LeBron’s Free Throw Unlikeliness

By Kurt Bullard

On Sunday afternoon, LeBron James stepped up to the free-throw line down one point to the Houston Rockets with four seconds left in overtime. His first attempt clanked off the rim. The second did the same, as James Harden was able to secure the rebound and the game for the Rockets.

Those weren’t LeBron’s only two misses from the line that night. James struggled mightily on the night, shooting just 3-for-11 from the charity stripe, which ended up being crucial misses given the close nature of the game.

LeBron’s performance from the line on the night was strikingly poor. LeBron – while not automatic from the line by any stretch of the imagination – holds his own on the line. The two-time NBA champion has hit 72.8% of his free throws this year, which ranks 102th in the association.

If we assume that the probability that any NBA player hits his free-throw is the same for every attempt – namely, that “pressure” and fatigue don’t affect free-throw percentage – one can use a simple binomial probability function to model the average missing eight out of eleven shots would only be predicted to happen randomly about .2% of the time.  In terms of basketball games, this occurrence would only be predicted to happen once every six NBA seasons playing 82 games a year.

To put this idea into broader context, there are other stat lines for LeBron that would be expected to happen .2% of the time based on his current season statistics. If LeBron – a 34% three-point shooter – were to take 20 threes in a game, he would be expected to hit one or none about .2% of the time. And, if LeBron were to take 11 two-pointers in a game, he would be expected to hit one or less two-point field goals.

The worst free throw shooter in the league – the Clippers’ DeAndre Jordan –would only be predicted to hit three of his eleven free throws 27.5% of the time. Meanwhile, Steph Curry – the league’s second leading free-throw shooter with a 90.7% clip – would be expected to do this poorly less than .00001% of the time. This equates to once every 17,160 season of basketball. Below is a graph of the probability a free-throw shooter hits three or less free-throws out of eleven.


Sometimes, you have off days, but you hope they don’t come when it matters. Unfortunately for LeBron, that was not the case.

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  • Kurt, Wilt’s night in 1962 was astonishing.
    I’ve wondered ever since how he sank 28/32
    FTs when he was such a poor FT shooter for
    his career (51%). Even a remarkable 27/32
    would have left him short of 100 points. Do
    you have any calculations about that?

    Could there be a video of that game
    somewhere that showed his style of
    of FT shooting? He shot underhanded
    FTs for a portion of his career.

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