Sure it's not basketball, but the Hack-a-Shaq works
Ideally, the NBA would do away with intentional fouls as a strategy, a case I made today. As long as the rules do permit fouling players without the ball before the last two minutes of the fourth quarter, however, coaches have to figure out how to best use the "Hack-a-Shaq" to their advantage. In this case as many others, they would do well to follow the example of five-time champion and three-time Coach of the Year Gregg Popovich, who has hacked more frequently and more successfully than anyone else in the league.
Hack-a-Shaq in practice
The merits of intentionally fouling have been broken down in theory repeatedly, perhaps in most detail last year by former Phoenix Suns consultant John Ezekowitz for FiveThirtyEight. While Ezekowitz was able to use some observed results like the L.A. Clippers' offensive rebound percentage on DeAndre Jordan's missed free throws, to my knowledge no one has ever publicly analyzed the full outcomes of actual attempts to Hack-a-Shaq. So I set out to do just that.
ESPN Stats & Information compiled a list, cross-referenced with Basketball-Reference.com, of every foul this season recorded in the NBA's play-by-play as an intentional "take" foul. I then whittled down that list to only fouls strategically given to send a bad shooter to the line, adding a few fouls that weren't listed on the play-by-play. I came up with 222 total intentional fouls this season on 23 different players -- nearly half of them (109) sending Jordan to the line.
Each time a player got hacked, I recorded the results of all possessions by both teams, so as to capture the effects on the hacking team of playing against a set defense after free throws. The results were surprising, to say the least.
FT% OR% HackOff OppOff Net
.462 .188 106.5 107.4 0.9
Overall, the hacking team has gained 0.9 points per 100 possessions while fouling intentionally. That's a better result than it sounds because teams tend to foul when they're behind, so the teams doing the hacking are typically worse than the ones getting hacked. If they played straight up, we'd expect their net rating to be minus-2.1 points per 100 possessions.
On average, players have made 46.2 percent of their free throws when intentionally fouled. That's better than their 42.1 percent shooting on all other foul shots. There are a few reasons we should expect them to exceed that mark. First, simple regression to the mean suggests players targeted for the Hack-a-Shaq are probably slightly better than their free throw percentages imply. Second, as ESPN.com's Henry Abbott has noted in the past, free throw percentages are typically higher on the second attempt than the first. Not only are all intentional free throws shot in twos, instead of the occasional and-1, repeated fouling may provide a similar routine benefit. Of course, the hacked team can also score additional points by rebounding a missed second free throw. As Ezekowitz noted, the Clippers rebound Jordan's missed free throws more often than the typical free throw (13.5 percent of the time since 1996-97, according to NBA.com/Stats via Nylon Calculus). That's not unique. Factoring in second chances, offensive fouls have yielded a 106.5 offensive rating.
The most interesting finding is how efficient the hacking teams have been on their subsequent possessions. They've scored 107.4 points per 100 possessions, nearly identical to what we'd expect based on the offenses and defenses involved. Key to Ezekowitz's case against the Hack-a-Shaq was its impact at the other end, since it doesn't allow the defense to fast break off a turnover or missed field goal attempt. In practice, this hasn't played out. I'm not sure whether that's simply noise in the data -- 216 possessions is slightly more than two games' worth, so the sample size is small -- or indicative of hacking teams playing offensive-minded lineups to get better shooters like Spurs forward Matt Bonner on the floor since there's no defensive penalty.
So there you have it: Proof the Hack-a-Shaq does work ... on average. Because of the high variability in results, success or failure can vary widely depending on who's getting hacked and who's doing the hacking.
A tale of two Texas teams
The two teams who have intentionally fouled the most this season both hail from the state of Texas. Popovich has long been the face of the Hack-a-Shaq from the coaching perspective, so it should be no surprise that the Spurs have committed the most intentional fouls, 67 -- including 30 on Jordan in the playoffs. The Dallas Mavericks and head coach Rick Carlisle rank second at 32, but the two Texas teams have seen very different results.
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Team FT% OR% HackOff OppOff Net
San Antonio .433 .108 95.5 109.1 13.6
Dallas .578 .286 138.7 112.9 -25.8
Others .451 .200 105.1 105.9 0.8
When intentionally fouling, San Antonio has outscored opponents by an incredible 13.6 points per 100 possessions. For the sake of comparison, the Golden State Warriors led the NBA in net rating at plus-11.5 points per 100 possessions. Using the same strategy, Dallas somehow got outscored by 25.8 points per 100 possessions on its intentional fouls.
While Carlisle and Popovich's choice to foul players with relatively similar free throw percentages on non-intentional tries (41.6 percent for the Spurs, 44.1 percent for the Mavericks), Dallas opponents shot far better at the line. Over such a small sample (64 free throws for Dallas), most of the difference is probably nothing more than luck. But Carlisle's results-based approach -- he tends to call off fouling as soon as a player makes a free throw or two -- is likely to lead to higher percentages than Popovich's more consistent style. San Antonio typically fouls until the player is either removed from the game, the quarter ends or the clock reaches the last two minutes of the fourth quarter when rules change for away-from-the-play fouls.
Worse yet, when players fouled by the Mavericks did miss the second free throw, they gave up offensive rebounds nearly 30 percent of the time. The Spurs allowed just four offensive rebounds in 37 opportunities, maximizing the value of fouling intentionally.
The fouling break-even point
If the observed results this year are a good indicator of what to expect in the future, the break-even point for intentional fouling being a favorable strategy is a player who makes between 44 and 45 percent of his non-intentional free throws. Given the offensive rebound rates and efficiency on those second chances (similar to teams' overall offensive ratings, another finding that contradicts an assumption based on past studies and comes on a small sample size of just 20 offensive rebounds), we'd expect teams to score at a league-average rate when a 44-45 percent free throw shooter is intentionally fouled.
That makes it tough to justify fouling players like Dwight Howard (52.1 percent) and Josh Smith (49.3 percent) under normal circumstances. But it suggests it makes sense to foul a class of players like Joey Dorsey (30.5 percent, explaining why he's yet to play for the Houston Rockets in the playoffs), Andre Drummond (39.5 percent) and, of course, Jordan (38.0 percent). Given that the Clippers boasted the league's best offense, the break-even point for fouling him would be even higher than 45 percent; for an average opponent, it makes sense to foul any Clipper shooting worse than about 48 percent.
In practice, the Clippers' defense was in fact stingier than usual while Jordan was getting hacked this season, meaning they played their opponents evenly. But remember, the Clippers typically outplayed all opponents because they were a 56-win team. Based on the teams fouling the Clippers, we would expect them to be plus-4.4 points per 100 possessions, making intentionally fouling Jordan a much more favorable strategy. And when the Spurs encountered the Clippers in the playoffs, the combination of one of the league's worst shooters and best fouling teams yielded positive results.
Situation FT% OR% HackOff OppOff Net
All Jordan .427 .172 99.1 99.1 0.0
Jordan Playoffs .417 .167 96.6 106.9 10.3
San Antonio outscored the Clippers by three points on the 28 possessions where Jordan was intentionally fouled, accounting for the entire margin between the two teams over the seven-game series.
When to foul
The logical endpoint of the numbers on fouling Jordan is that the Spurs should have fouled him every single possession he's on the court. Of course, that makes no sense in practice because everyone on San Antonio's roster would eventually foul out in the process. A less extreme version of that scenario did play out in the Clippers-Spurs series. Twice, Tim Duncan picked up intentional fouls on Jordan that imperiled his future availability. In Game 2, Duncan played the last 3:12 of regulation and all of overtime with five fouls. And in Game 6, San Antonio got burned when Duncan used an intentional foul (while Popovich was trying to tell him not to do so) and later picked up a third foul in the first half. He was on the bench as the Clippers finished the half on an 11-4 run to tie the game.
My methodology can't pick up the long-term impacts of fouls that aren't felt until after a team stops fouling -- including the belief that fouling a team can take it out of its offensive rhythm -- so I turned to Mike Beuoy of Inpredictable.com to use his win probability model.
Intentionally fouling didn't seem to matter much in terms of changing win probability. Before they were hacked, we'd have expected teams to win about 75 of the 104 games in which they were fouled. (Note that some games are included multiple times, if players were hacked at different points.) This makes sense because the Hack-a-Shaq is usually saved for desperate times, like the fourth quarter before the two-minute warning. When the hacking was over, that remained 75 expected wins.
In practice, though, the teams getting fouled eventually went on to win 80 of the 104 games, suggesting there may be a long-term cost to intentionally fouling.
At the same time, win probability also reveals two fascinating stories of improbable comebacks. When the Portland Trail Blazers started fouling Jordan on March 4, they were down eight with just over four minutes to play. Ordinarily, we'd expect them to win about 4.1 percent of the time in that scenario. A month earlier, the Brooklyn Nets were in an even more hopeless situation when they hacked Jordan, down six with 2:47 to play (3.1 percent win probability).
In both cases, the team made up no ground while intentionally fouling. Though Jordan missed all six of his free throws against the Blazers, they went scoreless on their subsequent three possessions and saw their win probability drop to 1.1 percent by the time Jordan was removed from the game. After Jordan split two free throws, the Clippers responded by intentionally fouling Brooklyn center Mason Plumlee, who missed both, leaving the Nets further behind and with a 1.3 percent chance of winning.
Yet both teams defied the odds by beating the Clippers. Brooklyn made four 3s in a row, including an Alan Anderson four-point play, to take the lead and win, a result that's hard to attribute to one intentional foul. The Portland game was more complex strategically. While the Blazers got hot, too, with Nicolas Batum hitting a pair of key 3s to help force an overtime they eventually won, the Clippers' offense sputtered after the hacking, scoring just eight points on their last 17 possessions. Did intentionally fouling produce those wins? That's tough to say.
It certainly makes sense for teams down more than a couple of possessions to intentionally foul poor free throw shooters in the fourth quarter before the two-minute mark. Fouling lengthens the game in terms of remaining possessions, and the odds of missed free throws are far better than in the last two minutes, when teams can only foul the player with the ball.
It also makes sense to use the Hack-a-Shaq as a tool to get talented players out of the game. While Doc Rivers has been more likely to stick with Jordan than his predecessor, Vinny Del Negro -- who rarely played Jordan in the fourth quarter for fear of intentional fouls -- even Rivers relented at times during the Clippers-Spurs series because the strategy was so successful for San Antonio. Given Jordan's value, getting him out of the game without accumulating fouls on key players is a clear win.
