** footballcommentary.com **

A model-based approach to football strategy.

April 4, 2004 |

Super Bowl XXXVIII
featured one of the more controversial coaching decisions from any Super Bowl: Panthers' coach John Fox's decision to go for two with 12:39 remaining in the game, trailing

The fallacy of this argument is that the actual sequence of scores was just one of many possible scenarios -- and an improbable one at that. To analyze this decision and others more systematically, we will use the *footballcommentary.com*
Dynamic Programming Model.

Following the attempt at an extra point or points, Carolina will be kicking off with 12:39 remaining. According to the Model, their probability of winning the game will be either 0.2965, 0.2304, or 0.2113 depending on whether they are behind by 3, 4, or 5 points. Assuming that a kicked extra point succeeds with probability 0.985, Carolina's probability of winning the game if they go for one is

0.985*0.2304+(1-0.985)*0.2113=0.2301.

On the other hand, if two-point conversions succeed with probability 0.4, then Carolina's probability of winning the game if they go for two is

0.4*0.2965+(1-0.4)*0.2113=0.2454.

So, according to the Model, Fox was right: going for two is the better choice. Indeed, since

0.22*0.2965+(1-0.22)*0.2113=0.2301,

Carolina's probability of success on the two-point conversion needs to be only 0.22 to justify going for two.

Notice that whether or not Fox goes for two affects Carolina's probability of winning the game by about 0.015. But once the decision is made to go for two, the success or failure of the try affects Carolina's probability of winning the game by more than 0.08. Overwhelmingly, it's the execution on the field that determines the outcome of the game.

We should mention that a 5-point deficit -- or lead, for that matter -- is particularly favorable for two-point conversions. If you lead or trail by 5 following a TD, the Model says you should go for two as early as four minutes into the second quarter -- although the benefit of doing so at that point is extremely small. (The same result emerges in Harold Sackrowitz's model.)

In a much less controversial decision, Carolina also went for two with 6:53 remaining in the game, after scoring a TD to go ahead

With 9:04 remaining in the first half of a scoreless game, New England had 4th and 1 at the Carolina 38 yard line. Bill Belichick decided to go for it.

Under these circumstances, according to the Model, if New England goes for it and makes the first down, their probability of winning the game is 0.5872, whereas if they fail, their probability of winning is 0.4833. If instead they punt, and we assume Carolina's expected field position is their own 12 yard line, then New England's probability of winning the game is 0.5238. (The reason these probabilities are skewed in New Englands's favor, notwithstanding the tie score, is that Carolina will be kicking off to start the second half.) Since

0.39*0.5872+(1-0.39)*0.4833=0.5238,

it follows that New England's likelihood of gaining the first down must only exceed 39% to make going for it preferable to punting. According to
data
assembled by *Football Outsiders*, during the 2003 season teams converted successfully on 68% of attempts on 3rd or 4th and 1. So, it appears that Belichick's decision was correct. In fact, assuming a 68% success rate for the conversion, New England's probability of winning the game if they go for it is

0.68*0.5872+(1-0.68)*0.4833=0.5540.

Leading

According to the Model, if New England goes for it, their probability of winning the game will be 0.7159 or 0.5725, depending on whether they succeed or fail. If they punt, their probability of winning the game is 0.6566 (assuming Carolina's expected field position is their own 30). Calculations analogous to those performed above then show that New England needs at least a 0.59 probability of making the first down to justify going for it. If the true likelihood of picking up the first down is about 68%, as the
data
assembled by *Football Outsiders* suggest, then going for it gives New England a 0.6700 probability of winning the game. In this case, Belichick should have gone for it. Of course, if Belichick feels that his chances of picking up the yard against Carolina are materially worse than against a league-average defense, punting is justified.

On two other occasions during the game, New England faced 4th and 1 and chose to punt. In both cases, according to the Model, by going for it they could have increased their probability of winning the game by about 0.015. But once again, Belichick might not have liked his chances against Carolina.

With 7:48 remaining in the game, New England led

This isn't really a decision, of course; no quarterback chooses to get picked off. Nevertheless, countless Patriots fans must have been thinking that the one thing you have to avoid in that situation is an interception. At least in principle, one can use the Model for guidance as to how much risk it would be worth taking in an effort to get a TD rather than a FG.

According to the Model, a FG would have given the Patriots a 0.9178 probability of winning the game. A TD and extra point makes that probability 0.9770. On the other hand, if a pass is intercepted in the end zone for a touchback, New England's probability of winning the game is 0.7906.

To illustrate how these numbers might be used, suppose Brady has no open receiver. He can throw the ball away, settling for a chip-shot FG. Alternatively, he can force a pass. Suppose that if he does so, there is a 0.3 probability of a TD, a 0.5 probability of an incomplete pass (leading to a FG), and a 0.2 probability of an interception.

If Brady throws it away, New England's probability of winning is 0.9178. On the other hand, if he forces the pass, the probability of winning is

0.3*0.9770+0.5*0.9178+0.2*0.7906=0.91.

So, with these assumptions, it's better to throw the ball away, although of course the actual probabilities Brady faced were presumably different from what we assumed for this example.

Copyright © 2004 by William S. Krasker