Hacking the Intentional Foul

Apr 26, 2015; San Antonio, TX, USA; Los Angeles Clippers center DeAndre Jordan (6) shoots a free throw against the San Antonio Spurs in game four of the first round of the NBA Playoffs at AT&T Center. Mandatory Credit: Soobum Im-USA TODAY Sports

DeAndre Jordan can do many things substantially well. There’s an extremely small chance you’ll ever reach as high as he can when jumping no matter how much you practice, unless Olympic high jumpers and seven-foot athletes are fans of NylonCalculus. He hops around the court swatting shots, collecting boards, and throwing in dunks all while never missing a game — I can’t imagine how strong his frame must be. But there’s one thing he cannot do: hit his free throws consistently.

10,000 Free Throws and One Lie

Of course, one of the most common complaints in basketball is, Why don’t these gargantuan guys just, you know, practice? There’s this notion that all you need to do to excise a weakness is practice, preferably 10,000 times because that’s the magical threshold. But just as you cannot jump 40 inches vertically, no matter how much you practice unless you were blessed genetically, it appears that some guys just cannot hit their free throws at a high conversion rate. All sorts of players have weaknesses, like Whiteside with assists and Crawford with rebounds. They’re just harder to see because we don’t have to watch them perform those actions solo with the game stopped because the other team doesn’t want to defend.

There are a few theories why guys like Shaq, Wilt, Howard, and DeAndre can’t hit their free throws — let’s remove hand size from this list because there’s no evidence to this and the guy most known for giant hands right now, Kawhi Leonard, shoots 80% for his career — but they’re not as bad as they appear. It’s tougher to hit those shots during the course of the game due to the pressure of the moment, how you’ve just been running around for a while, and that instead of a hundred in a row like practice, you’re there for two shots, maybe one more or fewer, and that’s it.

Let me show how these players are more skilled than you think and how hitting 80% of your free throws in the driveway doesn’t make you better than Dwight Howard. In this widely cited picture from the Lakers, you can see how their players from 2013 convert in practice versus the game. A tangent here on their math: they show that their players collectively hit 89% during practice but 69% during games, which was 29th in the NBA at that time. This is a fundamental failure in how to work with averages. During practice, they’re all basically taking the same number of shots, but during the game that’s obviously not true. Howard led his team in attempts and he’s the worst shooter. Generally, the best shooters are usually shooting specialists who don’t go to the line due to their playing style, while a lot of the worst shooters are fouled constantly partly because they’re bad at it and partly because they play close to the rim. If you take an average of their averages, ignoring the guys who’ve taken fewer than 30, then the team average is 73%, which is close to the league average.

Using beta regression in R, I modeled the numbers from the Lakers practices with three-year averages (I added the numbers for Duhon from 2011 and 2010, Ebanks’ from 2011, and Sacre from 2015 for a better sample size) from the actual games, weighing things by number of real-world free throws in the respective time frames. What I have is a rough translation of what a player would shoot in a game from their averages.

The model is:

100*exp(-8.76 +11.0*FT(practice)/FTA(practice) )/[1+exp(-8.76 +11.0*FT(practice)/FTA(practice)]

If you shoot 80% while no one’s watching, you have nothing over Dwight Howard — for an NBA player, 80% during practice translates into a poor percentage during the game. I wish I had more data on this, but I’m reasonably confident in assuming DeAndre Jordan is much better at free throws at practice and that he works harder at it than most people assume.

There is an unorthodox solution for guys like Jordan, however: shoot the free throw underhanded. Rick Barry famously used this at the end of his career, and he taught the athletic big man George Johnson, a shotblocker and rebounder like DeAndre, how to shoot underhanded — he was 73% from the line after he converted styles. According to Dr. Larry Silverbird, shooting underhanded is advantageous because it’s one motion rather than the four motions for the conventional free throw, and the statistical variation of the release speed is much lower with one motion. Basically, for a relatively uncoordinated guy with long arms like DeAndre, an overhead motion can’t be perfected because even with practice he can’t replicate the same movement on command consistently, so he needs a simpler motion to convert at an acceptable rate.

That’s a crazy demand for a professional player, sure, but it’s more reasonable than just saying practice more and hit your free throws. Even the commissioner Adam Silver is swayed by this overly simplistic and uneducated opinion. Practice doesn’t solve everything.

What Happens When They Miss?

Even if a player can’t hit from the charity stripe, there’s a factor here that people tend to overlook and it makes the strategy of hack-a-player significantly less valuable: offensive rebounds. Once you factor those in, it becomes obvious why it’s such a terrible strategy to hack guys like Howard and Shaq, both around 55% for their careers, because shooting around 55% from the line translates to a surprisingly good offensive rating with two shots and the modest boost from rebounding pushes it into elite offense territory. But how often is a free throw miss rebounded by the offense?

Using data provided by the wizard Darryl, I have every free throw rebound going back to 1997 via stats.NBA.com including the playoffs. The offensive rebound rate in that time span after free throw misses was 13.5%. Thus, one may to use that number to calculate the expected rates with hack-a-DeAndre. But we can’t assume that Jordan going to the line translates to a 13.5% rebound rate. People may argue, in fact, that the rate should be lower for his free throws because he’s their best offensive rebounder and he’s away from the basket. Yet the trend pretty clearly goes in the other direction.

Looking at everyone with at least 250 misses with a free-throw percentage under 55% in the table below, the rates are actually higher than you’d expect. Remember, these guys are also fantastic offensive rebounders and the team should be worse on the boards with one of their big men on the line. For instance, the rebound rate after a Rajon Rondo rate is 20.2%.

Reference the rebound numbers when the elites shooters below miss (this is everyone with a percentage over 88 with at least 100 attempts.) Over Steve Nash’s entire career, there have been only five offensive rebounds from his free throw misses. Even though these teams get to use both big men in the paint when these free throw are taken, they are recovering the misses at low rates.  The best shooting big man, Dirk Nowitzki, who came in under the threshold at 87.9%, had a 5.7% rate.

Taking this further, I built a model, similar in structure to the free throw practice one above, to estimate offensive rebound rates given a player’s free throw percentage and position. This isn’t perfect, of course, because I think it’s a useful tool when you don’t know how well teams rebound off certain player’s misses and to inform the current data for better future predictions, especially for guys with only a handful of misses in their careers. Filtering the data down to players with at least 50 attempts in the regular season from 1997 to 2015, you get the a model that looks challenging but is deceptively simple[1. exp(-1.28 +0.143*log(1-FT/FTA) – 0.132(log(1-FT/FTA))^2 – 0.321*C -0.187*PF -0.0582*SF)/[1+exp(-1.28 +0.143*log(1-FT/FTA) – 0.132(log(1-FT/FTA))^2 – 0.321*C -0.187*PF -0.0582*SF)] where SF, PF, and C are dummy variables (either 0 or 1) for positions.].

There are a couple important points. One is that position is definitely a real factor and poor shooting guards give up a lot of offensive boards. Another is that from the given data free-throw percentage has a tricky non-linear relationship with offensive rebound rate, and it took some experimentation to find a variable that reflected the non-linear residual problem I had. When there’s a complicated relationship like that it suggests that multiple factors are influencing the outcome. One is that poor shooters have different types of misses, including awkward bounces that are tougher for the defense to recover. For instance, the rebounds from DeAndre’s misses are significantly further from the basket than average. The other factor is probably psychological: why fight hard on offense for a rebound when Nash is shooting because there’s a 10% chance it’ll be for nothing? It could be why Nash has such a low rate compared to someone like Billups. There’s only a one percent difference in their free throws, but Nash’s reputation engulfs that disparity.

The Other Effects

Turning it back to DeAndre Jordan, you can see how this hurts the power of hacking him. Let’s give him a free-throw percentage of 42%, which translates to a rebound rate of 15.1%. His real rate was 20.6%, so let’s use a 2-to-1 weighted average to be conservative: the rebound rate is now 18.8%. It’s enough of a difference to boost the offensive rating of this play by roughly 4 points. Also, once the team grabs the rebound, they’re usually more efficient with the next play due to how close the rebounder is to the basket and how scattered the defense now is (teams usually don’t hack again after an offensive board.)  Here’s an old study showing field-goal percentages after free throws, and you can also peruse NBAWOWY for how well teams shoot after offensive boards. Given the offensive rating the Clippers had during the season, 112.4 via basketball-reference, and how much better they shoot after an offensive rebound, you can expect 1.22 points on average after a free throw rebound.

That translates to an offensive rating of 97.3 for hack-a-DeAndre, but obviously there are other factors and you can follow the steps in this FiveThirtyEight article. The Clippers get to set their defense and hack-a-player really only works in slowing down half-court offenses, which are less efficient. Plus there’s another huge factor: the Spurs have a great defense and have held the Clippers to an offensive rating of 104.9, which includes many non-hacking possessions. Depending on which values you assume for those factors, the strategy is almost neutral in its effectiveness.

However, I have one more factor to complicate matters. When you enact an aggressive hack-a-player strategy, you’re sending the player to the line multiple times, which means they can find a rhythm while shooting and convert a higher number of shots. This isn’t conjecture either, as this paper found that players shoot 3 to 4% better on second free throws. I also calculated the free throw percentage on the first and second free throws of every free throw pair from 1997 to 2015. The difference was 4.6% — players shoot much better on the second free throw. The thinking here is that with a “warm-up” shot players are much better, and you can understand how this makes a long string of intentional fouls even worse.

But you don’t have to believe the warm-up theory. Let’s turn to the data. Using the same play-by-play data from stats.NBA.com, where intentional fouls are coded as “Personal Take Foul” from the 2011 season and on, DeAndre Jordan had 294 intentional free throw attempts and shot 44.9%; on all other foul attempts he shot 41.1% for a difference of 3.7%[2. It appears that intentional fouls weren’t recorded properly before 2011. If you want to check, here’s a playoff game from 2008 where hack-a-Shaq is deployed at the end of the first quarter but they’re only labeled personal fouls]. It’s a pattern that holds for the other infamous wayward shooters: 59.2% versus 53.7% for Howard, even though he was hacked more often during the period where he was converting around 50%, and 41.7% versus 39.4% for Drummond. Those effects are probably being underrated too because the play-by-play may not capture every hack-a-player foul and the boost is larger, given what we know about these shots, the more free throws you take in a row.

Once one inputs DeAndre’s hacking FT%, the math is not clearly in favor of the defense — the percentage is too high and his team rebounds his misses too often. Using some of the aforementioned assumptions, a typical hack-a-DJ possession has an expected value of 1.02 points — that’s not much lower than what you’d expect from the Clippers given how good San Antonio’s defense is, and once you filter out fast breaks and factor in the effect of the Clippers setting their defense, then the hacking ploy is actually a negative for the defense.

Here’s a basic hack-a-player formula for estimating its efficiency:

2*(FT% +0.045) +OREB%*(1 – FT% – 0.022)*ORtg after OREB +DRtg advantage after FTs

where FT% is FT/FTA, the 0.045 component is the boost players get in percentage during hacking attempts, the 0.022 component is adjusted for players shooting better on the second attempt, and other factors discussed here.

Conclusion

Of course, the numbers here are sensitive to a number of things, like the expected efficiency from the Clippers and how well they rebound the misses. There are also other situations where the strategy makes sense, like holding a lead because you’re putting a ceiling on their offense by only allowing free throws. It can be used a psychological tool too, slowing down a high-octane team and frustrating its shooters. But even with a free throw shooter as poor as DeAndre, the advantage isn’t clear enough to muddy up the game. The fix here is simple for the league too, and I hope they get past the nonsense counter of “just make your shots,” as all they have to do is allow a team to choose to inbound the ball when there’s an off-ball foul in the penalty. If players need only to make their shots, why can’t we say to defenses just defend those shots? Remember, this is the same league that installed the shot clock because teams took advantages of leads and held onto the ball for entire quarters; rule changes aren’t bad. Fouls were created to penalize the offenders, not to grind the game to a halt — let’s end this now.

We’ve had 50 years of this hacking strategy, going back to Wilt Chamberlain, and with better data we can see the limited effectiveness of the tactic. DeAndre Jordan can’t hit his free throws. But who cares, and why do we need to watch more of it?