The Riddler: Basketball Fans Asked to Submit Solutions: When Should a Team Foul in a Close Game?

Courtesy of the brilliant minds at, a puzzle for basketball fans who think they have what it takes to solve a simple riddle:

When and why should a team foul in a close game, and a team is either in the bonus or about to be in the bonus?

The article by Zach Wissner-Gross explains this riddle and offers fans a chance to submit their solution. Read the riddle below and submit your response!

The Riddler

By Zach Wissner-Gross

From Dave Moran comes a riddle so foul it’s sure to bust your bracket:

In NCAA men’s basketball, when a team has committed between six and eight fouls in a half, the opposing team is “in the bonus.” This means that the next time they are fouled while not in the act of shooting, they get to shoot at least one free throw. If the player makes that first free throw, they get to shoot a second. If either free throw is missed, one team will rebound the ball, and play will continue with the rebounding team in possession.

Assume that an average team scores exactly 1 point per offensive possession, a figure that accounts for multiple shots if the team rebounds its own miss (or misses) on a single trip, and that it rebounds 15 percent of its own missed free throws.

Now suppose you are the coach of a team playing an average opponent that’s in the bonus. The other team has the ball, the game is tight, and you want to minimize the expected number of points your opponent will earn on this particular possession. How low does the ball-handler’s free throw shooting percentage need to be for you to instruct your team to foul that player (when they are not in the act of shooting)?

Solve it!

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David Keech
Author: David Keech

David Keech is a math teacher in Wisconsin Rapids and public address announcer for Abbotsord High School. He officiates basketball, baseball, and softball in central Wisconsin. He has reported on amateur sports since 2011, known as 'KeechDaVoice.' David can be reached at [email protected]