If you’ve watched any of the NBA Finals so far, you’ve seen San Antonio Spurs guard Danny Green making a 3-pointer. In less than five games, Green has broken then-Celtics now-Heat sharpshooter Ray Allen’s record for most made 3s in a single Finals. As impressive as that volume is, what’s been more absurd is Green’s accuracy. Allen set his record by shooting a red-hot 22-42 (52%) over six games. Green has made three more shots on four less attempts, putting him at 25-38 (66%). Frankly, it’s a miracle he hasn’t burst into NBA Jam style flames.
After sufficiently extolling Green’s performance, I started to wonder how improbable it really was. After all, Green was one of the most accurate long-range shooters in the NBA this season, and 38 shots isn’t a huge sample size. Furthermore, as Grantland’s Kirk Goldsberry informs us, Green is outstanding from the left corner, right wing (47.4% from both of these areas), and top of the key (49.4%). Maybe he’s shooting everything from his favorite spots? I decided to take a look at the data and find out just how unlikely Green’s run has been.
First, I assumed Green’s regular season shooting percentages are accurate estimates of his skill. It’s possible he has incrementally improved as the season progressed, but probably not in a major way. I also assumed that each shot is independent, which most basketball players will vehemently argue against. The existence of the “hot-hand” is still up for debate, but it seems that it’s at best a weaker phenomenon than most believe .
Given these assumptions, I simulated 10 million samples of Green shooting 38 3-point shots from the spots he has taken them from during the Finals. What I found makes what we’ve witnessed even more incredible.
Green made 25 or more shots in only 0.45% of simulations. No, that’s not a decimal-as-percent mistake. If we ran the Finals back every month from now until 2032, this would happen ONCE. That number is small enough that even if we take the cautious route and grant that Green could have underperformed during the regular season and his Finals shots might have been more open (I’m not claiming these to be true, I’m just hypothesizing), there was still no indication that he would shoot like he has. Green has legitimately defied the odds.
I don’t intend for this to read as an argument in favor of the hot hand. Green represents only one data point. Rare events are rare, not impossible. Maybe Green is hot, maybe he’s lucky, or maybe he found a flaw in the design of the universe. At this point, I’d believe anything. Whatever theory you subscribe to, enjoy this while you can. It’ll be a long time before we see another display this great and this unprecedented on this big of a stage.
In case you were wondering, Danny Green majored in communications at North Carolina. And no, statistics was not required.
 Studies have actually suggested that players shoot a little bit worse after a made shot, which is usually ascribed to a confidence increase that makes them more likely to take a bad shot. Even if we believe Green is immune to this effect, it hasn’t been shown that we can expect the “momentum” from his previous makes to carry over to his next shot.
Some will suggest that while shot-to-shot “heat” may not be real, athletes have certain days (or longer periods) where their bodies are simply more aligned or have a smoother rhythm, making them fundamentally better on those days. As an avid basketball player who hits everything some days and tosses bricks on others, I find this argument compelling. That said, it hasn’t been shown that there is any day-to-day carryover that would partially explain streaks like Green’s.
Some links about the hot-hand phenomenon:
Discussion from The Atlantic
The first academic investigation
A more recent study