Toward the end of very close football games, a team is often faced with the decision to kick a field goal to tie the game or go for a touchdown and a win on fourth down. More often than not, the team on offense calls a time-out to discuss the decision.
These discussions usually revolve around whether to go for a touchdown, rather than kick a field goal, and if so, what play to run. Thus, in most cases, the decision to go for a touchdown on fourth down is not made until after deciding what plays to run on first, second, and third down. Hurley (1998) argues that the fourth-and-goal conference should never involve the decision to go for a touchdown, because that decision should be made prior to the selection of the play to run on first down.
The author, who is an assistant football coach at the college level, as well as an operations researcher, came to this conclusion after using a decision tree to analyze such a decision made by his own coaching staff. That decision turned out to be the wrong one, not due to the choice that was made to go for the touchdown, but due to the timing of that decision. The coaching staff all agreed that, had the decision to go for it been made on first down, the sequence of plays selected on first, second, and third down would have been quite different. In other words, if you know that you are playing four-down football on first down, that knowledge affects the particular plays that will be called.
To summarize, in considering a case where a coach decides to go for a touchdown on fourth down, suppose we go back to the decision of what plays to run on the earlier downs and ask the following question: Should the coach choose a sequence of plays that gives him the best chance to score on three downs or on four downs? If he already has made the decision to go for it on fourth down, then the answer to this question is obvious: Choose the sequence that gives you the best chance to score in four downs. This is the primary lesson derived from the analysis of decision trees: The best decision at the present moment depends on best decisions that will be made in the future.