A two to tie? Or a three for the win? What the math says.

With six seconds left in their NCAA Tournament First Round matchup with New Mexico State, Auburn’s men’s basketball team led by one point. Samir Doughty had just missed the first of two free throws, and New Mexico State was out of timeouts. Doughty made his free throw, putting the Tigers up two.

With just under four seconds left in the national championship, Baylor’s women’s basketball team led Notre Dame by two points. Chloe Jackson had just evaded Brianna Turner and banked in a contested layup, and following a pair of timeouts, Notre Dame was set to inbound on the offensive side of half court.

Each of these games found itself in the same position:

Time for one shot, and likely only one shot.
Two points to tie, three points to win.

The situations were different, of course. Notre Dame had time to draw up a play. New Mexico State had to improvise. Notre Dame was about on par with Baylor in the talent department. New Mexico State was not a massive underdog, but was certainly at a disadvantage against Auburn should the game progress to overtime.

Still, the situations were largely the same, and while I haven’t researched how common the scenario is, my hunch is that we’ll see it at least once over the next two months in the NBA Playoffs.

So, what’s the right move? Play for two? Try to tie it and force overtime? Or go for the three? Play to win the game, then and there?

Obviously, the answer to that differs situationally. An open shot, regardless of where it is relative to the three-point line (provided it isn’t from, say, half court), is the preference. A team’s strengths and weaknesses, as well as those of their opponent, are impactful. Specific players make a difference, and fouls are in play. And, as in the New Mexico State example, if you’re the poorer team, you should more highly prioritize keeping an extra few minutes off the clock.

But some simple math, using the national averages in NCAA Men’s Basketball (Division I), NCAA Women’s Basketball (Division I), and the NBA, is revealing.

Note: I took these averages from the NCAA’s website, and from Sports Reference sites. The averages aren’t perfect, but they’re close to the true average.

In each league, a team finding itself choosing between a two to (attempt to) tie and a three to (attempt to) win should, all else being equal, look for a three.

Even in men’s college basketball, where the difference in win probability between a two-point attempt and a three-point attempt is lowest, an attempted three makes teams 36% more likely to win, raising their overall win probability from 25% to 34%.

And in women’s, where the difference is the greatest, win probability rises by nearly half with an attempted three, climbing from 22% to 31%.

The difference is so large that teams in each league would need to be so open and so close to the basket that the likelihood of making the shot rises to these levels to justify shooting a two:

And on the other side, teams would need to be so well-guarded and far from the basket that the likelihood of making the shot falls to these levels to justify passing up a three:

Yes, fouls are probably more common on two-point attempts. Data isn’t easily available for that in all these leagues, but it’s probably true. But even then, free-throw percentages would need to be above 79% in women’s college basketball, 83% in men’s college basketball, and 84% in the NBA to justify a two even with the guarantee of getting fouled (and, in this equation, missing the original attempt, which is overwhelmingly more probable in this situation).

The moral of the story is clear: Offensively, in these situations, draw up plays designed to create open three-point looks. Defensively, prioritize the perimeter, and prioritize keeping the ball away from your opponent’s best long-distance shooters.

Now we know.