The Logistics behind Hack-a-Shaq
Hack-a-Shaq is a basketball defensive strategy used in the National Basketball Association (NBA), where Dallas Mavericks coach Don Nelson adapted the strategy of committing intentional fouls (originally a clock management strategy) to the purpose of lowering opponents’ scoring. He directed players to commit personal fouls throughout the game against selected opponents who shot free throws poorly.
In the sport of basketball, the bonus situation (also called the penalty situation) occurs when one team accumulates a requisite number of fouls, which number varies depending on the level of play. When one team has committed the requisite number of fouls, each subsequent foul results in the opposing team’s taking free throws regardless of the type of foul committed.
Therefore, teams sometimes defended Shaquille O’Neal by bumping, striking or pushing him after he received the ball to deny him an easy layup or slam dunk. Because of O’Neal’s poor free throw shooting, teams did not fear the consequences of committing personal fouls.
To demonstrate how this is done, in 2016-17, before a new ban, Andre Drummond has been another player to bring back Hack-a-Drummond, as viewed in the video here: https://www.youtube.com/watch?v=2kKb7OxsPVQ.
This strategy, seemingly so simple, is actually a huge game of statistics, probabilities, and game theory. The home team, the Houston Rockets, can choose whether to foul the certain player with poor free throw percentages (let’s use Drummond for now), or to not foul Drummond. Whereas the away team, the Detroit Pistons, can choose whether to substitute Andre Drummond or not. This all comes down to the math and strategies of both teams, depending on the player’s free throw percentage, and teams points per possession.
For the home team, the payoffs for “hacking” different players are completely different. In order to determine whether the strategy is ideal, given the large amount of variables that are difficult to account for in these calculations, Hack-a-Shaq should only be considered when there’s a clear advantage to doing so. The Detroit Pistons averaged 0.928 points per possession. This would make 47 percent shooting the safe threshold (since two free throws each account for one point, assuming you win the ball back after the shots). Looking at Drummond’s stats, he had a history of being below the 40% free throw percentage shooting mark. Thus, it makes mathematical sense to start fouling him.
However, the Detroit Pistons also have a choice, whether or not to substitute Drummond out of the game and replace him with another player, with a higher free throw percentage, but less efficiency. This means that if fouled, player “alpha” will add more points to the score than Drummond would, but if not, the pistons would produce a lower “points per possession” than if Drummond had stayed on to ~0.849.
In the end, the Pistons coach decided to keep Drummond on, who performed fantastically decent with free throws that particular time, and they won the game. However, this is a surprisingly interesting game theory event that came to my interest when I first saw it online, relating to the choices two parties could take to maximize their own offensive output and defensive output to win the basketball game.