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    <title>SB Nation User Blog:  GOOCH24</title>
    <link>http://www.sbnation.com/users/GOOCH24</link>
    <description>Posts made by GOOCH24 on SB Nation</description>
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      <title>Rational Fielding:  When Should He &quot;Go for It&quot;?</title>
      <link>http://www.vivaelbirdos.com/2008/11/9/657414/rational-fielding-when-sho</link>
      <author>GOOCH24</author>
      <pubDate>Sun, 09 Nov 2008 23:31:40 -0000</pubDate>
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&lt;p&gt;A recent discussion on another forum spurred me to make this argument, and I thought it was interesting enough that I'd post it here for reaction. The discussion revolves around whether a baseball player can decide to 'let a ball go' that they could have fielded because they believe another defender can get it *and* have an easier throw to first base. The argument revolved around whether defensive metrics which give Pujols credit for his range are flawed, because his range is actually a detriment in that he fields balls that the 2B could get, but makes for a much harder throw to the pitcher covering. &lt;br /&gt;&lt;br /&gt;Quote:&lt;/p&gt;
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&lt;td class=&quot;alt2&quot;&gt;Look, it's just how infield is taught. A third baseman is taught to get everything they can. A shortstop is taught to get everything he can, and to take a shallow angle on slowly hit balls hit to his left. The 2nd baseman is taught to get everything he can, but takes a deeper angle than the shortstop both to avoid and collision and because it's a much easier play.&lt;/td&gt;
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&lt;p&gt;And, of course, 1B are taught to get everything they can, and when they can't to retreat to 1B for a throw to 1B on a grounder fielded by another player. Not that you really need to be 'taught' this. Even if we tried to 'teach' player to differentiate between the batted balls they can get versus those they can get but should let someone else get (the slow dribbler excepted) it wouldn't matter...because they simply aren't going to be able to do it most of the time. There simply isn't enough time. If you think you can get to it you try for it. That's undoubtedly the decision rule 99% of players use on 99% of plays. &lt;br /&gt;&lt;br /&gt;&lt;br /&gt;Quote:&lt;/p&gt;
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&lt;td class=&quot;alt2&quot;&gt;That same concept applies why Pujols snags a grounder when Kennedy is standing flat footed directly behind him, it's a more difficult play. That's why you don't see 2nd baseman snagging slow hoppers on the shortstop side of the bag very often.&lt;/td&gt;
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&lt;p&gt;Yes, all players have time on a slow grounder to consider whether another player can get to it. We don't need to keep talking about slow grounders since players will almost always let the player whose zone that ball was hit to field it. AP included.&lt;br /&gt;&lt;br /&gt;As far as making the determination as to whether or not to let the ball go, it is easier for the middle infielder because in most cases the other middle infielder is in their perephrial vision. For 1st baggers and 3rd baggers, this is only sometimes the case. Alot of the time they have no vision of the nearest fielder because that fielder is *behind* them. So they have to guesstimate based on pre-hit positioning. &lt;br /&gt;&lt;br /&gt;From simple game theoretic terms, I don't think it is ever rational to assume the other fielder will get the ball when there is a sufficiently non-zero probability that the other fielder will not, in fact, field the ball. On a slow dribbler in the other player's zone, let's say there's a .01% chance of the fielder not being in position to make the play (he falls down, etc.). And let's say there is a .05% chance of making an error on the play if I (the 1B) make the play. In this instance, it's rational, from a utility-maximizing stand point, to go ahead and retreat to 1B and presume the 2nd baseman will field the ball without even checking to see if he can. &lt;br /&gt;&lt;br /&gt;Now let's consider the question of whether or not to try for a ball at the outside of a 1B range (which overlaps with the outside of the 2B range). So we assume from the outset that there is no P = 1 situation--where we *know* that another fielder could make the play. Our chance of making an error in fielding the ball is still .05%. And the chance of the 2B making an error *if he gets to it* is .01%. So, if we knew before hand that both of us would make the play, clearly we could let the 2B make the play and hence reduce the chance of making the error. But we *don't* know that. Let's add an additional assumption: Let's assume that the probability of my fielding a ball is 99.9% when it is hit directly at me, and that probability monotonically decreases to zero as the trajectory of the ball moves off my centerpoint in either direction (as a 1B, of course, my range is censored by the foul line to my left). That point where my probability of fielding the ball goes to zero is the limit of my range. Given this, the decision on whether or not to try for a ball is a simple calculation:&lt;br /&gt;&lt;br /&gt;If P(FB1B) &amp;gt;= [P(E2B) - P(E1B)], attempt to field the ball.&lt;br /&gt;&lt;br /&gt;If P(FB) &amp;lt; [P(E2B) - P(E1B)], retreat to 1B.&lt;br /&gt;&lt;br /&gt;In words, if the probability of fielding the ball is greater than or equal to the difference between the probability of the 1B making an error on the play and the probability of the 2B making an error, then the first baseman should field the ball. If the probability of fielding the ball is less than the probability of the 1B making an error on the play (minus the probability of the 2B making that error), then the first baseman should retreat to first. As should be apparent, the decision rule here is almost *always* going to be to try and field the ball. And if we assume bounded rationality (IOW if we assume that players are not probability calculators but rather their probability decisions are 'fuzzy')...then it may *never* be the case that it is rational to retreat to 1B on a ball hit within his range where he cannot be sure another fielder will get it. &lt;br /&gt;&lt;br /&gt;Let's look at it from the manager's standpoint. What does he want his defenders to do when a ball is put in play? Naturally, he wants them to increase the chance that an out is recorded. So what should he teach his fielders to do? Naturally, they should do anything that increases the chance that an out is recorded. So let's consider the following case: A ball is hit sharply on the ground between the 2B and 1B. The following probabilites hold:&lt;br /&gt;&lt;br /&gt;If neither player attempts to field the ball, the probability of a hit is 1.&lt;br /&gt;&lt;br /&gt;If the 2B tries for the ball, he has a 20% chance of fielding the ball.&lt;br /&gt;&lt;br /&gt;If the 1B tries for the ball, he has a 20% chance of fielding the ball.&lt;br /&gt;&lt;br /&gt;If both players try for the ball, there is a joint probability of 30% that the ball will be fielded. IOW, 10% of the time when the both try for it, the 1B gets to it and the 2nd baseman wouldn't have. 10% of the time the 2B gets to it and the 1B wouldn't have. 10% of the time they both would have gotten to it (and thus the closest fielder makes the play but either would have recorded the out). 70% of the time, neither will get to the ball and it will be a hit. &lt;br /&gt;&lt;br /&gt;What should a manager teach? Well, if he teaches the 1B to retreat to 1B when there is a non-zero chance the 2B will get it, then the probability of a batted ball recorded as an out in our above scenario declines by 10%. He loses out on the times the 1B would have made the play and the 2B wouldn't have. Now let's consider an error. Let's say that when the 2B fields this ball there's a 1% chance of a throwing error and when the 1B fields the ball there's a 5% chance of a throwing error (note, I think that greatly exceeds the actual probability of making that error. If a 1B makes 4 throws a game to the pitcher covering first, that would mean that he makes 648 throws in a season. If he makes an error 5% of the time on those throws, that would mean 33 throwing errors in a season on just throws to the pitcher covering first). Even then, it is rational to teach your first baseman to try to get everything you can get to. Because the probability of an out being recorded teaching that is 26%.&lt;br /&gt;&lt;br /&gt;P(out) = U [P(1Bout), P(2Bout)] - U [P(1Ber), P(2Ber)&lt;br /&gt;&lt;br /&gt;P(out) = 30% - [5% - 1%] = 26%&lt;br /&gt;&lt;br /&gt;The chance of an out being recorded otherwise is 19% &lt;br /&gt;&lt;br /&gt;P(out) = P(2Bout) - P(2Ber)&lt;br /&gt;&lt;br /&gt;P(out) = 20% - 1% = 19%&lt;br /&gt;&lt;br /&gt;&lt;br /&gt;D.GOOCH&lt;/p&gt;

  
  


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      <title>Getting Phelps in the Lineup</title>
      <link>http://www.vivaelbirdos.com/2008/8/29/604046/getting-phelps-in-the-line</link>
      <author>GOOCH24</author>
      <pubDate>Fri, 29 Aug 2008 23:39:21 -0000</pubDate>
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&lt;p&gt;Consider Phelps line at AAA this season:&lt;/p&gt;
&lt;p&gt;461 AB, 31 HR, 97 RBI, .941 OPS&lt;/p&gt;
&lt;p&gt;Phelps has mashed.&amp;nbsp; However, he seems to only be a first baseman.&lt;/p&gt;
&lt;p&gt;Proposition:&amp;nbsp; moving Albert to Left Field and letting Phelps man first.&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Question:&amp;nbsp; would it be a net advantage (if so, how many games)?&amp;nbsp; or net disadvantage.&amp;nbsp;&lt;/p&gt;
&lt;p&gt;Con:&amp;nbsp; Moving Albert from a position where he is the best defender in baseball into a position where he is likely just average defenisvely.&lt;/p&gt;
&lt;p&gt;Con:&amp;nbsp; Albert has a balky right elbow which might be injured if he's throwing from LF.&lt;/p&gt;
&lt;p&gt;Pro:&amp;nbsp; You get Phelps in the lineup.&lt;/p&gt;
&lt;p&gt;Pro:&amp;nbsp; Albert wouldn't be throwing much more from LF than he does from 1B.&lt;/p&gt;
&lt;p&gt;Here's what a Phelps lineup might look like:&lt;/p&gt;
&lt;p&gt;Lopez (R)&lt;/p&gt;
&lt;p&gt;Ankiel (L)&lt;/p&gt;
&lt;p&gt;Pujols (R)&lt;/p&gt;
&lt;p&gt;Ludwick (R)&lt;/p&gt;
&lt;p&gt;Glaus (R)&lt;/p&gt;
&lt;p&gt;Phelps (R)&lt;/p&gt;
&lt;p&gt;Molina (R)&lt;/p&gt;
&lt;p&gt;Pitcher&lt;/p&gt;
&lt;p&gt;Miles (R/L)&lt;/p&gt;
&lt;p&gt;That's a scary looking lineup, folks.&amp;nbsp; Over 30 games, displacing Skip in the OF (who can't hit Lefties)...worth one game?&amp;nbsp; Maybe two.&amp;nbsp; If not for the &quot;you don't move superstars out of their defensive positions&quot; cultural stickyness...this would seem to make alot of sense.&amp;nbsp; D.GOOCH&lt;/p&gt;

  
  


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      <title>Some tidbits from my scorecard...</title>
      <link>http://www.vivaelbirdos.com/2008/5/29/541943/some-tidbits-from-my-score</link>
      <author>GOOCH24</author>
      <pubDate>Thu, 29 May 2008 19:15:19 -0000</pubDate>
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&lt;p&gt;Saw my first live game of the year last night.&amp;nbsp; Some tidbits from my scorecard...&lt;br /&gt;&lt;br /&gt;--I had two exclamation points last night, the first being Ankiel's diving catch on the sinking liner from Berkman in the 1st inning. Not only was it an outstanding defensive play but it killed a rally and kept the score all zeros. &lt;br /&gt;The second was Ryan's backhand stab of a smoked liner in the 6th. Beautiful play.&lt;br /&gt;&lt;br /&gt;--The one and two batters for Houston last night combined to go 1 - 8 with no runs scored. That's how you limit an offense. Keep the tablesetters off the table.&lt;br /&gt;&lt;br /&gt;--Even more importantly, Wagonmaker limited the 3-4-5 hitters to 2-12 with two singles, 0 runs scored, and no RBI's. He dominated the heart of a very good and comming in hot lineup. &lt;br /&gt;&lt;br /&gt;--Wagonmaker gave up one walk the whole game, in the 8th. He didn't allow a hit after the third.&lt;br /&gt;&lt;br /&gt;--The Cardinals scored 3 runs in the 1st while recording only one hit. Now that's efficiency!&lt;br /&gt;&lt;br /&gt;--No one Cardinal had a great offensive night last night, but it goes to show you what can happen when you are efficient in your opportunites. Of the 13 men who reached base last night, 6 scored. That's close to 50%, well above league average. &lt;br /&gt;&lt;br /&gt;-- The only extra base hit last night was Iztu's triple. &lt;br /&gt;&lt;br /&gt;D.GOOCH&lt;/p&gt;
&amp;lt;!-- / message --&gt;&amp;lt;!-- sig --&gt;

  
  


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      <title>PITCH F/X Analysis: Moving vs. Straight Fastballs
</title>
      <link>http://www.vivaelbirdos.com/2008/3/5/192320/4783</link>
      <author>GOOCH24</author>
      <pubDate>Thu, 06 Mar 2008 00:23:20 -0000</pubDate>
      <description type="html">


&lt;p&gt;The below post continues a debate I had in another forum over whether Matt Cain throws a &quot;straight&quot; fastball or a &quot;moving&quot; fastball relative to his peers. However, that particular point is of less interest, in my mind, than the findings on lefties vs. righties, starting vs. relief, and sinkers vs. 'normal' fastballs once the data is analyzed.&lt;/p&gt;&lt;p&gt;Having conceded XXXXX's point that my initial Pitch F/X sample--which showed that Cain's fastball was slightly above average in lateral movement--may be unrepresentative (especially given that it had an n = 20), I have since gone back to the Fogg Pitch F/X Player Cards and drawn a much larger sample (using the list of player cards as the sampling frame and a systematic random sampling procedure w/ skip &amp;amp; starting values randomly generated). This sample consists of 157 pitchers taken from the player card list (at: &lt;a href=&quot;http://baseball.bornbybits.com/plots/players.html&quot;&gt;http://baseball.bornbybits.com/plots/players.html&lt;/a&gt;).&lt;/p&gt;&lt;p&gt;If you're unfamilliar with the Pitch F/X data (a primer):&lt;/p&gt;&lt;p&gt;&lt;a href=&quot;http://mvn.com/mlb-stats/2008/01/14/a-pitchfx-primer/&quot;&gt;http://mvn.com/mlb-stats/2008/01/14/a-pitchfx-primer/&lt;/a&gt;&lt;/p&gt;&lt;p&gt;For the distinction b/w break &amp; movement:&lt;/p&gt;&lt;p&gt;&lt;a href=&quot;http://www.hardballtimes.com/main/ar...of-the-sinker/&quot;&gt;http://www.hardballtimes.com/main/ar...of-the-sinker/&lt;/a&gt;&lt;/p&gt;&lt;p&gt;For the method of determining types of pitches including a definition of what movement in the x &amp; z dimensions means:&lt;/p&gt;&lt;p&gt;&lt;a href=&quot;http://www.hardballtimes.com/main/ar...tion-tutorial/&quot;&gt;http://www.hardballtimes.com/main/ar...tion-tutorial/&lt;/a&gt;&lt;/p&gt;&lt;p&gt;OK, so now that you've familliarzed yourself with the method and details, let's consider the data. In examining the x-dimension data, I employ the absolute value of that dimension (as the left vs. right direction of the pitch is irrelevant for the purposes of assessing how much the pitch moves). For the z-dimension, I subtract the z scores from a constant (20 inches)...so that the data analyzed is distance from that constant (and thus can be compared). For example, if pitcher X's z-score is 10, then their z_abs = 10. If their z-score is 6, then their z_abs will be 14. If their z-score is -5, then their z_abs will be 25 and so forth. The sink variable is whether or not the pitcher throws a sinker (it's import will be discussed later).&lt;/p&gt;&lt;p&gt;ALL PITCHERS&lt;/p&gt;&lt;p&gt;Code:&lt;br /&gt;
Variable &amp;nbsp; &amp;nbsp; &amp;nbsp;N &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Mean &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Std Dev &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Minimum &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Maximum&lt;br /&gt;
-------------------------------------------------------------------------------&lt;br /&gt;
x &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 157 &amp;nbsp; &amp;nbsp; &amp;nbsp;-1.5543949 &amp;nbsp; &amp;nbsp; &amp;nbsp; 6.0245805 &amp;nbsp; &amp;nbsp; -10.4200000 &amp;nbsp; &amp;nbsp; &amp;nbsp;12.3000000&lt;br /&gt;
z &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 157 &amp;nbsp; &amp;nbsp; &amp;nbsp; 9.3687261 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.5669379 &amp;nbsp; &amp;nbsp; &amp;nbsp;-3.3400000 &amp;nbsp; &amp;nbsp; &amp;nbsp;15.3900000&lt;br /&gt;
sink &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;157 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.1464968 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.3547351 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.0000000&lt;br /&gt;
x_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;157 &amp;nbsp; &amp;nbsp; &amp;nbsp; 5.7012739 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.4524100 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.6400000 &amp;nbsp; &amp;nbsp; &amp;nbsp;12.3000000&lt;br /&gt;
z_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;157 &amp;nbsp; &amp;nbsp; &amp;nbsp;10.6312739 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.5669379 &amp;nbsp; &amp;nbsp; &amp;nbsp; 4.6100000 &amp;nbsp; &amp;nbsp; &amp;nbsp;23.3400000&lt;br /&gt;
-------------------------------------------------------------------------------&lt;/p&gt;&lt;p&gt;So from this table, the average horizontal movement (left or right) for a pitcher is 5.7 inches. Recall, Matt Cain's x-score was -5.01, hence it would appear initally that Sonic was right (my previous sample was biased). As that would put Matt Cain's movement south of the average movement for a pitcher, right around the 45th percentile.&lt;/p&gt;&lt;p&gt;Yet it should be noted that still means that a good bulk of the pitchers in the league have less movement than Matt Cain on their fastball. And furthermore, we should recall that the mean is influenced by higher values, and these dimensional scores are censored at zero. The median (middle score) for the x_ab variable is 5.03, hence Cain's x-dimension movement is almost squarely in the center of the distribution. And note, this is the worst case for Cain, as we've compared him to every pitcher in the sample, making no allowances for potential confounding factors. I consider those in the following analysis.&lt;/p&gt;&lt;p&gt;STARTING VS. RELIEF PITCHERS&lt;br /&gt;
It is the conventional wisdom that relief pitching is a different animal than starting pitching. Starters have to &quot;pace&quot; themselves, as they are likely to deliver 90-140 pitches in a start. Whereas relievers may only throw 10-40 in an appearance. Thus we expect starters to have to &quot;dial it back&quot; on their pitches...giving considerably less than maximal effort whereas relief pitchers are not so constrained. Furthermore, starting pitchers may deliver many more pitchers in a &quot;tired&quot; state, and hence are more likely to throw more pitches to the plate that are less than their best stuff. It stands to reason that this may not merely effect velocity. It could also effect movement as well. A starting pitcher may not give full effort throughout his start, resulting in less movement on his pitches. A starting pitcher may tire in latter innings, causing his stuff to &quot;straighten out.&quot;&lt;/p&gt;&lt;p&gt;Code:&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; MEANS: STARTING PITCHERS&lt;/p&gt;&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; The MEANS Procedure&lt;/p&gt;&lt;p&gt;&amp;nbsp;Variable &amp;nbsp; &amp;nbsp; N &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Mean &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Std Dev &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Minimum &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Maximum&lt;br /&gt;
&amp;nbsp;------------------------------------------------------------------------------&lt;br /&gt;
&amp;nbsp;x &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 64 &amp;nbsp; &amp;nbsp; &amp;nbsp;-1.7575000 &amp;nbsp; &amp;nbsp; &amp;nbsp; 5.6690426 &amp;nbsp; &amp;nbsp; &amp;nbsp;-9.5800000 &amp;nbsp; &amp;nbsp; &amp;nbsp;10.9100000&lt;br /&gt;
&amp;nbsp;z &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 64 &amp;nbsp; &amp;nbsp; &amp;nbsp; 9.3792188 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.5907726 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.1700000 &amp;nbsp; &amp;nbsp; &amp;nbsp;15.3900000&lt;br /&gt;
&amp;nbsp;sink &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;64 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.1718750 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.3802542 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.0000000&lt;br /&gt;
&amp;nbsp;x_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;64 &amp;nbsp; &amp;nbsp; &amp;nbsp; 5.3731250 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.4386770 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.6400000 &amp;nbsp; &amp;nbsp; &amp;nbsp;10.9100000&lt;br /&gt;
&amp;nbsp;z_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;64 &amp;nbsp; &amp;nbsp; &amp;nbsp;10.6207813 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.5907726 &amp;nbsp; &amp;nbsp; &amp;nbsp; 4.6100000 &amp;nbsp; &amp;nbsp; &amp;nbsp;19.8300000&lt;br /&gt;
&amp;nbsp;------------------------------------------------------------------------------Code:&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;MEANS: RELIEF PITCHERS&lt;/p&gt;&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; The MEANS Procedure&lt;/p&gt;&lt;p&gt;&amp;nbsp;Variable &amp;nbsp; &amp;nbsp; N &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Mean &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Std Dev &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Minimum &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Maximum&lt;br /&gt;
&amp;nbsp;------------------------------------------------------------------------------&lt;br /&gt;
&amp;nbsp;x &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 93 &amp;nbsp; &amp;nbsp; &amp;nbsp;-1.4146237 &amp;nbsp; &amp;nbsp; &amp;nbsp; 6.2839989 &amp;nbsp; &amp;nbsp; -10.4200000 &amp;nbsp; &amp;nbsp; &amp;nbsp;12.3000000&lt;br /&gt;
&amp;nbsp;z &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 93 &amp;nbsp; &amp;nbsp; &amp;nbsp; 9.3615054 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.5644649 &amp;nbsp; &amp;nbsp; &amp;nbsp;-3.3400000 &amp;nbsp; &amp;nbsp; &amp;nbsp;14.3200000&lt;br /&gt;
&amp;nbsp;sink &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;93 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.1290323 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.3370526 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.0000000&lt;br /&gt;
&amp;nbsp;x_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;93 &amp;nbsp; &amp;nbsp; &amp;nbsp; 5.9270968 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.4493316 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.1400000 &amp;nbsp; &amp;nbsp; &amp;nbsp;12.3000000&lt;br /&gt;
&amp;nbsp;z_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;93 &amp;nbsp; &amp;nbsp; &amp;nbsp;10.6384946 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.5644649 &amp;nbsp; &amp;nbsp; &amp;nbsp; 5.6800000 &amp;nbsp; &amp;nbsp; &amp;nbsp;23.3400000&lt;br /&gt;
&amp;nbsp;------------------------------------------------------------------------------&lt;/p&gt;&lt;p&gt;As is apparent from this data, it looks like there is evidence to support the above intuition. Relief pitchers have about a half-inch more movement on their fastballs than do the starting pitchers on average. Taking a look once again at Cain among starting pitchers, his z-score, while still below the mean, is much closer (probably in the 48th-49th percentile [2.99 25th, 6.33 75th ]).&lt;/p&gt;&lt;p&gt;LEFTIES VS. RIGHTIES&lt;/p&gt;&lt;p&gt;There's an artifact in the Pitch F/X data that we've yet to account for that should be accounted for. For whatever reason (and I'm open to speculation on this), Lefties demonstrate much more lateral movement in their pitches than do Righties. Whether it's because there are much fewer Lefties in the league (you have to be 'better' to slot in as a Lefty), whether it is a function of their delivery...whether it is a function of them pitching to off-handed batters more...whatever. It's apparent and it is consistent, as you can see below:&lt;/p&gt;&lt;p&gt;Code:&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;MEANS: RIGHTIES&lt;/p&gt;&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; The MEANS Procedure&lt;/p&gt;&lt;p&gt;Variable &amp;nbsp; &amp;nbsp; &amp;nbsp;N &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Mean &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Std Dev &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Minimum &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Maximum&lt;br /&gt;
-------------------------------------------------------------------------------&lt;br /&gt;
x &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 113 &amp;nbsp; &amp;nbsp; &amp;nbsp;-5.0404425 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.0764033 &amp;nbsp; &amp;nbsp; -10.4200000 &amp;nbsp; &amp;nbsp; &amp;nbsp;-0.6400000&lt;br /&gt;
z &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 113 &amp;nbsp; &amp;nbsp; &amp;nbsp; 9.5243363 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.2673092 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.7900000 &amp;nbsp; &amp;nbsp; &amp;nbsp;13.0200000&lt;br /&gt;
sink &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;113 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.1504425 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.3590971 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.0000000&lt;br /&gt;
x_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;113 &amp;nbsp; &amp;nbsp; &amp;nbsp; 5.0404425 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.0764033 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.6400000 &amp;nbsp; &amp;nbsp; &amp;nbsp;10.4200000&lt;br /&gt;
z_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;113 &amp;nbsp; &amp;nbsp; &amp;nbsp;10.4756637 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.2673092 &amp;nbsp; &amp;nbsp; &amp;nbsp; 6.9800000 &amp;nbsp; &amp;nbsp; &amp;nbsp;19.2100000&lt;br /&gt;
-------------------------------------------------------------------------------Code:&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;MEANS: LEFTIES&lt;/p&gt;&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; The MEANS Procedure&lt;/p&gt;&lt;p&gt;&amp;nbsp;Variable &amp;nbsp; &amp;nbsp; N &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Mean &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Std Dev &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Minimum &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Maximum&lt;br /&gt;
&amp;nbsp;------------------------------------------------------------------------------&lt;br /&gt;
&amp;nbsp;x &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 44 &amp;nbsp; &amp;nbsp; &amp;nbsp; 7.3984091 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.5484696 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.6300000 &amp;nbsp; &amp;nbsp; &amp;nbsp;12.3000000&lt;br /&gt;
&amp;nbsp;z &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 44 &amp;nbsp; &amp;nbsp; &amp;nbsp; 8.9690909 &amp;nbsp; &amp;nbsp; &amp;nbsp; 3.2075121 &amp;nbsp; &amp;nbsp; &amp;nbsp;-3.3400000 &amp;nbsp; &amp;nbsp; &amp;nbsp;15.3900000&lt;br /&gt;
&amp;nbsp;sink &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;44 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.1363636 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.3471418 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.0000000&lt;br /&gt;
&amp;nbsp;x_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;44 &amp;nbsp; &amp;nbsp; &amp;nbsp; 7.3984091 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.5484696 &amp;nbsp; &amp;nbsp; &amp;nbsp; 2.6300000 &amp;nbsp; &amp;nbsp; &amp;nbsp;12.3000000&lt;br /&gt;
&amp;nbsp;z_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;44 &amp;nbsp; &amp;nbsp; &amp;nbsp;11.0309091 &amp;nbsp; &amp;nbsp; &amp;nbsp; 3.2075121 &amp;nbsp; &amp;nbsp; &amp;nbsp; 4.6100000 &amp;nbsp; &amp;nbsp; &amp;nbsp;23.3400000&lt;br /&gt;
&amp;nbsp;------------------------------------------------------------------------------&lt;/p&gt;&lt;p&gt;This is the most significant difference found in the sub groups. There is a more than two-inch differential between the fastball of lefties and the fastball of righties on the X dimension. Once we take this in to account, Cain's movement is dead-on the average movement for Righties.&lt;/p&gt;&lt;p&gt;SINKERS&lt;/p&gt;&lt;p&gt;Finally, the last sub-group I want to identify is the sinker-ballers. These are pitchers whose &lt;strong&gt;only&lt;/strong&gt; fastball is a sinker. What's interesting is that, not only do sinkerballers have more downward movement on their pitches...they also tend to have more lateral movement on their pitches. Most likely a consequence of how they grip the pitch (thus giving it a different spin). Let's continue looking at righties, and examine the difference b/w sinkerballers and those pitchers who feature a normal fastball:&lt;/p&gt;&lt;p&gt;Code:&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp;MEANS: RIGHTIES W/ SINK&lt;/p&gt;&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; The MEANS Procedure&lt;/p&gt;&lt;p&gt;&amp;nbsp;Variable &amp;nbsp; &amp;nbsp; N &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Mean &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Std Dev &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Minimum &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Maximum&lt;br /&gt;
&amp;nbsp;------------------------------------------------------------------------------&lt;br /&gt;
&amp;nbsp;x &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 17 &amp;nbsp; &amp;nbsp; &amp;nbsp;-7.7823529 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.4706356 &amp;nbsp; &amp;nbsp; -10.4200000 &amp;nbsp; &amp;nbsp; &amp;nbsp;-4.3400000&lt;br /&gt;
&amp;nbsp;z &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 17 &amp;nbsp; &amp;nbsp; &amp;nbsp; 5.4111765 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.8157673 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.7900000 &amp;nbsp; &amp;nbsp; &amp;nbsp; 8.2100000&lt;br /&gt;
&amp;nbsp;sink &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;17 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.0000000 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.0000000 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.0000000&lt;br /&gt;
&amp;nbsp;x_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;17 &amp;nbsp; &amp;nbsp; &amp;nbsp; 7.7823529 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.4706356 &amp;nbsp; &amp;nbsp; &amp;nbsp; 4.3400000 &amp;nbsp; &amp;nbsp; &amp;nbsp;10.4200000&lt;br /&gt;
&amp;nbsp;z_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;17 &amp;nbsp; &amp;nbsp; &amp;nbsp;14.5888235 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.8157673 &amp;nbsp; &amp;nbsp; &amp;nbsp;11.7900000 &amp;nbsp; &amp;nbsp; &amp;nbsp;19.2100000&lt;br /&gt;
&amp;nbsp;------------------------------------------------------------------------------Code:&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; MEANS: RIGHTIES NO SINK&lt;/p&gt;&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; The MEANS Procedure&lt;/p&gt;&lt;p&gt;&amp;nbsp;Variable &amp;nbsp; &amp;nbsp; N &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Mean &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Std Dev &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Minimum &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Maximum&lt;br /&gt;
&amp;nbsp;------------------------------------------------------------------------------&lt;br /&gt;
&amp;nbsp;x &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 96 &amp;nbsp; &amp;nbsp; &amp;nbsp;-4.5548958 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.7706329 &amp;nbsp; &amp;nbsp; &amp;nbsp;-8.6000000 &amp;nbsp; &amp;nbsp; &amp;nbsp;-0.6400000&lt;br /&gt;
&amp;nbsp;z &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 96 &amp;nbsp; &amp;nbsp; &amp;nbsp;10.2527083 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.3934708 &amp;nbsp; &amp;nbsp; &amp;nbsp; 5.0600000 &amp;nbsp; &amp;nbsp; &amp;nbsp;13.0200000&lt;br /&gt;
&amp;nbsp;sink &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;96 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0&lt;br /&gt;
&amp;nbsp;x_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;96 &amp;nbsp; &amp;nbsp; &amp;nbsp; 4.5548958 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.7706329 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.6400000 &amp;nbsp; &amp;nbsp; &amp;nbsp; 8.6000000&lt;br /&gt;
&amp;nbsp;z_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;96 &amp;nbsp; &amp;nbsp; &amp;nbsp; 9.7472917 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.3934708 &amp;nbsp; &amp;nbsp; &amp;nbsp; 6.9800000 &amp;nbsp; &amp;nbsp; &amp;nbsp;14.9400000&lt;br /&gt;
&amp;nbsp;------------------------------------------------------------------------------&lt;/p&gt;&lt;p&gt;Again, the difference between the two subsets is striking. Not so much on the vertical plane, as expected sinkerballers throw fastballs that &quot;fall off the table&quot; much more than regular fastballs (14.6 inches to 9.7 inches). What's interesting is that sinkerballers also have much more horizontal movement on their pitches. Again, it is an over two inch difference (4.55 for our 96 fastballers and 7.78 inches of lateral movement for our 17 sinkerballers). Note, once we factor out the pitchers that feature sinkers as opposed to normal fastballs, Cain's fastball now rates as above average in movement. His 5.01 slots in somewhere around the 60th to 65th percentile (75th 5.7).&lt;/p&gt;&lt;p&gt;CONCLUSION&lt;/p&gt;&lt;p&gt;Finally, let's take into account all these factors and truly compare apples to apples: Cain's fastball vs. the fastball of Righty starting pitchers sans sinkerballers:&lt;/p&gt;&lt;p&gt;Code:&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;MEANS: RIGHTY STARTING PITCHERS N/S&lt;/p&gt;&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; The MEANS Procedure&lt;/p&gt;&lt;p&gt;&amp;nbsp;Variable &amp;nbsp; &amp;nbsp; N &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Mean &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Std Dev &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Minimum &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Maximum&lt;br /&gt;
&amp;nbsp;------------------------------------------------------------------------------&lt;br /&gt;
&amp;nbsp;x &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 38 &amp;nbsp; &amp;nbsp; &amp;nbsp;-4.3907895 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.9775201 &amp;nbsp; &amp;nbsp; &amp;nbsp;-7.8300000 &amp;nbsp; &amp;nbsp; &amp;nbsp;-0.6400000&lt;br /&gt;
&amp;nbsp;z &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 38 &amp;nbsp; &amp;nbsp; &amp;nbsp;10.2652632 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.3632012 &amp;nbsp; &amp;nbsp; &amp;nbsp; 7.1000000 &amp;nbsp; &amp;nbsp; &amp;nbsp;13.0200000&lt;br /&gt;
&amp;nbsp;sink &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;38 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0&lt;br /&gt;
&amp;nbsp;x_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;38 &amp;nbsp; &amp;nbsp; &amp;nbsp; 4.3907895 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.9775201 &amp;nbsp; &amp;nbsp; &amp;nbsp; 0.6400000 &amp;nbsp; &amp;nbsp; &amp;nbsp; 7.8300000&lt;br /&gt;
&amp;nbsp;z_ab &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;38 &amp;nbsp; &amp;nbsp; &amp;nbsp; 9.7347368 &amp;nbsp; &amp;nbsp; &amp;nbsp; 1.3632012 &amp;nbsp; &amp;nbsp; &amp;nbsp; 6.9800000 &amp;nbsp; &amp;nbsp; &amp;nbsp;12.9000000&lt;br /&gt;
&amp;nbsp;------------------------------------------------------------------------------&lt;/p&gt;&lt;p&gt;In this group, Cain's fastball is well above average in lateral movement. His fastball is more than a half-inch better in &quot;busting in on the hands&quot; of right-handed hitters than his fellow right-handed starting pitchers (sans sinkers). He slots in somewhere around the 70th percentile here. Certainly no Jake Peavy or Sergio Mitre, but no where close to a Yovanni Gallardo or Chris Young. D.GOOCH&lt;br /&gt;&lt;/p&gt;



  

  


      </description>
    </item>
    <item>
      <title>Runs Created by Decade: An Analysis in Variance
</title>
      <link>http://www.vivaelbirdos.com/2008/2/10/183145/195</link>
      <author>GOOCH24</author>
      <pubDate>Sun, 10 Feb 2008 23:31:45 -0000</pubDate>
      <description type="html">


&lt;p&gt;In the discussion over Albert Pujols's status as a Hall of Famer, a statistical debate arose over how we should compare players from by-gone decades in terms of OPS+. &amp;nbsp;Valentin pointed out that a comparison to the average player (what OPS+ does) might be biased if there's a significant difference in the variance in OPS in past eras. &amp;nbsp;IOW, Valentin suggested that it would matter if, say, a player who posted a 130+ in the 1950's was an extreme abnormality while a player who posted a 130+ in the 1990's was relatively common. &amp;nbsp;&lt;/p&gt;&lt;p&gt;Well, this presents an empirical question: is there a substantial difference in the variance in offensive production in previous eras. &amp;nbsp;To help answer this question, I have examined the Runs Created for MLB from 1950 to the present. &amp;nbsp;Specifically, I've looked at the average Runs Created for each decade from 1950 to 2005 (latest year available), to see if there has been a substantial difference in the variation in runs created over those decades. &amp;nbsp;&lt;/p&gt;&lt;p&gt;I employed the dataset on batting provided in Sean Lahman's Baseball Database. &amp;nbsp;I excluded all players with less that 150 at bats in a season. &amp;nbsp;The following data include the mean, median, &amp;amp; modes, the variance and standard deviations for Runs Created. &amp;nbsp;I've used the following runs created formula:&lt;/p&gt;&lt;p&gt;rc_X1 = (H + BB - CS + HBP - GIDP);&lt;br /&gt;
rc_X2 = TB + (.26 * (BB - IBB + HBP));&lt;br /&gt;
rc_X3 =(.52 * (SH + SF + SB));&lt;br /&gt;
rc_X4 = AB + BB + HBP + SH +SF;&lt;/p&gt;&lt;p&gt;rc = rc_X1 * (rc_X2 + rc_X3) / rc_X4;&lt;/p&gt;&lt;p&gt;I've also included a quantile breakdown for runs created in each of the decades:&lt;/p&gt;&lt;p&gt;The Fifties (1950-1959)&lt;/p&gt;&lt;p&gt;N &amp;nbsp; &amp;nbsp; 1813&lt;br /&gt;
Mean &amp;nbsp;55.9209845 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Std D 31.5128001 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Var &amp;nbsp; 993.056569&lt;br /&gt;
Med &amp;nbsp; 49.45367&lt;/p&gt;&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Quantile &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Estimate&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 100% Max &amp;nbsp; &amp;nbsp; &amp;nbsp; 187.62018&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 99% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;148.14395&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 95% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;114.88000&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 90% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;100.00556&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 75% Q3 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;76.41856&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 50% Median &amp;nbsp; &amp;nbsp; &amp;nbsp;49.45367&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 25% Q1 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;30.34681&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 10% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 20.05333&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 5% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;16.39892&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 1% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;11.37026&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0% Min &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 8.57665&lt;/p&gt;&lt;p&gt;The Sixties (1960 - 1969)&lt;br /&gt;
N &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;2289&lt;br /&gt;
Mean &amp;nbsp; &amp;nbsp; 52.29305 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Std Dev &amp;nbsp;29.53063&lt;br /&gt;
Median &amp;nbsp; 47.23479 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Variance 872.05787&lt;br /&gt;
Range &amp;nbsp; &amp;nbsp;169.64884&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Quantile &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Estimate&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 100% Max &amp;nbsp; &amp;nbsp; &amp;nbsp; 177.66250&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 99% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;132.01471&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 95% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;107.21445&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 90% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 94.02014&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 75% Q3 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;70.89245&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 50% Median &amp;nbsp; &amp;nbsp; &amp;nbsp;47.23479&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 25% Q1 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;27.71607&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 10% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 18.39132&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 5% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;14.82995&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 1% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;10.43723&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0% Min &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 8.01366&lt;/p&gt;&lt;p&gt;The Seventies (1970 - 1979)&lt;/p&gt;&lt;p&gt;N &amp;nbsp; &amp;nbsp; &amp;nbsp; 2918 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Mean &amp;nbsp; &amp;nbsp;52.75782 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Std Dev 28.66373&lt;br /&gt;
Median &amp;nbsp;47.93912 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Var &amp;nbsp; &amp;nbsp; 821.60919&lt;br /&gt;
Range &amp;nbsp; 154.24352&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Quantile &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Estimate&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 100% Max &amp;nbsp; &amp;nbsp; &amp;nbsp; 160.26340&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 99% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;129.96813&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 95% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;103.82451&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 90% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 92.60296&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 75% Q3 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;72.36598&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 50% Median &amp;nbsp; &amp;nbsp; &amp;nbsp;47.93912&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 25% Q1 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;28.57147&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 10% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 19.13247&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 5% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;15.67842&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 1% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;10.78744&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0% Min &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 6.01988&lt;/p&gt;&lt;p&gt;The Eighties (1980 -1989)&lt;br /&gt;
N &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;3162&lt;br /&gt;
Mean &amp;nbsp; &amp;nbsp; 51.70840 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Std Dev &amp;nbsp;28.05438&lt;br /&gt;
Median &amp;nbsp; 46.96388 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Var &amp;nbsp; &amp;nbsp; &amp;nbsp;787.04827&lt;br /&gt;
Range &amp;nbsp; &amp;nbsp;147.99317&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Quantile &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Estimate&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 100% Max &amp;nbsp; &amp;nbsp; &amp;nbsp; 153.60612&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 99% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;126.75796&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 95% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;105.90848&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 90% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 90.73343&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 75% Q3 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;70.23333&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 50% Median &amp;nbsp; &amp;nbsp; &amp;nbsp;46.96388&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 25% Q1 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;28.43210&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 10% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 19.38759&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 5% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;16.01681&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 1% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;11.61000&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0% Min &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 5.61295&lt;/p&gt;&lt;p&gt;The Nineties (1990 - 1999)&lt;br /&gt;
&amp;nbsp;N &amp;nbsp; &amp;nbsp; &amp;nbsp;3395&lt;br /&gt;
Mean &amp;nbsp; &amp;nbsp;56.06562 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Std Dev 31.74681&lt;br /&gt;
Median &amp;nbsp;49.65593 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Var &amp;nbsp; &amp;nbsp; 1008&lt;br /&gt;
Range &amp;nbsp; 186.91802&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Quantile &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Estimate&lt;/p&gt;&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 100% Max &amp;nbsp; &amp;nbsp; &amp;nbsp; 193.33921&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 99% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;146.74168&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 95% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;115.88431&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 90% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;101.28195&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 75% Q3 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;76.41611&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 50% Median &amp;nbsp; &amp;nbsp; &amp;nbsp;49.65593&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 25% Q1 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;30.25041&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 10% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 20.69598&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 5% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;16.86006&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 1% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;12.17636&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0% Min &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 6.42118&lt;/p&gt;&lt;p&gt;The Oughts (2000 - 2005)&lt;br /&gt;
N &amp;nbsp; &amp;nbsp; &amp;nbsp; 2639&lt;br /&gt;
Mean &amp;nbsp; &amp;nbsp;59.70025 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Std Dev 34.02325&lt;br /&gt;
Median &amp;nbsp;53.48486 &amp;nbsp; &amp;nbsp;&lt;br /&gt;
Var &amp;nbsp; &amp;nbsp; 1158&lt;br /&gt;
Range &amp;nbsp; 223.95212 &amp;nbsp;&lt;/p&gt;&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; Quantile &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;Estimate&lt;/p&gt;&lt;p&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 100% Max &amp;nbsp; &amp;nbsp; &amp;nbsp; 230.40970&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 99% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;154.90486&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 95% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;124.12382&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 90% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;108.89175&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 75% Q3 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;80.00087&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 50% Median &amp;nbsp; &amp;nbsp; &amp;nbsp;53.48486&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 25% Q1 &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;31.56901&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 10% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 21.79130&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 5% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;18.15000&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 1% &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;12.58929&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 0% Min &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 6.45758&lt;/p&gt;&lt;p&gt;============&lt;br /&gt;
OK. &amp;nbsp;So what do all those numbers mean? &amp;nbsp;Well, for one, it is apparent that there has been some shifts in the variance in runs created over time. &amp;nbsp;The maximum RC's have increased in some eras relative to other eras (Max RC in the Oughts: &amp;nbsp;230.40, Max RC in the 1980's: 153.60). This is consistent with the notion that the runs created distribution has expanded over the last few decades.&lt;/p&gt;&lt;p&gt;However, there doesn't seem to be a substantial difference in the standard deviations in each decade. IOW, while we've seen an expansion of the distribution at the tails, for the most part, the standard deviations in the bulk of the distribution remain relatively the same. &amp;nbsp;We've seen a slight increase in standard deviations, relative to other decades:&lt;/p&gt;&lt;p&gt;1950's 31.51 runs&lt;br /&gt;
1960's 29.53 runs&lt;br /&gt;
1970's 28.66 runs&lt;br /&gt;
1980's 28.05 runs&lt;br /&gt;
1990's 31.75 runs&lt;br /&gt;
2000's 34.02 runs&lt;/p&gt;&lt;p&gt;So the max variance in comparing any one decade to another is 5 runs created in a season. &amp;nbsp;So even if we weighted our OPS+ calculations to account for this difference in SD, I doubt we'd get much of a difference in our results.&lt;/p&gt;&lt;p&gt;I invite comment on my baseline assumptions, the results, and the conclusions I've drawn. &amp;nbsp;D.GOOCH&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&lt;/p&gt;



  

  


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      <title>The LaRussification of the Roster
</title>
      <link>http://www.vivaelbirdos.com/2008/1/7/153859/0571</link>
      <author>GOOCH24</author>
      <pubDate>Mon, 07 Jan 2008 20:38:59 -0000</pubDate>
      <description type="html">


&lt;p&gt;Well folks, I think the verdict is in. While those of us looking for a fresh outlook going forward were somewhat encouraged by Tony's initial indication that he was willing to go with younger players and that Mo might not hew as closely to the 'veteran at all cost' line that Tony prefers...the facts are in.&lt;/p&gt;&lt;p&gt;Other than the Rule 5 draft, every move the Cardinals have made in this offseason has been straight out of the VAAC strategy employed by Tony.&lt;/p&gt;&lt;p&gt;Now, I say this as a fan of Tony's and a fan of his system. I think it worked great when the trade market was fruitfull (i.e. alot of productive veterans available for young talent), when the Cardinal farm system was particularly bare, and when the Cardinals were looking to shore up spots around their core producers in order to make deep playoff runs.&lt;/p&gt;&lt;p&gt;But this is a new day. We're on the downswing of the competition cycle. We've got numerous promising young players in the system that need to move up and get a shot at the majors. The trade market is decidely NOT conducive to veteran acquisitions.&lt;/p&gt;&lt;p&gt;Yet what have we seen? Russ Springer resigned. Joel Pinero signed. Cesar Isturiz and Jimenez signed. Matt Clement signed. And god help us, Aaron Miles resigned.&lt;/p&gt;&lt;p&gt;Each of these players (except for Pinero) is blocking a young player in our system who a) may be better than the signee now b) has greater upside offensively or defensively and c) is cheaper. Anthony Reyes, Brendon Ryan, Jarrett Hoffpauir, Chris Perez...all young players who should have major league positions locked in for the 08 season so their value can be established (and because they're likely to outperform the veterans signed in front of them). &amp;nbsp;&lt;/p&gt;&lt;p&gt;And now we hear the Cardinals are looking at Louis Gonzalez? &amp;nbsp;What other reason, other than VAAC, would the Cardinals be interested in a 40 year old, lefty-hitting, .750 OPS outfielder? &amp;nbsp;&lt;/p&gt;&lt;p&gt;This is a mistake. It is going to stunt the growth of these players. Some of them may be lost (to trade or waiver claims). We won't know whether they can play at the major league level and thus be able to evaluate our needs for the 09 season.&lt;/p&gt;&lt;p&gt;It's wrong. It hurts the Cardinals as an orgainzation. Yet it is clear who is in charge here. And Tony's style simply does not fit where the Cardinals are headed right now. He said he could adapt. So far, the only adapting I've seen is the organization's to his wishes. D.GOOCH&lt;br /&gt;
&lt;em&gt;_&lt;/em&gt;&lt;em&gt;_&lt;/em&gt;&lt;em&gt;_&lt;/em&gt;&lt;em&gt;_&lt;/em&gt;&lt;em&gt;_&lt;/em&gt;&lt;em&gt;_&lt;/em&gt;&lt;br /&gt;&lt;/p&gt;



  

  


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