Jeffrey Rosenthal analyses the probabilities of the popular basketball game HORSE

June 16, 2022 by Josslyn Johnstone - A&S News

For both NBA All Stars and driveway amateurs, the basketball shooting game HORSE conjures up memories of schoolyard competitions and neighbourhood hangouts. A new statistical analysis could help make those recollections of simpler times a bit more interesting.

“When I was growing up, I would play with my dad, and I remember that he would attempt these really easy shots,” Jeffrey Rosenthal, a professor in the Department of Statistical Sciences in the Faculty of Arts & Science, recalls. “That goes against what most of us would think to do, which is to make a difficult shot in hopes that your opponent won’t be able to match it.”

When shooting hoops together at the Willcocks Common just south of Sidney Smith Hall last summer, Rosenthal and his half-brother Daniel, a U of T alumnus who studied advanced mathematics as well as philosophy and psychology, wondered if they could mathematically determine the effect of shot difficulty on the probability of winning points.

“It may not be the deepest mathematical analysis we’ve ever done,” Rosenthal says with a laugh. “But trying to justify the rules of HORSE presented us with an interesting question about the probabilities: what is the optimal shot to take, to increase your chances of winning?”

The co-authors published their results in the June/July 2022 issue of the journal Notices of the American Mathematical Society (PDF).

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