Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

By Wayne Winston | Go to book overview

25
TO GIVE UP THE BALL IS BETTER
THAN TO RECEIVE

The Case of College Football Overtime
In college football tie games are resolved with overtime. The winner of a coin toss chooses whether to start with the ball or to give the ball to his opponent. The first team with the ball begins on the opponent's 25- yard line and keeps going until they attempt a field goal, score a touchdown, or lose possession. Then the other team gets the ball on their opponent's 25- yard line and keeps going until they attempt a field goal, score a touchdown, or lose possession. The team that is ahead at this point is the winner. If the score is still tied, the order of possessions is reversed and the pro cess is repeated. After the second overtime each team must attempt a two- point conversion. Rosen and Wilson tabulated the outcomes for all overtime games through 2006 and found that the team that had the ball second won 54.9% of the time.1 This would indicate that the coach who wins the toss should elect to give the other team the ball. The intuitive appeal of giving the ball up is that when you finally get the ball you will know what you need to do to win or keep the game going. For example, if the team that has the ball first scores a touchdown, the other team must go for a touchdown. If the team with the ball first fails to score, then the other team needs a field goal to win. Can we model the “flexibility” of the team that possesses the ball second in a way that is consistent with Rosen and Wilson's findings? Rosen and Wilson give the following parameter values:
probability team with ball first scores touchdown: .466
probability team with ball first scores field goal: .299
probability team with ball first does not score: .235

1 Rosen and Wilson, “An Analysis of the Defense First Strategy in College Football Over-
time Games.”

-172-

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