A model-based approach to football strategy.
|January 6, 2008|
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The Steelers attempted a pair of two-point conversions in this game. The second, coming with 6:21 left in regulation and Pittsburgh leading by a point, was not a difficult decision. According to the Chart prepared using the footballcommentary.com Dynamic Programming Model, Pittsburgh should go for two in that situation as long as the probability of success exceeds about 0.15.
A more interesting situation arose after the Steelers scored a touchdown with 10:25 left in regulation to pull within five points prior to the try. The two-point conversion apparrently succeeded, but Pittsburgh was flagged for holding, resulting in a re-try from the 12-yard line. The Steelers once again went for two, but failed.
The Chart isn't applicable in this case, because it doesn't take into account that if the Steelers kick the extra point, it's a 30-yard attempt rather than the normal 20-yard attempt, and the likelihood of making the kick is only about 90% rather than 99%. However, direct calculations using the model indicate that the Steelers should go for two provided the probability of success exceeds 0.17. Therefore, Pittsburgh's decision to go for two despite the penalty was reasonable. However, the proper conclusion in this case is that there is very little difference in win probability regardless of Pittsburgh's choice—and this conclusion holds up even if Pittsburgh's probability of success on the two-point conversion deviates substantially from 0.17. In fact, even if Pittsburgh's likelihood of success on the two-point try were only 10%, going for two would yield a win probability just 0.006 lower than they would obtain by kicking.
Late in the game, with Jacksonville trailing by a point and driving for what turned out to be the game-winning score, NBC's commentators debated whether the Jaguars should try to score a touchdown, or whether they should run the clock down as much as possible and then attempt a field goal. Jacksonville did in fact try to score a touchdown, but running back Maurice Jones-Drew was stopped at the Pittsburgh 2-yard line on 3rd down, and the Jaguars settled for a field goal. Using our model for the two-minute drill, we will examine whether failing to score the touchdown actually helped Jacksonville.
Had Jones-Drew scored with about 1:19 left to give the Jaguars a 34-29 lead pending the try, Jacksonville would certainly have attempted a two-point conversion. Following the ensuing kickoff, the Steelers would have taken possession with about 1:14 left, trailing by either 5 or 7 points, and with no timeouts. According to the model, Pittsburgh's probability of scoring a touchdown would be about 0.13. (This estimate incorporates a small "convexity" effect due to the uncertainty in Pittsburgh's starting field position; see our analysis of the Indianapolis-Detroit game in 2004 Week 12.) Assuming Jacksonville's success probability on the two-point conversion is about 0.43, and that Pittsburgh's win probability in overtime is about 0.5, the Steelers' win probability if Jones-Drew scores is about
|0.43 × 0.13 × 0.5 + (1−0.43) × 0.13 = 0.10.|
Alternatively, the Jaguars can run the clock down and kick a short field goal. After the subsequent kickoff, the Steelers get the ball with about a half-minute left, trailing by two points. In this case, according to the model, Pittsburgh's win probability is about 0.11. So in this case, it appears that it makes little difference whether the Jaguars try to score a touchdown or focus on running down the game clock. Their win probability is about the same either way.
Finally, a comment on Jacksonville's decision to take a delay-of-game penalty prior to kicking the game-winning field goal, in order to take as much time as possible off the game clock. This made the field-goal attempt 25 yards rather than 20 yards. Coaches seem to believe that this makes no difference. However, 20-yard attempts succeed about 99% of the time, compared to 96% for 25-yard attempts. Put differently, Jacksonville made the probability of missing the field goal four times as large as it needed to be. It's better to snap the ball with a second left on the play clock, and keep the field goal a true chip shot. (We examined a similar decision made by New England coach Bill Belichick in Week 2 of the 2006 season.)
Copyright © 2008 by William S. Krasker