Introducing Free Throw Splits

If only golf allowed for a second swing if the first one led the golf ball to the nearest hazard. An expensive experiment for another time, it seems like the scorecard would improve quite a bit if do-overs were allowed. The closest thing basketball games come to those are the second and third free throws after a foul. A post at TrueHoop back in 2011 noted that a player’s free throw percentage improved from their first free throw to their second by about four percent. The difference when for fouls on attempted three-pointers was larger, about seven percent from the first to second free throw, about two percent from the second to third free throw, and some quick math means there’s a nine percent improvement from the first to third free throw.

This matches what I looked at since the 1999-00 season, looking at free throw percentage by specific free throws like 1 of 1, 1 of 2, and 2 of 2, but also fouled three-point shots and technical free throws. Over the last 17 seasons, players averaged an improvement of about four to five percent better on the second free throw compared to the first.[1. I included flagrant and clear path free throws into regular. The sample was very small anyway, 276 free throws as of February 21.] The improvement from the first of three throws to the third, with a significantly smaller sample after weeding out players who don’t have the three-point shot in their arsenal, varies slightly more, typically between six and nine percent.

Below is a Tableau project looking at every player from this season, though a filter was set at 50 free throw attempts. This, of course, can be changed as well as the seasons to look at, going back to 1999-00:[1. And-1 totals on NBA.com from the mid-2000s differ a decent amount from Basketball-Reference. I’m not sure why. There are a handful of the 1,230 games missing from each of those seasons, but that doesn’t explain it. The free throw totals match up for each player except for those involved in the five missing games or so from each of those seasons.]

There were a few things to mess around with these stats. To start, we could go back to a few seasons ago to another TrueHoop post noting discussion of players fouled in the act of shooting or in the penalty attempting only a single free throw. If there was a foul on a two-point shot or the defense was in the penalty, the shot would be worth two points and fouls on three-point attempts would lead to one free throw worth three points. The idea was to help speed up the game, but how much would it hurt scoring since players typically shoot worse on the first free throw? Now, we can see how much of an impact would be made if this change happened in the D-League and worked its way up to the NBA league, or started back in the 1999-00 season. I took the increase in free throw percentage from the first free to the second free throw and multiplied it by the total second free throw attempts. A similar thing was done for fouled threes but averaged the increase on the second and third free throws. Lastly, basket interferences and lane violations were factored in.

Game to game, we should expect some variance, but it doesn’t look like there would be a major change overall:

Of course, not every player improves just slightly with an extra free throw, and some players shoot worse.[1.Checking if there was a correlation between overall free throw percentage and improvement from the first free throw to the second was difficult since the larger the amount of free throws required, the smaller the player pool and the same players showing up from year to year.]Below are the top and bottom 10 from this season as of February 21, minimum 50 pairs of free throws, and who would benefit or be harmed by such a change. For now, the splits could be helpful when deciding to crash the boards on a free throw attempt:

These might be random lists or maybe some observers have picked up on a few of these players being significantly better or worse on second free throws, but there are some who have been better or worse over several years. Using a smaller filter of 20 pairs of free throws to catch more players in more seasons, it isn’t just sharp shooters who improve. I took six players who had several seasons of above-average improvement on the second free throw: Boris Diaw, Ersan Ilyasova, Roy Hibbert, Rudy Gay, Tim Duncan, and Tony Parker. Finding players who consistently shot worse on the second of two free throws was more of a challenge but Tristan Thompson fit the bill, shooting five percent or worse each season after switching from shooting with his left hand to his right.

In Thompson’s case, this could definitely be used to crash the boards on free throws instead of walking towards the other hoop once the shot goes up, but Seth Partnow found last season that the Cavaliers rebounded none of Tristan Thompson’s missed shots.

There were some more ways to fool around with this data. When it comes to technical free throws and the option to choose who on the floor takes the shots, free throw percentage in this situation is anywhere from five to 10 percent higher than the percentage on and-1 free throws and the first of two free throws. Sometimes this can be a way to boost a primary scorer’s numbers, but the players who have accumulated the most points off technical fouls have been, for the most part, solid shooters.

We can also find out who has been the most reliable to make technical free throws or who could give someone else a chance at an easy point or two. It’s probably no surprise when looking at this season and career numbers, the latter with a minimum 100 technical free attempts since 1999-00, that LeBron James has recorded the worst technical free throw percentage:

When taking out technical free throws, LeBron’s career scoring average drops from 27.22 to, well, 27.05. Not a huge difference whether or not he takes these freebies, but as he climbs the points leaderboard they could come back to be of some help.

You can find the full Tableau project here at the ‘Our Stats’ section<.

All stats according to play-by-play data from NBA.com.