Is the “Hot Hand” in Sports a Myth?
New analysis shows the ‘hot hand’ is real, and Klay Thompson had it during the finals.
The hot hand is a myth, like betting ‘red’ after a string of ‘black’ results on a roulette wheel, or betting on a coin flip turning up ‘heads’ after a bunch of ‘tails’ in a row.
If you ask, “What are the odds that Steph Curry, LeBron James, or Kevin Durant make their next shot,” you know that if they’re a 50% shooter, the odds are probably 50/50. But what if the idea of going on a streak had some merit? What if you make three or four baskets in a row, previously?
While gambler’s fallacy was taught in statistics class, many statisticians subscribe to hot streaks and believe hot streaks are real and do affect the outcome of probabilities.
Let’s say you’re studying the game, maybe researching best prop bets, looking to know whether there’s a chance of a streak in your favorite player’s future stats. They come out of the locker room for halftime, and you missed the first four minutes of the quarter. You return to the game and you find out that Curry has attempted three shots already. “Did he make a shot,” you ask? “Yes,” your friend tells you, “I remember I saw him make the second shot.” So you immediately start wondering to yourself if Curry made the third shot, and if there’s a streak happening (or about to happen) here.
If he took three shots, there are eight possible outcomes:
- Make, Make, Make. (Active streak: 3)
- Make, Make, miss. (Inactive streak.)
- Make, miss, Make. (Active streak: 1)
- Make, miss, miss. (Inactive streak.)
- miss, Make, Make. (Active streak: 2)
- miss, Make, miss. (Inactive streak.)
- miss, miss, Make. (Active streak: 1)
- miss, miss, miss. (Inactive streak.)
Based on the information your friend gave you, you know that only four possibilities are valid now: an active streak of 3, an active streak of 2, or two chances of an inactive streak. You have four possibilities, and 50% of them give you an active streak with a chance for more, while 50% don’t. You might think, if Curry is a 50% shooter, this is right in line with what you expect.
But what if you biased yourself, just by the way you phrased the question? You’re looking for ‘winning’ streaks, right? And so when you asked “Did he make a shot,” you only began paying attention because the answer was “yes.” But in reality, for one out of every eight times, the answer will be “no, he didn’t make any,” but you didn’t pay attention to those. Instead, you just focused on the 7/8ths of the time where a shot was made. And if, when your friend says, “I remember I saw him make the second shot,” they’re just picking a made shot at random, then what are the odds they would tell you that?
Well, there are four possibilities again, but they’re not the same:
- Make, Make, Make. (Active streak: 3) — 33% chance, as your friend could have remembered the 1st or 3rd make just as easily.
- Make, Make, miss. (Inactive streak) — 50% chance, as your friend could have remembered the 1st make just as easily.
- Miss, Make, Make. (Active streak: 2) — 50% chance, as your friend could have remembered the 3rd make just as easily.
- Miss, Make, miss. (Inactive streak) — 100% chance, as your friend only had one make they could have remembered.
If you weight these probabilities successfully, now, you’ll find that there’s only a 36% chance that Curry is on an active streak, and a 64% chance that the streak is already over.
This is a stunning example of what scientists call “selection bias,” where you’ve restricted the chances of various possible outcomes just in the way you’ve obtained information about your data.
There was a cognitive psychology paper published back in 1985 about the fallacy of the “hot hand” in the NBA, and their statistics showed that the hot hand was a myth. In fact, if you look at the chart above, you’ll notice that there’s a drop-off of more than 50% (in most cases, significantly more than 50%) in each player’s success rate in hitting that next tier of a long hot streak. “Myth confirmed,” you conclude.
Not so fast! 30 years after that study first came out, two economists, Joshua Miller and Adam Sanjurjo, showed that there is a selection bias when you’re looking at streaks in the NBA. When you’re picking out which shots you look at in a problem, and those shots are conditional on the sequence of other shots made before it, you change the game, which effectively suppresses the likelihood of continuing the streak. And while it’s not as bad an effect as the makes-and-misses we laid out above, it needs to be accounted for.
Sports Handicappers Work the Same…
Over the past 10 years, we’ve noticed this trend happen frequently. Handicappers will be red hot, winning 60%+ for 1–3 weeks at a time, followed by poor performance. At Verified Cappers, we make it easy to track sports handicappers from some of the best sites in the industry. If you like going head to head with Vegas, we’re your #1 resource.