Thursday, January 31, 2008

Is NFL defense mostly luck?

My last post linked to a study by Brian Burke that showed the Patriots scored a touchdown twice as often as the Giants, but that the Patriots' defense *prevented* a touchdown only slightly more often than the Giants'.

I wondered whether this meant that defense didn't vary between teams as much as offense does, and commenter "w. jason" confirmed that.

Now there's another confirmation, from
this study at (by Doug Drinen?). Near the end, Drinen found that the year-to-year correlation of NFL teams' defensive stats is ... *negative*:

-.10 Turnovers forced
-.11 Touchdowns

I assume it's just random chance that these numbers are negative, unless you think there's some reason teams that are above-average this year should be below-average next year. If you had enough data, you'd probably find a positive, but small, correlation.

Does this mean that defense doesn't matter much? Is any player pretty much as good as any other on your defensive line?

That's possible. It's also possible, for instance, that a defense is only as good as its weakest link, and it's your *worst* players that make the difference, not your best. Or, it could be that teams can't tell the good defenders from the bad, and wind up with a random assortment.

In any case, shouldn’t this imply that you shouldn't pay a premium for defenders? I assume teams pay more for their offensive squad than their defensive, but probably not as much as these results say they should. I'll check it out if I have a chance.

That Drinen link, by the way, came from
today's "The Numbers Guy" article by Carl Bialik. He notes that the outcomes of sporting events are hard to predict. An organization called "Accuscore" is able to predict only 63% of NFL games, 57% of baseball games, and 68% of basketball games. (Hockey gets screwed again – not even mentioned.) Bialik attributes the difference to the amount of information known about the teams, but I think it's actually that basketball is intrinsically less random than baseball – as I have argued here and elsewhere.

Bialik also debunks one of the naive arguments against sabermetrics: that since statistical analysis thought the Giants should have lost all three games, and was wrong three times, the analysis must be wrong. I've seen that argument a couple of times lately, and it goes beyond silly. Even the best analysis only gives you a probability estimate, and even low-probability events happen sometimes.

And one last interesting tidbit: For NFL games, Accuscore has 54% accuracy against the spread. That seems pretty impressive to me.

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At Friday, February 01, 2008 3:24:00 AM, Anonymous Anonymous said...

Just picking the home team should get you to 54%. Bruce Bukiet at was at about 55% this year, and his system appears to have some glaring flaws. I'm working on a blog for this season that'll track the predictions of a run-estimator-type-dealie with other bells and whistles, and I'll compare Bukiet and Accuscore too, to see where progress can be made.

At Friday, February 01, 2008 11:06:00 AM, Blogger Brian Burke said...

I've found the same thing. Defenses are more of a passive victim to offenses in the NFL. Only very rarely do defenses rise to the level where they can dominate--the Ravens when healthy in recent years, for example.

'Interceptions thrown' auto-correlate very well from the first half of a season to the second half, meaning it is a skill (or lack thereof). But 'interceptions taken' do not auto-correlate at all, meaning that they are the result of offensive mistakes and luck more than any defensive ability.

Also, the distribution of yards per play is wider for offenses than for defenses. In other words, the standard deviation is larger for offenses, suggesting they drive the show.

Instead of a 'weakest link' theory, I prefer the 'singular importance' theory. Defensive squad ability is more of an average of 11 players. A weaker cornerback can 'get help' from a better safety, for example. Or a good pass rush can help compensate for a poor secondary.

On offense, however, no one can help compensate for a poor passer. The QB's individual ability is so singularly critical that the squad's ability is more like the average of 10 guys + one large factor for the QB (or maybe RB too in some cases). Since individual skill levels vary more widely than for averages of many individuals, offensive abilities would vary more widely as a consequence of the importance of the QB.

At Friday, February 01, 2008 11:14:00 AM, Blogger Phil Birnbaum said...

Brian: that makes sense, that the SD of offense is based on the skills of 2 or 3 players.

So why don't only those players make the big bucks? Why don't teams "bid down" (as it were) the prices of individual players on defense?

At Friday, February 01, 2008 11:25:00 AM, Blogger Nate Hebel said...

brian, your analysis of yards/play distribution and the consequences of smaller defensive variance is right on. i firmly believe that yards/play is the best simple measure of a team's ability.

i threw together 2003-2007 y/p data and ran the season N vs season N+1 correlation. It turns out that the correlation of defenses y/y is +.3 while for offenses it is +.4

this ratio of 4 to 3 isn't too far from brian's ratio of 5 to 4 on standard deviations.

taken together, i suppose that means that defensive players as a group "should" have a market price of 20%-25% less than offensive players.

would the same be true of coaches?

At Friday, February 01, 2008 11:28:00 AM, Blogger Phil Birnbaum said...

A defensive y/y correlation of 0.3 is pretty high in my book. I was expecting a lot lower, especially if offense is only 0.4.

At Friday, February 01, 2008 12:51:00 PM, Blogger Nate Hebel said...

And these relative correlation #s are a bit conservative from the point of view of defense. The one downside to the yards/play metric is that it has a small bias towards offenses who calla high % of passes. (passing plays have a higher y/p mean, but also a higher variance). Since i would imagine play-calling correlates highly y/y (think andy reid in philly) i think the correlation on offense is artificially high by a little bit.

you don't get the same problem on defense as defensive play calls don't have much of an impact on pass vs run %.

At Friday, February 01, 2008 3:44:00 PM, Anonymous Anonymous said...

The "Singular Importance" (for lack of a better term) seems to make a lot of sense

How many defensive players are asked to cover recievers? As many as seven or eight positions throughout the game, so one linebacker or safety who is poor or great at pass coverage won't make a huge difference. Same is true for pass rush, a team can have a below average outside linebacker and still be adequate overall. Or having one truly great player on one side might not mean too much if the other players are weak

On offense how many players are asked to pass or carry the ball? Sometimes only one guy. Having one great running back automatically gives a team a good running attack no matter who the other players are

At Saturday, February 02, 2008 3:50:00 PM, Blogger Brian Burke said...

Why do players other than the QB or other hyper-important positions get big bucks?

I'd guess the salary cap is the biggest factor. Imagine Brady's or Manning's salary in an NFL without a cap.

Compare the pitcher in baseball with the QB in football. The pitcher position is comprised of 10+ guys. Add up all their salary on a team as a proportion of team payroll--it might be 40% or more. A QB might be able to pull in that share of team salary without the cap.

Another reason might be the complexity of the sport. The performance of a football team is not linearly additive like it is in baseball. The players skills all interact, so a great QB cannot play at his potential without good blocking or receiving. In contrast, Barry Bonds doesn't need any help from teammates to hit home runs.

Lastly, there are only a handful of elite QBs, certainly not enough to go around the league. How do the teams without them compete? By building strength in the other positions I suppose. The market for those players drives up their salaries.


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