One of the biggest problems today that challenges the NBA as a whole is the Hack-a method of intentionally fouling a poor free throw shooter to send them to the line and end the opponent’s possession. The strategy is employed invariably to a handful of 7-footers who made their way into the NBA because of a huge wingspan, vertical and ability to create and finish shots around the rim, not their fine-motor skill to make stationary 15 foot shots. Generally it is employed as a last resort to try and slow down the offense, or in hopes of catching the player on a cold shooting night. But what is the statistical effectiveness of hacking a particular player? What free-throw percentage should players aim for to avoid getting hacked? This short article aims to answer those questions.

To determine when it is an effective strategy to hack a player, we need to construct a formula that calculates the expected points when you send a free throw shooter with a particular FT% to the line. Calculating expected points for the first possession is relatively easy. It can be expressed as 2* the likelihood of making both free throws, plus the likelihood of making 1 and missing one: 2*FT%*FT% + (1-FT%)*FT% + FT%*(1-FT%). This simplifies to a nice wholesome 2*FT%. But as my high school coach taught me, the possession isn’t over until the board has been cleared. So we have to account for the likelihood of an offensive rebound. According to SportVU’s data, the likelihood of the offense rebounding a missed free throw is 11.5%. So the probability of catching an offensive rebound and restarting the possession is 11.5%*(making the first, missing the second + missing both): 11.5%*(FT%*(1-FT%) + (1-FT%)*(1-FT%)), which simplifies to 11.5%*(1-FT%).

For the purpose of this exercise, we’ll assume the defending team decides to hack again after an offensive board. So we’re back in the same position again, and there’s a chance that we go round and round in a continuous stream of missed free throws and offensive rebounds. Luckily maths provides an easy solution to these infinite sums. So we eventually find that the formula looks like 2*FT%/(85.5%-11.5%*FT%).

So that’s expected points off every possession, but we want to know whether that’s better than letting the opponent run its offense. Simple, a player’s score is the difference between their team’s offensive rating and their expected points off shooting foul shots. Below is a table of every player with ≥50 attempts whose score is negative, meaning it’s effective to try and hack them.

Player | Team | FT | FTA | FT% | Points lost/Possession |
---|---|---|---|---|---|

Andre Drummond | DET | 208 | 586 | 35.5% | 0.294 |

Clint Capela | HOU | 80 | 211 | 37.9% | 0.266 |

DeAndre Jordan | LAC | 266 | 619 | 43.0% | 0.162 |

Andrew Bogut | GSW | 24 | 50 | 48.0% | 0.123 |

Thomas Robinson | BRK | 47 | 109 | 43.1% | 0.109 |

J. J. Hickson | DEN | 27 | 59 | 45.8% | 0.079 |

Dwight Howard | HOU | 232 | 474 | 48.9% | 0.043 |

Festus Ezeli | GSW | 70 | 132 | 53.0% | 0.024 |

Find the spreadsheet with every player’s scores here.

First on the list to nobody’s surprise, Andre Drummond. Also featuring are the two other players most noted for being hacked, DeAndre Jordan and Dwight Howard. Some surprises on the list, Andrew Bogut and Festus Ezeli. Sure, Bogut only has 50 attempts on the season, but the numbers would suggest that hacking him is an effective strategy, one that is never discussed when discussing how to beat the Warriors. Sure, he only plays 20.7 minutes per game, and the Warriors love their small-ball lineups, but sending Bogut to the line might work for the time where he is out there. Throw in a cold season and only making 24 free throws in the entire season, and he might be a bit shaky at the charity stripe. So just keep that in mind coaches facing the warriors in future.

Those numbers should be taken with the understanding that it’s the team’s average offensive rating. Hacking a player may be more or less effective against certain line-ups.

So, without advocating for an ugly basketball tactic, those are the players who should be intentionally fouled. But what should players aim for to avoid having to play a game of tag against every player on the opposition? Obviously this changes slightly depending on the strength of your team’s offense, but this graph would suggest a pretty boring old 50%.

Find the full graph here.

BONUS QUESTION: How good of a free throw shooter should I be to make both of my shots more than I miss one of them? 71%. What about a 3-point foul? 79.4%. What about 10 in a row? 93.3%. The solution to making n shots in a row ≥50% of the time is 0.5^(1/n). Just a little nugget I discovered a while ago that I needed to share but haven’t found the right time.

So that’s that. For all the NBA coaches out there reading, feel free to use this formula to your advantage when scheming on how to slow down a superior offense. Terry Stotts, I’m talking to you.

- An Article by Jack Neubecker
- Statistics Sourced from Basketball Reference
- If the above numbers file doesn’t run, try this excel document