The Science of Hack-A-Shaq: A Free Throw Conundrum
The struggles of many poor free-throw shooters have revived the “Hack-A-Shaq” strategy, but is fouling the opposing team’s worst free-throw shooter worth it?
This postseason has been notable for many reasons: historically great individual performances, several injuries to star players, and a host of teams looking to win their first title. But among the waves of headlines dominating the NBA news cycle daily, one key aspect of the game has been featured prominently: free throws.
That’s right. Free throws, which are perhaps the least exciting aspect of basketball, have been emphasized as teams look to gain a competitive advantage.
More specifically, teams are trying the “Hack-A-Shaq” strategy — the strategy of intentionally fouling the opposing team’s worst free-throw shooter named after Shaquille O’Neal. O’Neal, during his prime, was so dominant as an interior scorer that fouling him was seemingly the best way to slow him down.
Aside from Giannis Antetokounmpo and Ben Simmons, the former of which has come under fire for his long, drawn-out free-throw routine and the latter of which has been historically bad at the line, there have been other horrendous performances at the line. Clint Capela (47.8%) and Rudy Gobert (63.6%) stand out as clear examples.
So, should more teams play the “Hack-A-Shaq” game? What other deciding factors — basketball is not played in a simulation, after all — might push a coach towards fouling the other team’s worst free throw shooter? Using probability and basketball strategy, many of those questions can be answered.
- Random Variable: A random variable “X” assigns a numerical value for each outcome of an experiment.
- Independent Events: Two events are independent if the occurrence of one does not affect the probability of occurrence of the other (Google).
- Expected Value: A predicted value of a variable, calculated as the sum of all possible values each multiplied by the probability of its occurrence (Google).
In basketball, no event is as “controlled” (referring to the restriction of other, non-controlled variables) as free throws. Every player shoots from the same distance, has the same allotted time, and stands in the same area of the court. Naturally, pressure, the non-quantifiable variable that comes into play during the postseason when the stakes are highest, affects the outcome of free throws, but generally, free throws are a binomial experiment, meaning they have independent, repeated, and identical trials.
Applying this concept to basketball, we can use the probability of events (in this case, the number of made free-throws) to suggest whether or not a team should intentionally foul their opponent’s worst foul shooter.
Using Ben Simmons, who has been mercilessly fouled by the Atlanta Hawks for his historically bad free throw shooting (33.8% after Game 6), we see an instance in which fouling may be helpful to the Hawks.
In this situation, there are three outcomes assigned to the random variable X: 0, 1, and 2. These values come about, of course, because there are only three possible values for the number of free throws that a free throw shooter like Simmons can make in one trip to the free throw line (3 cannot be a value in this experiment because intentional fouls rarely coincide with a three-point attempt).
The last aspect in setting up this statistical experiment is assigning a probability to each possible outcome. In other words, the question “What is the chance that Ben Simmons makes 0, 1, or 2 out of 2 free throws?” is being answered.
In probability, free throws would be considered independent events: the occurrence of one event, such as Simmons making a free throw, would not affect the occurrence of the next event (whether or not he makes his second free throw attempt). In practicality, due to the psychological effect of confidence, this may not necessarily be true — but it must be assumed true mathematically.
The values for the probability of X — “P(X)” — are given below by multiplying the probabilities of Simmons either making or missing a certain number of free throws. In simple terms, there is about an 88.5% chance Simmons will make at most one free throw when being intentionally fouled, and only an 11.5% chance he will make both of his free throws when fouled, based on his current free throw percentage of 33.8%.
So when do these statistics, random variables, and probability come into play?
Well, what the Atlanta Hawks coaching staff and stats department must be weighing is the average number of points the Sixers will score on a normal offensive possession and the average number of points the Sixers score when Simmons is at the line.
That second value, the number of points generated by Simmons shooting two free throws, can be calculated using the expected value (also known as the “weighted average”), which in this case is the expected number of points generated by Ben Simmons at the free throw line.
As defined above, the expected value is calculated as the “sum of all possible values each multiplied by the probability of its occurrence.” That gives us this equation below, where each possible value (0, 1, and 2) is multiplied by its respective probability.
That number, E(X), is exactly 0.676, and in basketball terms, it means the Sixers score only 0.676 points per possession when Simmons is at the free throw line — a horrendously low number.
Simmons’ free-throw shooting becomes even worse when considering that even an average free throw shooter (75% for instance) would be expected to score 1.5 points per possession in the same scenario, and that, per 100 possessions, the Sixers would only score roughly 68 points per game if Simmons’ free throws were their only offensive action.
So, compared to the Sixers offensive rating (an estimate of the number of points scored per 100 possessions) of 113.2, it’s fairly obvious that the Hawks are right in fouling Ben Simmons and sending him to the line as often as possible.
But why aren’t more teams intentionally fouling? This same binomial experiment could be applied to any poor free-throw shooter, and it will always result in an expected value (points per possession) that is less than the team’s offensive rating. The answer lies in the basketball conundrum that is the “Hack-A-Shaq” strategy.
While “Hack-A-Shaq” can be proven as a winning strategy with simple probability and weighted averages, it becomes a complicating variable in many other ways that put its effectiveness into question.
The most obvious and pressing issue with the “Hack-A-Shaq” strategy is that it removes transition opportunities away from the team that is intentionally fouling. Even if the team being intentionally fouled is at an offensive disadvantage, they are at a defensive advantage because they can set up their defense in a half-court setting.
Transition is nearly impossible to quantify on its own (how does one distinguish between fast breaks and a fast-paced half-court offense?), so the effect of its absence is also hard to quantify. But thinking logically, a team such as the Hawks will suffer to an extent by limiting their opportunities for Trae Young to attack a scrambling Sixers defense. Likewise, the Nets probably avoid fouling Giannis Antetokounmpo excessively just to have the chance for Kevin Durant to attack a non-set Bucks defense.
Another issue presented by the strategy is even simpler: who should use their 6 fouls to intentionally foul the other ?
The Hawks have elected to have their wings, such as Kevin Huerter, Bogdan Bogdanovic, and Danilo Gallinari, intentionally foul Simmons, mostly because most of Philadelphia’s wings outside of Tobias Harris are not a threat to draw fouls during the course of a game.
But what if, say, the Sixers wanted to foul Clint Capela and force him to rely on his 47.8% average from the line? Well, there are no good options for Sixers players to intentionally foul with. Any guard or wing who guards Trae Young desperately has to stay out of foul trouble, eliminating Simmons, Matisse Thybulle, Tyrese Maxey, and George Hill as candidates; the Sixers’ centers also need to stay out of foul trouble because they are relied upon to protect the rim, which eliminates Joel Embiid and Dwight Howard as options.
Would Philly really put one of their starting forwards (Tobias Harris and Furkan Korkmaz) in foul trouble just to test Capela’s free throw shooting? The answer is an obvious and resounding no.
The last reason why Hack-A-Shaq may be a losing proposition is the other penalty to fouling in basketball: the “bonus.”
The “bonus” is the situation in which any team foul causes the opponent to get two free throws. Because teams with star players like the Bucks and Hawks generate so many fouls already, particularly due to the exploits of Giannis Antetokounmpo and Trae Young, intentionally fouling them would create a secondary issue: it is almost impossible to win a game if your opponent is in the bonus for entire quarters at a time.
So much of the Hack-A-Shaq strategy involves the intricacies of basketball that are, at the moment, statistically impossible to measure. Can teams eventually figure out how to quantify the impact of eliminating transition opportunities, or the impact of playing with an opposing team in the bonus for long stretches?
That reality makes Hack-A-Shaq less of a sure bet than what probability and expected value make it out to be.
However, the effects of confidence (or the lack thereof) and its psychological (and perhaps physiological) impact on athletes cannot be ignored. Although it is, again, impossible to measure, the “pressure” a player will feel to win a playoff game with free throws must be significant. That pressure also must only increase in particularly tense scenarios, such as elimination games and Game Sevens.
If a coach believes in the effects of pressure on athletes, then Hack-A-Shaq becomes more of a winning proposition. But if a coach is worried about the very real basketball effects (the bonus, foul trouble, etc.) of Hack-A-Shaq, then it may be a losing proposition.
In the end, then, Hack-A-Shaq, which seems like a sure bet mathematically, is more of a coin-flip: for all of the positive benefits it has, it can have equally as many negative effects on a team. With so much at stake in the remainder of the postseason, only time will tell if the strategy continues its revival.
