NBA Free Throws: Median vs Average

By Josh Margles

In statistics class we are taught the difference between average and median. Both are useful in certain situations however for some reason, lots of people use average when the situation calls for the median. Medians are particularly useful in taking out outliers that would normally skew the data but in sports there is no stat that uses the median instead of average.

One place where medians could be used instead of averages is with team free throw percentage, particularly in end of game situations. The team\’s median free throw represents the probability of a free throw going in if a random player gets fouled. Average free throw rate gets weighted down or lifted up by players that shoot more often. In situations where the team knows the opponent will foul, they will give the ball to another player that will be a better shooter. The end of games play out much differently than the rest of the game so the normal free throw numbers shouldn’t apply because it is different players taking the shots. As the season goes on, the free throw percentage gets more skewed as the distribution of shots gets spread thinner between the players.

In the chart below are all the teams in 2018-2019 free throw stats; one column being the overall percentage and the other being the median free throw percentage (min 50 FTA). As you can see the Bucks, Sixers and Pistons are the teams with the biggest difference in rates. This is because they each have a player that is weighing them down and takes a lot of shots but with a poor rate. For the Sixers and Pistons, Andre Drummond and Ben Simmons shot 59% and 60% respectively from the line last year while taking over 400 attempts each from the line. Even though Giannis shot a respectable 72.9% last season, since he shot close to 10 free throws a game, he brought the teams rate down by a lot.

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Drummond brings down Detroit\’s rate so much that they go from the 8th worst shooting free throw team in the league to 8th best. Aside from Drummond, every other player on Detroit’s roster last season with more than 50 free throw attempts shot better than 75%. Philly’s situation is even more extreme. The rest of the starting lineup last season Embiid (80.4%), Butler (86.8%), Redick (89.4%), Harris (84.1%) were all over 80% from the line. In the Bucks case, the next 6 highest volume free throw shooters last season shot a combined 84% from the line in 2018-19.

It is clear that the Pistons and 76ers free throw distributions shift at the end of games. Drummond in the regular season shot 21.7% of the Pistons free throw attempts, but when they were up by 5 or less in the last 2 minutes only shot 12.5% of the team\’s attempts. For Simmons it is a similar case where his share dropped from 19% to 11.6%.

Shown below is the 2019-2020 stats (min 50 attempts) as of Mar 7. Three teams stand out from the crowd. The Clippers are shooting a very solid 79.1% from the line but have an absurd 87.1% median free throw rate. This is largely due to Montrezl Harrell shooting 5.5 attempts per game but only at 66%. The other high volume shooters, Lou Williams, Kawhi Leonard and Paul George all shoot above 86.3% which brings the median up.

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The other two teams, the Bucks and the Heat also have a large gap between actual and median. It\’s a similar story to the Clippers as Bam Adebayo and Giannis both bring the free throw rate down significantly. The Bucks have the same reasoning as above and in the Heat’s case, Bam is the only shooter under 75% that have above 50 attempts.

Boxplots are a great tool to show the distribution of the free throw attempts of a team. Below are the 2019-20 Clippers, Bucks and Heat boxplots. The bottom blue dots are Harrell, Bam and Giannis. Bam and Harrell take so many shots that the whole lower quartile is taken up by their shots showing how many attempts they take but at a poor rate. Giannis is even more extreme as he is considered an outlier. He shoots a lot of free throws but so much worse than the rest of his teammates.

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The next three are the 2018-19 boxplots. The Bucks are less extreme as Eric Bledsoe shot 75% which is similar to Giannis but for Drummond and Simmons the difference is staggering. The rest of both teams are above 75% while they both are around the 60% mark.

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So what does this mean for basketball analysis? Overall free throw percentage is still a good measure for total games but in certain situations, namely end of game, that is not the best stat. Next time a team is up late in the game and an analyst talks about the teams free throw percentage, keep in mind the median free throw percentage as it could be more indicative of who is shooting the shots down the stretch. Even though players like Simmons, Drummond and Harell take a lot of free throws during the game, in the final minutes it most likely won\’t be them who makes or breaks the game from the line.

All data is from NBA.com

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