.000000
					95% Confidence Interval of the Difference
	t	df	Sig. (2-tailed)	Mean Difference	Lower	Upper
slope	1.35	17	0.19	.01	-0.003	0.013

T-TEST

I f we include goalies who made their debut at 21, we add in:

Anderson

Aubin

Biron

Bryzgalov

Crawford

Denis

Finley

Giguere

Halak

Harding

Howard

Johnson

Leclaire

Leighton

Noronen

Quick

Toivonen

Ward

One-Sample Statistics

	N	Mean	Std. Deviation	S.E. Mean
slope	36	0.003	0.010	.00

One-Sample Test

	Test Value = 0.000000
					95% Confidence Interval of the Difference
	t	df	Sig. (2-tailed)	Mean Difference	Lower	Upper
slope	1.18	35	.25	.00	-0.002	0.007

T-TEST

So neither group achieves statistical significance.

The following goalies made their debut at 19 or 20, and had at least 3 years of data. The first four made their debut at 19, the remainder at 20.

Backstrom

Dipietro

Fleury

Ouellet

Auld

Emery

Esche

Fiset

Labarbara

Lehtonen

Luongo

Pavelec

Pelletier

Price

Ramo

Rask

Raycroft

Schwarz

One-Sample Statistics

	N	Mean	Std. Deviation	S.E. Mean
slope	18	0.005	0.016	.00

One-Sample Test

	Test Value = 0.000000
					95% Confidence Interval of the Difference
	t	df	Sig. (2-tailed)	Mean Difference	Lower	Upper
slope	1.35	17	0.19	.01	-0.003	0.013

T-TEST

I f we include goalies who made their debut at 21, we add in:

Anderson

Aubin

Biron

Bryzgalov

Crawford

Denis

Finley

Giguere

Halak

Harding

Howard

Johnson

Leclaire

Leighton

Noronen

Quick

Toivonen

Ward

One-Sample Statistics

	N	Mean	Std. Deviation	S.E. Mean
slope	36	0.003	0.010	.00

One-Sample Test

	Test Value = 0.000000
					95% Confidence Interval of the Difference
	t	df	Sig. (2-tailed)	Mean Difference	Lower	Upper
slope	1.18	35	.25	.00	-0.002	0.007

T-TEST

So neither group achieves statistical significance.

Beating Save Percentage to Death Part 1: Age

DoctorMyBrainHurts — Wed, 28 Apr 2010 02:20:46 -0000

I've looked at even strength save percentage for all goalies from 1998-2010. The data for 1997-1998 for special teams on the NHL.com web site is flawed, so I have omitted it.

Unweighted

A first look at the relationship comes from unweighted data. Each goalie is one data point, whether he played 1 game or 80. Here is the scatter plot:

via 2.bp.blogspot.com

Model Summary

	R	R Square	Adjusted R Square	Std. Error of the Estimate
	.04	.00	.00	.04

REGRESSION

	Sum of Squares	df	Mean Square	F	Significance
Regression	.00	1	.00	1.23	.27
Residual	1.22	960	.00
Total	1.22	961

Coefficients

	B	Std. Error	Beta	t	Significance
(Constant)	.90	.01	.00	129.87	.00
Age	.00	.00	.04	1.11	.27

So, the slope of save percentage over age isn't just close to 0.0, it is 0.0.

Weighted

We can rerun the regression, using shots faced as a weighting factor. The scatter plot does not look any more promising:

via 2.bp.blogspot.com

Model Summary

	R	R Square	Adjusted R Square	Std. Error of the Estimate
	.11	.01	.01	.00

REGRESSION

	Sum of Squares	df	Mean Square	F	Significance
Regression	.00	1	.00	.26	.61
Residual	.00	21	.00
Total	.00	22

Coefficients

	B	Std. Error	Beta	t	Significance
(Constant)	.91	.00	.00	261.15	.00
Age	.00	.00	.11	.51	.61

And, indeed, it is not any better.

Serial Measures

One last way to look for a relationship would be to look at each goalie relative to himself as he ages. For this analysis, I have restricted the analysis to goalies with at least 3 seasons. For each goalie, I computed his personal slope. We can then look at the average of these slopes. The null hypothesis is that the average slope is 0.0.

DISTRIBUTION PARAMETER ESTIMATES

========================================================

Slope (N = 140) Mean = -0.001 Variance = 0.000 Std.Dev. = 0.011

0.950 Confidence Interval for mean : -0.003 to 0.001

Once again, the slope is not significantly different from 0.0.

Conclusion

Analyzing the data every way I can think up, there is no evidence whatsoever of any relationship between goalie age and even strength save percentage.

I've looked at even strength save percentage for all goalies from 1998-2010. The data for 1997-1998 for special teams on the NHL.com web site is flawed, so I have omitted it.

Unweighted

A first look at the relationship comes from unweighted data. Each goalie is one data point, whether he played 1 game or 80. Here is the scatter plot:

via 2.bp.blogspot.com

Model Summary

	R	R Square	Adjusted R Square	Std. Error of the Estimate
	.04	.00	.00	.04

REGRESSION

	Sum of Squares	df	Mean Square	F	Significance
Regression	.00	1	.00	1.23	.27
Residual	1.22	960	.00
Total	1.22	961

Coefficients

	B	Std. Error	Beta	t	Significance
(Constant)	.90	.01	.00	129.87	.00
Age	.00	.00	.04	1.11	.27

So, the slope of save percentage over age isn't just close to 0.0, it is 0.0.

Weighted

We can rerun the regression, using shots faced as a weighting factor. The scatter plot does not look any more promising:

via 2.bp.blogspot.com

Model Summary

	R	R Square	Adjusted R Square	Std. Error of the Estimate
	.11	.01	.01	.00

REGRESSION

	Sum of Squares	df	Mean Square	F	Significance
Regression	.00	1	.00	.26	.61
Residual	.00	21	.00
Total	.00	22

Coefficients

	B	Std. Error	Beta	t	Significance
(Constant)	.91	.00	.00	261.15	.00
Age	.00	.00	.11	.51	.61

And, indeed, it is not any better.

Serial Measures

DISTRIBUTION PARAMETER ESTIMATES

========================================================

Slope (N = 140) Mean = -0.001 Variance = 0.000 Std.Dev. = 0.011

0.950 Confidence Interval for mean : -0.003 to 0.001

Once again, the slope is not significantly different from 0.0.

Conclusion

Analyzing the data every way I can think up, there is no evidence whatsoever of any relationship between goalie age and even strength save percentage.