Statistical analysis of NFL 4th down strategy
elsa.berkeley.edu
elsa.berkeley.edu
TL;DR for football fans: The take-away graph is Fig. 4 on pg. 353. The solid line represents when a team SHOULD go for it on 4th down to maximize expected points. The dashed line represents when teams DO go for it. Bottom line is that teams go for it MUCH less often than would maximize their expected points.
TL;DR for economists: NFL coaching could be assumed to be a case where (a) a lot of objective data is available to base decisions on (b) the result to be maximized (wins) would appear to be fairly obvious (c) decision makers (coaches) are highly qualified and highly motivated. Yet in practice, coaches systematically deviate from the strategy that would maximize wins. It's not clear whether this is due to (I) the "true" result coaches are trying to maximize is NOT wins or (II) coaches not making strictly rational decisions.
TL;DR for hackers: I found the analytical reasoning (opportunity cost; etc) interesting, and found it worth reading the whole thing for that.
No matter what the math says, no coach will do this (save for maybe Billichek, but even he's not that bold). Sports is one of those areas where the "gut" and conventions are more important than stats and probabilities. Moneyball is a great book for anybody whose interested in the intersection of sports conventions and math.
http://www.amazon.com/Moneyball-Art-Winning-Unfair-Game/dp/0...
http://sportsillustrated.cnn.com/2009/writers/jon_wertheim/0...
I've read Moneyball, and I find it interesting that statistical methods have been accepted so much more in baseball over the last decade or so, but seem to still be shunned in football, at least for this particular situation.
http://sports.espn.go.com/espn/page2/story?page=easterbrookp...