By the Numbers: To Foul, or Not to Foul (When Up By Three)

Eight seconds to go, and you’re up by three. The other team inbounds the ball to their three-point sharpshooter – say, Kobe Bryant – and you’re responsible for guarding him. Do you stick a hand in his face, hoping that he takes – and misses – the shot? Or do you foul him before he gets a chance, giving him two free throws, knowing that he’ll probably make the first and intentionally miss the second, hoping his team gets the rebound and a chance to win with a three?

It’s a surprisingly contentious issue in the NBA. Situations like this aren’t unique to basketball, either. There are comparisons in football (fourth and one at midfield, do you punt or go for it?) and baseball (bases loaded, two outs, and their best hitter up, do you walk him to avoid possibly giving up four runs?) that cause similar crises in coaches’ minds. Numbers and statistics will give you a clear idea of what is most likely the best course of action, but there are so many variables and mitigating factors that come up in the course of play that it’s difficult to know exactly what to do.

Does fouling when you're up by three points prevent a tying shot like this from happening?

Besides, if you go with the play that looks better statistically but isn’t as common (like trying to convert a fourth and one) and blow it, the media holds you responsible afterward (think Bill Belichick).

As this column is titled “By the Numbers”, you can imagine that I’ll be looking at things through the lens of statistics, but hopefully we’ll be able to understand why a coach would be hesitant to call a play that looks great on paper.

The “foul when you’re up by three” issue has strong opinions on both sides. A lot of people think it makes sense to prevent the other team from having a chance to tie the game with a three. Others think that it’s a dangerous move, because if your opponent gets the offensive rebound, that opens up the possibility of tying the game with a two or winning it with a three.

But how likely is it that the opponent will get the offensive rebound, let alone get the shot off in time?

Let me phrase it another way: As worrisome as this scenario probably sounds, can you think of a single time you’ve seen a game end this way? I can’t, and I’ve watched a lot of NBA games.

In order to figure out how likely it is that a team could win after being fouled when down by three points, I figured I’d need to know how likely it is that a team picks up an offensive rebound from a missed free throw. Before looking at the numbers, I thought about games I’ve seen. Sure, teams pick up the offensive rebound sometimes, but it doesn’t happen often. After all, the rules are set up so it doesn’t happen very often – the defending team gets to put two of its players right next to the basket who can box out their opponents. I can think of far more games where I haven’t seen an offensive rebound from a missed free throw than those where I have.

But just because I don’t remember it happening very often doesn’t mean it doesn’t happen very often. To find how often it happens, I went through play-by-play records of 30 games from February. (I would have analyzed more for a larger sample size, but I was doing this all by hand, and you’d be surprised how long it takes to go through even just one game.) I only considered free throw attempts where there could be a rebound in play, so first attempts out of two (or second out of three) and technical free throws were thrown out.

The most common result of a free throw, as you can probably imagine, is a make. 78% of the attempts I looked at resulted in a make, which lines up neatly with NBA’s free throw average this season (77.5%). That means just 22% of the time, there’s a rebound in play. That would seem to bode well for our idea that fouling is the best strategy, but you have to remember that in this situation, the shooter is going to intentionally miss, almost guaranteeing that there will be a rebound up for grabs. So let’s ignore that first 78% and focus on those rebounds.

When there is a rebound in play after a free throw, it ends up in the hands of a defender 88% of the time. Again, this shouldn’t come as a surprise, based on the way potential rebounders are standing (defense, offense, defense, offense, with defense closest to the rim). The shot ends in an offensive rebound just 11% of the time, according to the data I was looking at (the other 1% was split between jump balls and offensive loose ball fouls, neither of which is helpful to the team trying to catch up).

Let’s think about where that puts us right now. If you let Kobe take his shot, it has a 30-40% chance of going in, depending on how accurate he has been from beyond the arc that night. But if you foul him before he has a chance to shoot, he only has an 11% chance of even taking the shot, and even that will probably be rushed, reducing the shot’s accuracy.

Foul him! We're up by three! But be careful not to foul in the act of shooting! And, uh, be sure to let some time slip off the clock!

So based on that information, why would anyone even consider letting their opponent take the shot? Well, for starters, that 11% figure isn’t quite as cut and dry as it would seem. The rebounders are expecting a missed shot, so they might find a way to get themselves in a better position to grab the ball. Second, defenders have to be careful when fouling a three-point shooter. If you foul Kobe in the act of shooting, he gets three attempts instead of just two. If you can foul him before he gets close enough to take a shot, you’re in good shape, but if he gets closer, he could be expecting the foul and might prepare himself to get a shot off.

And third, sometimes it’s just more valuable to let time slip off the clock. It’s obviously a bad idea to foul if you’re up by three with six minutes left on the clock. It’s probably worth a try if there are only three seconds to go. But what if there are ten? You probably gain more by letting some time run off the clock to prevent them from having enough time after the shot to run another play.

So, strictly based on the numbers, it seems like it’s a good idea to foul when you’re up by three, but it’s best not to make that a hard and fast rule. And now, if you see a game where a coach doesn’t have his players foul in that situation, you can at least understand why they might be hesitant to do so.