The Hackulator: A Win Probability Based Guide for When to Foul

In which we use advanced analytics to ruin basketball (as foretold by prophecy).

What good is a sports win probability model? For one, it is the ultimate narrative statistic. It boils down the various components of a sporting event into the impact we care about most: winning. When charted, it can provide a quick distillation of what type of game was played: a dramatic comeback, a wild see saw battle, or a predictable snoozefest.

A win probability model also has strategic value, although how much value does depend on the sport. For a sport like football, they can be of great use, particularly late in the game where a coach may have to decide between punting or going for it, whether to onside kick, or when to go for two.

When it comes to basketball, there are fewer strategic opportunities for win probability to be of use. You don't need a fancy model to know that possession has a higher win probability than not having possession or that scoring points is better than not scoring points. But there is one common basketball situation where win probability can be of use: when to foul late in the game.

In general, fouling the opposing team and giving them two free throw attempts is not, to borrow a gambling term, positive EV. At the league average free throw rate of 76%, expected points when fouling is around 1.55 points, well above the 1.09 points per possession NBA teams averaged in the 2018-19 season. But what fouling does do is cut short your opponent's time of possession and extend the length of the game. When you're trailing, that has value.

Win probability can help quantify that value. And to that end, I have leveraged this site's win probability model to create a new tool that tells you when fouling should increase your team's odds of winning: The Hackulator.

How the Hackulator Works

The tool itself is pretty straightforward. On the left enter how much time is remaining, how many points the team is trailing by, and the expected free throw percentage of the player being fouled (pre-populated with the league average 76% free throw rate):

After clicking the "Hackulate!" button, you get the following output on the right:

Baseline Win Probability is just the output from this site's win probability model, and implicitly reflects what teams do in this situation (on average). The Hackulator calculates the expected win probability if a team fouls and then compares that to the Baseline Win Probability. If the fouling win probability is higher, the Hackulator recommends you foul.

To calculate the win probability when fouling a team, you need to play out six distinct possibilities. For the first free throw, there are just two possibilities: make or miss. For the second free throw, there are three: make, miss followed by a defensive rebound, and miss followed by an offensive rebound. These possibilities, their associated likelihoods, and resulting win probabilities are shown in the table on the right. For the purposes of these calculations, the Hackulator assumes a league average free throw offensive rebound rate of 18.6%.

In addition to the foul/not foul recommendation, the tool also tells you the breakeven free throw percentage. In the situation above, where a team is down by 8 with 1:01 left, the recommendation to foul holds as long as the expected free throw accuracy is no higher than 81%.

Of course, the standard disclaimers hold here. All models are wrong, yada, yada, yada. And they represent league-wide averages that may not be applicable for certain teams. But, like any analytics model, it provides a data driven starting point from which to evaluate decisions.

The overall results of the tool are summarized in the chart below (for a league average 76% free throw percentage):

With a minute left and trailing by 8 or more, the Hackulator recommends fouling. But what do teams actually do? The chart below summarizes how often teams foul when trailing late in the game.

With 60 seconds left, teams trailing by 8 only foul about 50% of the time. And in general, teams foul less often than what the Hackulator would recommend. That teams should foul more often when trailing late is not a new recommendation. This 2015 paper presented at the Sloan Sports Analytics Conference came to the same conclusion. However I am highly skeptical of some of the results presented in the paper, such as that the Indiana Pacers would have generated more than 8 additional expected wins in a single season by following the strategies outlined in this paper.

I am also aware that "teams should foul more" is not a very fan-friendly recommendation. Free throws, in general, are boring, and no one likes to see the back and forth flow of an NBA game brought to a grinding halt for multiple trips to the charity stripe. Contrast that to the NFL, where the "analytics" recommendations would lead to more exciting games: fewer punts and field goals, surprise onside kicks, and more two point conversion attempts; which makes the NFL's relatively slow adoption of analytics all the more puzzling.

If you play around with the tool, you'll quickly notice that the marginal gains in win probability due to fouling are, well, marginal. At best you are taking a dire situation and making it just a little bit less dire. For this reason, I don't expect this tool to turn basketball strategy on its head, the way three point shooting has in recent years. Or how the work of Brian Burke and others has led to a slow but steadily rising acceptance in the value of going for it on 4th down in the NFL (Burke's now defunct Fourthdownulator was a key inspiration for the Hackulator).
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