Math Madness #2: The “Jinx” & The “Choke”

During their 2009 game against Villanova, Duke guard John Scheyer was getting ready to take his fifth foul shot of the game. He’d made all four previous attempts. Announcer Verne Lundquist made reference to Scheyer’s high career free throw success rate (86%). Scheyer missed the shot, causing Lundquist to publicly flagellate himself for jinxing Scheyer.

Scheyer was one of the best foul shooters to ever play for Duke (3rd best). An 86% success rate is so high that we expect Scheyer to make any given free throw. Yet, at the moment of Lundquist’s apology, Scheyer was 4 for 5 (80%) from the line. Even over that small sample set, his short term 80% success rate was effectively identical to his career rate of 86%.

Verne didn’t jinx Scheyer. He just made a statement that, by chance, happened to coincide with a normal, probabilistic event. Superstitions get started that way.

But what about that choke? That’s not black magic. Its the end of the game. The pressure is on. You know the situation. Final seconds of the game. Your team is down by two. Your star drives the lane. Attacks the rim. And, is fouled, hard, making sure the shot cannot drop. He goes to the line with a chance to tie the game. He makes the first. Misses the second. Did he choke?

Over the last 40+ years, the average NCAA free throw percentage has hovered around 69%2. In the 2011-2012 season, it was 68.9%. An average free throw shooter will only make both free throws 48% of the time and will miss both shots almost 10% of the time.  Even a world class free throw shooter like Scheyer will hit both free throws 74% of the time. So, when your team loses after your favorite player makes 1 of 2 foul shots, don’t call it a choke.  Call it the odds.

But, what if you are on the other side of the scenario painted above? What if you are clinging to the two point lead and an opposition player is headed to the basket? Do you foul?

Fouling (assuming you foul hard enough to make sure the shot fails, but not hard enough to get a flagrant foul) is a good idea if the probability of the offensive player making both foul shots is less than their success rate. Contested short range shots, like dunks and layups, are incredibly efficient ways to score, but are not guaranteed. My estimate, from the limited statistics available, is that these shots are made about 60% of the time. At this rate, you should probably foul any player that has a free throw shooting percentage below 77.5%. Unless the offensive player is an exceptionally good free throw shooter, like John Scheyer, a good hard foul is a better bet than a contested layup. But, its not as fun to watch.

I wrote the original version of this back in 2009. For this year, I’m breaking it into more digestible chunks, with a lot of rewriting and up to date statistics, when possible. 


Author: Josh Witten

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