## Fantasy football rankings, Week 11: Defense/special teams

"I was told there would be no math," they said. But they lied. Today, there is math. It might be dumb math, but there is math. Journey into the math with me.

Last week's defense/special teams rankings column was not my best moment. I really wanted to include a chart plotting defenses' average scoring against their consistency rating (as created and explained by me here several weeks ago). Unfortunately, as it turns out, I'm bad at that stuff. The graph was there, but it was (a) poorly labeled, and (b) illegible.

Other than that, though, I crushed it!

Anyway, I had a request in the comments to make a more visible version of the graph. I tried. I failed. So instead, I set out to make it into a table this week, thinking that would be equally helpful, with the added advantage of being something I actually have the technical acumen to accomplish.

As I worked on it, I came up with what (I think) is an interesting system for ranking defenses. So I'm going to try it this week, with the up-front caveat that I'm somewhat figuring out this particular metric as I go, so there is the possibility that I will be completely, totally wrong. But you get the bonus of learning with me, and that's valuable.

What I'll do, then, is explain my methodology, and go to the results. At the end of the column, I'm going to list this week's rankings as my system dictates, but I'm also going to list the rankings I came up with beforehand. We'll see how they compare; we'll see how they turn out this weekend. It might be an exercise in futility, but an exercise in futility is still an exercise, you know?

Here we go.

### The problem

The easiest way to rank defenses, if you aren't interested in significant research, is average scoring. It's tidy, and it's reasonable reliable. The problem, though, is consistency. Would you rather have a defense that averages 12 points a game, but scores in the negative once every three weeks, or a defense that averages 11, but is always between nine and 13? I'd gladly sacrifice the one average point for the greater reliability.

That is why I came up with my defense consistency ranking, a system that, once I get it ironed out here, I plan to apply to all positions eventually. Without considering actual value of performance, the system simply calculates how consistent a specific defense is.

Now, I'm not crazy - I'd rather a high scorer that is moderately inconsistent than an awful team that scores exactly one point every week. I know the average score needs to be more weighted in this system (a problem I was running into with my simple graph last week). So how to properly scale the two measurements?

### The forgotten concern

One thing I've stressed since the preseason is that there are always two major factors to consider in picking a defense - the defense playing (obviously), and the offense it is playing against. The Kansas City Chiefs have been the best defense in the league this season, but few people would rank them first this week going against the Denver Broncos. Honestly, a lot of the time, I think the opposition is at least as important as the specific defense, and it doesn't always get enough attention.

So in addition to finding average scores and consistency ratings for all the defenses, I found average scores and consistency ratings for all the opposing teams (in other words, the data versus each team). I'm now to four total data points for this.

### The data

Below, I've included the charts of the average score and m rating for each defense and each opponent, with the rankings in parentheses:

 Team Defense average score Defense m score Opposition average score Opposition m score Arizona 10.11 (5) 2.3 (18) 9.33 (9) 1.03 (2) Atlanta 3.56 (30) 1.98 (12) 6.89 (17) 2.65 (26) Baltimore 7.67 (12) 2.43 (22) 7.78 (13) 1.43 (7) Buffalo 6.4 (19) 1.95 (9) 9.5 (7) 1.53 (10) Carolina 12.67 (2) 2.3 (17) 6.33 (19) 2.58 (25) Chicago 7 (16) 2.22 (16) 5.11 (26) 2.02 (27) Cincinnati 9.7 (6) 2.5 (23) 6.8 (18) 2.87 (27) Cleveland 8.22 (10) 2.08 (14) 7.56 (14) 1.45 (9) Dallas 6.5 (18) 3.55 (32) 3.4 (28) 1.08 (3) Denver 7.33 (15) 2.63 (25) -0.4 (32) 2.52 (23) Detroit 4.78 (25) 1.97 (10) 2.67 (30) 1.32 (4) Green Bay 6.22 (20) 2.63 (26) 3.22 (29) 2.25 (18) Houston 5.89 (23) 1.43 (2) 11.56 (3) 3.55 (32) Indianapolis 6.67 (17) 2.68 (27) 6.22 (20) 2.52 (22) Jacksonville 2.78 (32) 1.98 (11) 12.78 (2) 2.02 (14) Kansas City 16 (1) 2.68 (28) 5.56 (24) 0.4 (1) Miami 7.33 (14) 2.4 (20) 10 (6) 1.4 (6) Minnesota 4.67 (26) 2.35 (19) 8.89 (10) 1.43 (8) New England 8.22 (9.5) 1.88 (8) 5.56 (23) 2.57 (24) New Orleans 7.78 (11) 1.57 (3) 1.67 (31) 2.03 (16) NY Giants 4.44 (27) 3.02 (30) 15 (1) 1.77 (12) NY Jets 5 (24) 2.1 (15) 11 (4) 3.2 (29) Oakland 7.44 (13) 3.08 (31) 10.67 (5) 3.27 (30) Philadelphia 3.7 (29) 1.85 (6) 5.3 (25) 3.32 (31) Pittsburgh 3.89 (28) 2.4 (21) 9.44 (8) 1.82 (13) San Diego 3.22 (31) 1.87 (7) 4.78 (27) 2.28 (19) San Francisco 10.33 (4) 1.83 (5) 5.78 (22) 2.97 (28) Seattle 10.9 (3) 1.34 (1) 5.8 (21) 1.71 (11) St. Louis 9.5 (7) 2.83 (29) 7.3 (15) 2.13 (17) Tampa Bay 6 (22) 1.78 (4) 8.22 (11) 1.38 (5) Tennessee 8.89 (8) 2.08 (13) 8.11 (12) 2.45 (21) Washington 6.11 (21) 2.53 (24) 7 (16) 2.35 (20)

### The system

Now, the easiest way to do this would be to add a unit's ranking in average score to its average ranking in consistency, and the lowest number wins. That, though, forgets the problem I mentioned several paragraphs ago - consistency is important, sure, but actual score is moreso.

To correct for this, I double-weighted average score, then took the average ranking. So, if a team was first in average scoring, but 13th in consistency, it would be 1+1+13=15. Divide that by three to get five, and that is that unit's overall score. Ranking those scores - lowest best - should yield an approximately accurate ranking for which defenses would fare best against a neutral opposition.

Of course, no one is facing a neutral opposition (except perhaps the Bills, who are facing the uber-neutral Jets this week). Which brings me back to the opposition scores - perform the same tactics, and you get the ranking of opponents you would want your neutral defense to face.

### The results

So what I did then was combine scores of Week 11 opponents. Seattle is playing Minnesota - I took the Seahawks' first-ranked defense and combined it with the Vikings' seventh-ranked opposition score, for a composite of 8. That brought that matchup in at first this week. In my initial just-looking-at-them ranks, I had the Seahawks in first, as well, matching those numbers up rather well, actually. Of course, those rankings go both ways; the Vikings' defense rank 28th right now, while the Seahawks are the 18th-ranked opponent, for a composite of 46, which is 27th this week; I had them at 28th.

(The numbers and my opinion didn't match up nearly this well in all the matchups, but I won't lie; that was nice to see.)

Okay, I hope that was clear. If it wasn't, or if you want more information, or if you can find some fatal flaws in my methodology (which would not remotely surprise me), feel free to get down in the comments. I'll respond to everything relevant.

With that, here are the rankings. In the case of tiebreakers in the numbers, I leaned toward the higher-scoring defense before the better consistency rating. As a reminder, the first column of rankings is the list I made before I started my calculatin', while the second column is the rankings that resulted from all this figgerin'. I'm definitely going to revisit this whole thing next week, and we'll see if I've cracked some sort of code:

 Rank My rankings Opponent System rankings Opponent 1 Seattle Seahawks Minnesota Seattle Seahawks Minnesota 2 Arizona Cardinals at Jacksonville Arizona Cardinals at Jacksonville 3 Carolina Panthers New England Cincinnati Bengals at Cleveland 4 Cleveland Browns Cincinnati Buffalo Bills NY Jets 5 Cincinnati Bengals at Cleveland Chicago Bears Baltimore 6 New York Jets at Buffalo Green Bay Packers at NY Giants 7 Oakland Raiders at Houston New York Jets at Buffalo 8 San Francisco 49ers at New Orleans New England Patriots at Carolina 9 Tennessee Titans Indianapolis Detroit Lions at Pittsburgh 10 New England Patriots at Carolina Carolina Panthers New England 11 Baltimore Ravens at Chicago Tennessee Titans Indianapolis 12 New Orleans Saints San Francisco Houston Texans Oakland 13 Houston Texans Oakland San Diego Chargers at Miami 14 New York Giants Green Bay New Orleans Saints San Francisco 15 Tampa Bay Buccaneers Atlanta Cleveland Browns Cincinnati 16 Kansas City Chiefs at Denver Oakland Raiders at Houston 17 Green Bay Packers at NY Giants San Francisco 49ers at New Orleans 18 Denver Broncos Kansas City Denver Broncos Kansas City 19 Indianapolis Colts at Tennessee Jacksonville Jaguars Arizona 20 Detroit Lions at Pittsburgh Tampa Bay Buccaneers Atlanta 21 Chicago Bears Baltimore Indianapolis Colts at Tennessee 22 Buffalo Bills NY Jets Atlanta Falcons at Tampa Bay 23 Miami Dolphins San Diego Baltimore Ravens at Chicago 24 San Diego Chargers at Miami Kansas City Chiefs at Denver 25 Atlanta Falcons at Tampa Bay Philadelphia Eagles Washington 26 Pittsburgh Steelers Detroit Miami Dolphins San Diego 27 Philadelphia Eagles Washington Minnesota Vikings at Seattle 28 Minnesota Vikings at Seattle Pittsburgh Steelers Detroit 29 Washington Redskins at Philadelphia Washington Redskins at Philadelphia 30 Jacksonville Jaguars Arizona New York Giants Green Bay

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