footballcommentary.com

A model-based approach to football strategy.

May 29, 2004

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Going For It On Fourth Down

The Tables shown below, computed using the footballcommentary.com Dynamic Programming Model, are intended to provide guidance regarding when to go for it on fourth down rather than punt.

Tables are provided for four different field positions: Our own 5, 20, and 40 yard line, and the opponent's 40 yard line. The Tables are computed under the assumption that a punt nets 40 yards, except when the line of scrimmage is the opponent's 40 yard line, from which we assume a punt nets 30 yards.

For the first half of the game, the results depend in principle on whether we or the opponents will be kicking off to start the second half. But not surprisingly, the Tables are almost identical for these two cases.

As an example of how to use the Tables, suppose we trail by 7 points with 12:00 left in the first half, and face fourth down near our own 40 yard line. Suppose also that we will be kicking off to start the second half. In the Table labeled "Own 40 yard line, first half, we will kick off to start the second half" we go to the row corresponding to a lead of minus seven points, and the column corresponding to 12:00 remaining. The Table entry is 0.48. This means that if the probability of picking up the first down exceeds 0.48 we should go for it, and otherwise we should punt. Certainly if we have just 1 yard to go for the first down, we should go for it.

Own 5 yard line, first half, we will kick off to start the second half.
Own 5 yard line, first half, opponents will kick off to start the second half.
Own 5 yard line, second half.

Own 20 yard line, first half, we will kick off to start the second half.
Own 20 yard line, first half, opponents will kick off to start the second half.
Own 20 yard line, second half.

Own 40 yard line, first half, we will kick off to start the second half.
Own 40 yard line, first half, opponents will kick off to start the second half.
Own 40 yard line, second half.

Opponent's 40 yard line, first half, we will kick off to start the second half.
Opponent's 40 yard line, first half, opponents will kick off to start the second half.
Opponent's 40 yard line, second half.

Copyright © 2004 by William S. Krasker