# Exactly How Unlikely Was Klay Thompson’s Third Quarter?

By William Ezekowitz

Klay Thompson’s third quarter was stuff of video game-esque proportions, the likes of which we have never really seen in real life. The man scored 29 points in 6 minutes. In the whole third quarter he was 13 for 13 from the field (9 for 9 from 3) for a total of 37 points. Exactly how improbable is that? I tried to figure it out.

Using official shot distances from play by play data and my own judgment when watching the highlights for court area and degree of openness, I compiled a database of all of Thompson’s shots in the third quarter, including the free throws. I then turned to NBA.com, which has a profile for Thompson complete with shooting percentage values from varying distances and areas on the court with varying degrees of openness. I combined these two data sets to discover exactly how often Thompson would make all of those exact shots. NBA.com doesn’t have super specific splits – for example, it doesn’t have Klay Thompson’s shooting percentage on pull up 2s from midrange with a defender within 4 feet – but it does have more general splits. I averaged these splits to come up with a reasonable expected shooting percentage for each shot. So, in the example I just mentioned, his estimated shooting percentage on pull up 2 from midrange with a defender within 4 feet became an average of his shooting percentages on pull up 2s, midrange shots, and 2 point shots with a defender within 4 feet

 Shot Type % made Area on court % made Distance Openness % made Average Pull up 2 44.70% midrange 41.20% 12 Feet 4 feet 44.40% 43.43% Pull up 3 48% straight away 3 45.80% 26 feet 6+ feet 41.50% 45.10% Catch and Shoot 46.20% wing 3 45.80% 26 feet 4 feet 54.10% 48.70% Dunk 98% at rim 98.00% 0 Feet 4 feet 98% 98.00% 2 dribbles 42.90% wing 3 45.80% 25 feet 2-4 feet 39% 42.57% Catch and Shoot 46.20% straight away 3 45.80% 28 feet 4 feet 39% 43.67% Catch and Shoot 46.20% wing 3 45.80% 25 feet 2 feet 39% 43.67% Catch and Shoot 46.20% wing 3 45.80% 25 feet 0-2 feet 50% 47.33% Lay Up 78.40% at rim 78.40% 0 feet 0-2 feet 78% 78.40% Catch and Shoot 46.20% wing 3 45.80% 26 feet 2-4 feet 39% 43.67% Pull up 2 44.70% midrange 41.20% 15 feet 0-2 feet 51% 45.73% Catch and Shoot 46.20% left corner 3 41.90% 25 feet 0-2 feet 50% 46.03% Catch and Shoot 46.20% straight away 3 45.80% 25 feet 4 feet 51.40% 47.80% Free Throw 87% Free Throw 87% 0.0094%

The above table shows my results, which states that he would make all of these shots 0.0094% of the time. It is important to note that the NBA.com data that is available to the public only differentiated between 3s from each corner and all other 3s. Ideally we would have a value for left wing and right wing, but those would differ negligibly from the value we used anyway. Also, due to small sample size, I had to estimate that Thompson makes 98% of his open dunks. This number may be a bit lower, but, again, that won’t change the overall data much.

Importantly, though, there is also an issue of sample size with Thompson’s 3s taken with a defender 0-2 feet away from him. He’s taken so few this year that he’s made 50% of them, which is surely not indicative of his long term performance on such shots. As a side note, this indicates how crazy Thompson’s night was: he took and made shots that are so unadvisable that he’s hardly ever taken them this season (1.2% of his 3’s, to be exact). But if we assume that he makes these shots at the same clip that he makes 3s with a defender 2-4 feet away, 39%, then the overall probability of his 3rd quarter drops to 0.008%. If you drop the percentage to 31, which is arbitrary but seems closer to the truth, the value drops down to 0.007%.

0.007% might not even capture the full value of the unlikelihood of such a stretch, though, because it doesn’t take into account the incredibly high usage rate Thompson had. Taking 13 shots in a quarter is an incredible feat in and of itself. This run could very easily have been less impressive simply by virtue of Thompson not throwing enough shots up.

To conclude, it is important to note the purpose of this post. We are assuming that Thompson is just as likely to make every shot as he has been all season. The Hot Hand debate is one for another time, even though a new study (done by a former HSAC president, no less) indicates that it does exist. Our value shows the likelihood in terms of regular Klay Thompson, independent of the relative hotness of his hand, or lack thereof.

Furthermore, as Scott Van Pelt tells us on Twitter, analytics don’t have a place in this discussion of Thompson’s incredible feat. He’s just in The Zone, and that’s that. But we would argue that we are not trying to “explain away” The Zone that Thompson was in, rather we are just quantifying how extremely unlikely it is to be in that kind of a Zone. To say it was extremely unlikely is not to say that Thompson just happened to get lucky. Contrary to what some statisticians may say, there is room for The Zone and math in the same discussion. Klay Thompson’s night was incredible. We know this by watching the tape. We also know this by figuring out that if he tried that again, he’d do it about 0.007% of the time.

#### harvardsports

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• Jammer says:

I estimate there have been 550,000 quarters of nba basketball played. If your odds are correct an average Klay would have repeated that quarter about 4000 times. I think that performance was much closer to the proverbial one in a million

• Brian Duddy says:

How many of those quarters have had a player try 9 3’s and 4 2’s?

• Michael says:

4000/550000 = .0072 which is .7%. If the true percentage is .007% that is the decimal number .00007, so (550000)*(.00007) = 38.5 times. I think we need to reexamine some of the average percentages from the spots on the floor that Thompson shot. I don’t know how to do that, given the information available.

• anonymous says:

Consider that Thompson is a far better shooter than anyone else in the NBA, and is one of the best ever. So if you assume that everyone in the NBA has been like him for all of history, then yes, it should have happened more often. But that’s an inappropriate assumption. Furthermore, another thing driving the likelihood down that’s not in that .007 number is that a player is incredibly unlikely to take 13 shots in a quarter in the first place. But the article isn’t concerned with that; it’s just trying to say given that he’s Klay Thompson and given that he shot those 13 shots, how likely is it that this would happen.