Football Outsiders reprints some nifty analysis by William S. Krasker, who has launched an excellent analytical site on football, footballcommentary.com. Krasker picked up where David Romer left off, adding refinements to the dynamic programming model of a football game. The post at Football Outsiders analyzes controversial choices made in critical situations from last season. Here's a taste:
Packers Go For The Touchdown Versus The Eagles
In the divisional round of the playoffs, with 2:00 remaining in the first half, Green Bay led Philadelphia 14-7, and faced 4th and goal at the Philadelphia 1 yard line. Packer coach Mike Sherman made the controversial decision to go for it rather than kick the field goal, but Ahman Green was stopped for no gain, and the Eagles took over on downs.
This situation is quite similar to the one the Panthers faced in the wildcard round against the Cowboys, which we have already analyzed. Once again, a naive analysis based solely on expected points would say that Green Bay should go for the TD if the probability of success exceeds 3/7.
There are two factors which complicate matters beyond the naive analysis: field position conditional on success or failure, and diminishing returns to scoring. The latter dominates in Krasker's model, which raises the required probability of a touchdown from .43 (3/7) to .46. Even so, Krasker concludes that Sherman made the right call in going for the TD.
There's more good analysis at both sites. But be prepared to spend some time there if you go - neither site is for hit and run readers.