Football + Math == A Good Time
I mentioned before that I wanted to do some statistical analysis of football to prove coaches are too conservative. Well, reader Alton Hollingsworth pointed out that someone beat me to it. The paper linked is a real, official, get-your-Ph.D. statistics paper, so be warned: it's got things with superscript and double subscript--not for the faint of heart. In between the mean numbers, though, is a really interesting discussion of correct football strategy--at least according to game theory.
The paper is a pretty thorough analysis of third and fourth down plays from the first quarters of NFL games from 1998 to 2000. Third downs are used to stand in for fourth down plays because there just aren't enough fourth down attempts to get a statistically significant sample. First quarter plays are used because presumably in the fourth quarter you won't be settling for a 38 yard field goal attempt to win the game... you want as many points as you can.
The money shot is this:
Teams' actual choices are dramatically more conservative than the choices recommended by the dynamic-programming analysis. One the 1575 fourth downs in
the sample where the analysis implies that teams are on average better off
kicking, they went for it only 7 times. But on the 1100 fourth downs where the
analysis implies that teams are on average better off going for it, they kicked
On another note, there are a lot of fascinating little statistical bits derived from the assignation of expectation to yard lines. The value of a first and 10 at your own one is -1.8 points. This value rises quickly to 0 at the 15 yard-line. Team's average starting position after a kickoff is the 27, which has a value of 0.6 points, so the net value of a field goal is actually only 2.4 points, a touchdown ~6.4 points. The value of a first and ten equals the value of a made field goal at approximately the opponent's 41. On your half of the field the difference between kicking and just giving the opponent the ball right there is 2.1 points, which is equal to a punt of 38 yards, which means that 38 yards is the dead center average net punt. Anything more than that is a good one.
Maybe this only interests me, I dunno. I don't fully understand everything going on here (IANA statistician) but I believe that this guy has a point... he gives 4.7% as *very* ballpark estimate on how more likely a coach using an improved fourth-down strategy is to win a game, which would correspond to an extra Michigan victory every other year. Like, say a Rose Bowl decided by a single point.
Anyone who can point out other papers of this type, please drop me a line (check the sidebar for my mailto). The willingness to take on extra risk for greater reward is at the heart of another hobby of mine, poker, and the difference between football coaches' and poker players' respective approaches to risk is really interesting. There isn't a good poker player in the world that wouldn't put all his money in the middle with the most razor-thin margin of positive expectation (tournaments excepted). Almost every football coach ever born would rather take the relatively sure thing.
Football is ripe for a Moneyball-ish revolution. The key for football won't be identifying undervalued players based on statistics but identifying common game situations that are the source of incorrect decisions. If Mike Martz wasn't such a flawed coach in so many other ways, he could be the guy. Unfortunately, he's a giant tool. Too bad.