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November 16, 2009 |

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Leading by 6 points with 2:08 remaining in the 4th quarter, the Patriots faced 4th down and nearly 2 yards to go at their own 28-yard line. Indianapolis had one timeout left. New England coach Bill Belichick made the remarkable decision to go for the first down rather than punt. Quarterback Tom Brady completed a pass to Kevin Faulk, but Faulk was ruled down just short of the necessary line of gain. Indianapolis took possession near the New England 30-yard line, and scored a touchdown to win the game.

Belichick has been ridiculed for the decision. However, our analysis indicates that going for the first down is as good as punting.

We will do a simple analysis, focusing on the main scenarios. Any reader could do the same analysis, using tables available on this Website.

If the Patriots pick up the first down, they are highly likely to win the game. If they go for it and fail, the Colts have probability *q* of scoring a touchdown. If the Patriots punt, the Colts have probability *p* of scoring a touchdown.

The probability of making a first down with a little less than 2 yards to go is about 0.55. Therefore, if the Patriots go for it, their probability of winning the game is about *q*). *p*. Equating these expressions and simplifying the result, we find *q*=2.22*p*. Thus, the decision depends on the Colts' probability of scoring a touchdown if the Patriots go for it and fail, relative to the Colts' probability of scoring a touchdown if the Patriots punt. If the Colts' probability of scoring after a failed New England 4th-down conversion is more than 2.22 times the Colts' probability of scoring after a New England punt, then the Patriots should punt. Otherwise they should go for it.

Estimates of *q* and *p* can be found in the
Tables
associated with our model for the
two-minute drill.
In the table labeled "Trailing by > 3 points, probability of scoring a touchdown," we look at the sub-table labeled "2:00 left." The first column is the Colts' starting field position; this would be about the 30-yard line if the Patriots punt, and about the 70-yard line (i.e. the New England 30-yard line) if the Patriots go for the first down and fail. The third number in any row is a team's probability of scoring a touchdown if they have one timeout. Thus, *q* is around 0.4929, and *p* is around 0.2218. Coincidentally, the ratio of these probabilities is 2.22, so it appears that New England's win probability is roughly the same whether they go for it or punt.

The numbers in the Table are estimates for an average team, and the Colts' offense is far from average. Still, *q* and *p* separately are not relevant to the analysis; only their ratio matters. It's not clear whether the Table-derived ratio should be raised, or lowered, to account for the Colts' offensive prowess. Our analysis contains many additional simplifications. For example, if New England punts there could be a long punt return; Indianapolis could win even if New England makes a first down; and New England could win even if Indianapolis gets possession and scores a touchdown. However, we doubt that formal consideration of those additional factors would alter our conclusion that New England's probability of winning the game is roughly the same whether they go for the first down or punt.

Copyright © 2009 by William S. Krasker