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A model-based approach to football strategy.

November 6, 2006 |

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* Brief strategy reviews will appear occasionally during the 2006 season, limited to situations that differ from those analyzed in previous years. *

A routine two-point-conversion decision wouldn't merit inclusion in this year's strategy reviews, but this one was hardly routine: With 12:55 left in the * second quarter * of the game between
Dallas and Washington,
Dallas coach Bill Parcells elected to go for two after Dallas scored a touchdown to take a 6-5 lead. This is the earliest two-point attempt we are aware of in a non-preseason NFL game.

This isn't the first time that Parcells has elected to go for two in the first half. Against Seattle in Week 13 of the 2004 season, Parcells went for two when trailing 14-12 with 6:08 left in the second quarter. In our analysis of that game we concluded that Parcells's choice was actually correct—or at least would have been if he hadn't wasted a timeout thinking it over.

Not only did the decision to go for two against Washington come considerably earlier in the game, but leading by 1 is a situation less favorable for two-point conversions than trailing by 2. Calculations using the
*footballcommentary.com*
Dynamic Programming Model
indicate that there was little benefit to Dallas from going for two. According to the Model, kicking gives Dallas a win probability of 0.562. If the Cowboys go for two, their win probability becomes either 0.592 or 0.537, according to whether the try succeeds or fails. One can check that the probability of success has to be nearly 0.46 to make going for two worthwile.

Overall success rates on two-point conversions have in fact been running above 46% in recent seasons, so we see no reason to criticize Parcells's decision. Actually, the proper conclusion is that Dallas's probability of winning is almost exactly the same whether they kick or go for two. Even if their probability of success on the two-point conversion is only 0.4, their win probability if they go for two is

The Chart we prepared for two-point conversions, using the Model, omits the first half of the game. That's because going for two early in the game will never provide a sustantial increase in win probability. But if going for two early in the game is never required, neither is it ever a significant mistake. As we explained in a previous article, over a small range of points, win probability is approximately linear in the point differential in the early part of the game. In particular, early in the game, your win probability if you lead by two points is almost exactly midway between your win probability if you lead by one point and your win probability if you lead by three points. Consequently, as long as the likelihood of success on a two-point conversion is in the vicinity of 50% and it's early in the game, your probability of winning is about the same whether you kick or go for two. This conclusion is independent of any model.

Copyright © 2006 by William S. Krasker