### Playing Defense

A few posts back I asked

*Is anyone playing defense in the NFL this year?*That led me to compile a few stats.

While the NFL has devised complex formulae like QB rating to measure offensive production, it weirdly has no such metric for defense. Instead, defenses are ranked on gross yardage per game, which is far from a true measuring stick. So I started (and unsurprisingly, half-completed) a journey to find a comparative metric of effectiveness for defense.

We begin with points allowed, since you win by scoring more points than your opponent, not by gaining more yards. A defense that gives up yards, but not points, is much more effective than a defense which gives up a lot of points. But again, the NFL does not maintain a 'defensive points allowed' stat, but lumps in all points allowed together - including punt/kick returns and fumble/INT returns. Obviously, it's foolish to include these scores in any measure of a defense's effectiveness, since they aren't even on the field when they happen. So that was step one - removing seven points for each return TD from the total points allowed. Note: Seven is a bit arbitrary, since extra points could be missed after return TDs, or two-point conversions could have been tried, but it should be close enough to be a representative number.

Next, I subtracted seven points from the defensive points allowed (DPA) for each TD scored by the defense. Based on the momentum swings of defensive scores (~83% of teams with a defensive score win the game) I should probably award more than 7 points, but assigning a point value to momentum is total guesswork, so I'm just sticking with the actual points on the scoreboard. So if a defense gives up a TD and scores a TD in a game, it would equate to giving up 0 points...not perfect, perhaps, but logical. There are some weird edge cases here that I wasn't able to distinguish, for instance the INT by a Redskin defender who then fumbles, and the resulting fumble is picked up by a Saints WR and returned for a TD...in this case the Redskins defense is rewarded for the INT and Saints defense is rewarded for a fumble return TD, when in fact neither should be. However, these cases are few and far between, and do not significantly impact the rankings, so I'm simply ignoring them.

Next, I subtracted 1.2 points from the DPA for each turnover that was not returned for a TD. This is because it provides an extra possession for the offense, which has a 1/3 chance of scoring on each possession. 60% of offensive scores are TDs (that number's a lot higher than I expected, anyone else? feel free to double-check my calculation here), so the average points scored on a possession is (.6*7 + .4*3) or 5.4...divide by 3 to get 1.8 for the number of points each turnover is worth to the offense. I'm arbitrarily reducing this number to 1.2, because turnovers that happen on 3rd or 4th down don't award an extra possession (and occasionally result in worse field position), and also turnovers at the end of a half or game do not always happen with enough time left for the offense to take advantage.

Finally, I reduced the DPA number by 3.2 for each safety the defense records, since there are two points on the scoreboard plus the additional 1.2 for an extra possession. Again, this may not be perfect, as the defense will receive credit for any safeties recorded by special teams, but I'm ignoring this too.

There are still more imperfections with my calculations, because defenses can be put in bad spots by poor special teams play or offensive turnovers. Witness the Eagles' defense starting at the 50 yard-line or worse on about a half-dozen possessions last week...can you say that 7 points surrendered by a defense starting on it's own 20-yard line is equivalent to a defense that surrenders 7 points after an 80-yard drive? But I don't have stats for average starting field position, and even if I did I'm not sure exactly what I'd do with it. But still, this adjusted defensive points allowed is a pretty good measure, and reveals some mildly surprising insights:

- The Jets are having a tremendous defensive season, a full 2 points better than their nearest competition. If I could figure out how to account for bad field position, I suspect they'd separate even further, since Sanchez has been a turnover machine.
- The Patriots, Panthers, Steelers, and Cowboys have been quietly playing very well. The 8 return TDs against the Steelers, as well as some memorable late-game meltdowns, have obscured their overall strength.
- The Redskins at 20? This shocked me, as their defense has been overhyped all season. Most football talking heads agree the defense has played well while the offense sucked, but these number tell a different tale. Although, again, this isn't helped by the offense's turnovers.

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