NBA Hackathon Fouling Project

In this project, we explored the effect of changing the National Basketball Association’s traditional method of awarding a player two foul shots, to instead see every fouled player given one free point.

This was the topic we chose to analyze at the 2017 NBA Hackathon, given a plethora of player tracking data, because of:

1) Injuries: There are has been a rise in injuries to top players because of increased fouling. As this affects players like Kawhi Leonard and Kevin Love and costs their teams millions of dollars we must examine new ways to solve such a problem. We wanted to focus on player safety as the NBA has been proactive in examining the issue, with major steps being taken after the injury to Paul George and new Hack-A-Shaq rules.

2) Time: Fans across all sports are beginning to desire a shorter game time period. Obviously, the fouling and its associated “stopping and starting,” is very time-intensive and is one the NBA’s best potential spots to cut time from.

3) Risk: Though physical play is obviously part of all contact sports, overly fouling players could lead to occasional physical altercations. We believed that if we increased the risk involved with fouling a player, meaning that we raised the expected value for the opposite team when they are fouled, then we would see an increase in the distance between defenders and players, something that was evident in our findings.

PowerPoint Link:


Consequently, we decided to create two models to analyze this effect. Our first model looks at the current free throw system and replaces it with our proposed method. This allows us to see what the score would be under the new format for every game over the last 10 years.

We replaced each shooting foul worth two or more shots as follows:

In each case of such a foul, we replaced the actual result of the free throws with this expected value, and also kept track of how many fewer free throws would be shot during the game; we found that on average, the two teams would combine to shoot fewer free throws. Since free throws slow down the pace of play, this might potentially be a welcome change for the fans and broadcasters.


We also used the raw tracking data to examine the distance each shooter was from his nearest defender when he releases the ball.

Our hypothesis was that the average distance to nearest defender would be longer on made field goals than misses; we plotted this info for the Thunder’s field goal attempts in a game in November 2016 and the results are in line with this hypothesis. This is critical, because if the stricter free throw rule is implemented, defenders are forced to sag off the shooters, especially on three-point attempts, and we can expect higher scoring as a result of more open shots.

Game Theory Model

Our second model brings a slight twist on new projections for scoring of games over the last decade. The twist exists this: assume that you know the shooting percentages and distributions (meaning standard deviation and variance) of a given player when he rises up for a shot in a given area. When would you foul, and when will you let him take the shot?

Well, this entirely lies on how what action will minimize his utility. Therefore, we wrote a minimizing agent and calculated hypothetical records of teams, running 50 samples, for the last 10 years.

Time Saved

To find the reduction in time, we calculated the average time spent for a free throw, by the wall clock time in the play by play file.

However, when we ran a regression on this time as a result of the next play, we realized that the the wall clock time in between free throws was significantly increased if there were one or more substitutions made in between the free throws. To account for this, we isolated the free throws where the next play in the game log was also a free throw.

This had a twofold impact, as these were the free throws that we would be replacing, so we could isolate all of the free throws that would be affected by this rule change, and so that we could get the average time of a non-substitution free throw.

We then multiplied this number by the total number of free throws impacted per game, and averaged that value per season to get the total time changed as a result of the reduction in free throws. This value likely understates the actual total time saved, as it doesn’t account for other potential reductions in game time, including a diminished number of injury stoppages as a result of defenders playing farther away to diminish fouls.


We ultimately found that this would shorten the average game by 422 seconds from less free throws and change the average team’s win number by 1.3.

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