A model-based approach to football strategy.
|November 4, 2008|
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With 7:01 remaining in the 4th quarter, the Redskins trailed 23-6, and faced 4th-and-goal just inside the Steelers' 1-yard line. Washington coach Jim Zorn elected to go for the touchdown rather than settle for an easy field goal that would bring his team within two scores. Unfortunately for Washington, Jason Campbell's attempted touchdown pass fell incomplete.
A simple analysis, requiring no model, suggests that Zorn was right to go for the touchdown. The analysis is similar to a more detailed one we did for the game between Detroit and Minnesota in 2003 Week 3.
Washington's chances of scoring the required three times are slim. We can simplify the analysis by ignoring the possibility that they score four or more times in regulation. Then, if the Redskins settle for the field goal, they have only one winning scenario: they must score two unanswered touchdowns and win in overtime. Let q denote the probability of scoring those two unanswered touchdowns, and let pOT denote Washington's probability of winning if the game goes to overtime. Then if the Redskins kick a field goal at 7:01, their probability of winning the game is qpOT.
Now suppose the Redskins decide to go for the touchdown at 7:01, and decide more generally that they will not attempt any field goals for the rest of the game. Let pTD denote the probability of scoring the touchdown from just inside the 1-yard line. Then under the no-field-goals strategy, Washington's win probability is pTDq. Comparing this to the expression at the end of the previous paragraph, we see that the no-field-goals strategy yields a higher win probability than kicking if
Of course, Washington is not precluded from attempting a field goal on a subsequent possession. Thus, if the Redskins score a touchdown at 7:01, they reap an additional benefit: the option to settle for a field goal later in the game, should it be optimal to do so. This implies that going for the touchdown is correct even if pTD is the same as, or slightly less than, pOT.
Copyright © 2008 by William S. Krasker