Is There a "Hot Hand" in Chess?
Thursday, March 29, 2018 at 11:34PM The notion of a "hot hand" in sports is regularly debated by fans. The idea, simply put, is that a player who has just succeeded (or just succeeded a certain number of times) is likelier than usual to succeed in his next attempt. To take the usual example, a basketball player who shoots 50% but has made his last two or three shots can now be expected to make his next shot more than 50% of the time.
Many, probably most, take it as obvious that there is such a thing as the "hot hand", and not only casual fans but professional commentators and the players themselves seem to believe it. Statisticians, by contrast, have generally pooh-poohed the idea. In any random series of independent events there will be streaks, even surprisingly long ones. Because those streaks are so impressive to behold, we find it natural to accept the idea of a "hot hand". Here's an example of a positively incandescent, supremely combustible hand:
That's a mic drop for the pro-hot hand side, but again, statisticians have generally rejected the notion as not standing up to careful scrutiny. There was some recent statistical research suggesting that there might be something to the "hot hand" idea after all, but it wasn't conclusive.
Let's turn to our favorite sport (assuming one's doing it right): is there a "hot hand" in chess? I turn the floor over to our favorite mathematics/computer science guy, IM Ken Regan. Have a look.
Ken Regan
Reader Comments (4)
The "gambler's fallacy" is the mistaken belief that prior events impact future outcomes in situations based solely on random chance, or luck - for example, dice rolls or spins of a roulette wheel. These are indeed a "random series of independent events." In a game of skill, where playing form is all-important, a recent improvement of skill based on practice and training, and the confidence gained thereby, is not random at all. Success feeds on success. Streaks and slumps abound in sporting events.
[DM: Human beings are not coins or dice, but nevertheless it doesn't follow that, or from the existence of streaks and slumps, there are "hot" or "cold" hands. If someone is, say, a 50% shooter in basketball, the "hot hand" hypothesis (let's call it HHH for short) would suggest that over the long haul, if the player has just made a shot, his average on the next shot will be greater than 50%. (Or maybe that only counts after having made two shots, or three shots.) Lots of studies disconfirmed this claim, though as I noted in the post, there was a recent outlier. And Ken's tentative conclusion was that there's no HH in chess.
By the way, while humans are not coins, the analogy is a valuable one because the cases are structurally similar. We all know that the odds of a fair coin coming up heads are 50%; nevertheless, in a string of coin flips there are going to be streaks. Let's say you flip a coin 40 times; what are the odds of getting (at least) seven heads in a row at some point? The answer is slightly greater than 13% - pretty substantial. We can imagine Marv Albert calling our game and shouting that the coin is "on fire!" But it's not; it's random. Streaks happen.
I would add that human shooting is random, within certain limits. When Stephen Curry fires up a three, the ball's not going to go behind him, or over the backboard and into the stands. It's going to be either in the basket or extremely close. But he doesn't always make it, even when it's an open shot - no one does. We're not machines, so there will always be a tiny bit of variance, and all the practice in the world isn't going to eliminate that. (And even machines will experience variance, but on a smaller scale.)]
Clearly there are complex factors and interactions when talking about human performance. For example, in baseball the home team wins about 52% of the time while in basketball the home team wins about 67% of the time (or at least that was true some years ago - no idea if it is still true). So clearly there is something psychological and/or physical going on that enables one to perform better in a familiar and friendly place, as opposed to an unfamiliar and hostile one. Presumably it wouldn't matter (or would affect both sides equally) in a neutral venue where visitor and home have no meaning.
I suspect chess is probably close to a neutral venue since it's hard to see what the equivalent of "home" or "away" games might be. During competition there are no roaring fans and chessboards are pretty much the same - and it's hard to see what advantage there might be. Maybe if one is playing in one's home town, one is more comfortable away from the board, sleeps better in one's own bed, etc., perhaps? Also, chess is an individual sport which probably simplifies the number of relevant factors relative to a team sport.
So if there is such a thing as a hot hand, it seems more likely to manifest itself in something like basketball than in baseball and even less likely in chess - whatever factors might be involved. Seems like IM Regan's work comes to about the same conclusion.
[DM: I think we have to distinguish between psychological factors and the "hot hand". If there is a hot hand, it might be due to psychological factors. But that's stage two, where we try to explain why the hot hand is hot. The preliminary question is whether there is a hot hand in the first place, as opposed to an illusion because streaks like Klay Thompson's or Bobby Fischer's stick in our memory and are "immortalized" in the annals of their respective sports.
I'm also hesitant to call home-field advantage a (primarily) psychological factor. It may be mostly physiological: a player gets much better rest and sleeps at home, not in a hotel room; additionally, if the home game wasn't the first in a series, the home-player didn't have to travel. The pace of baseball, along with the fact that they're generally playing three-game series each time, diminishes the negative effects of travel fatigue. Basketball is a constant action sport, so it's not surprising that playing at home would offer a greater advantage there than in baseball.]
Dennis,
It's funny that you bring up basketball since I just watched some Larry Bird highlight films on You Tube last week. I remember from my days as a kid playing driveway b-ball that shooting is all about touch. I knew from the instant the ball left my hands whether it was definitely going in, might go in, or just be an airball. I knew if it might bounce off the rim, just missing going in, or clang off the rim like a total brick. It takes a lot of practice to develop that touch, and it's hard to sustain because you have to keep practicing to maintain that level. A few days and weeks of not playing means it goes away.
Hitting a baseball was the same way for me. It knew before the bat came around mid swing whether I would make contact with the pitch or not. In Major League ball, I would imagine that the biggest factor is the effectiveness of the particular opposing pitcher. The pitcher has the advantage against the hitter and that advantage is greatest early in the game when the hitter hasn't seen a pitch yet.
Maybe hot hand should be defined as something like being able to sustain percentages in your favor against normal odds for that person in a particular situation over a certain period of time.
I’m sure Dennis has had an event where he has won several in a row to start and even beat or drew a couple titled players or so, that may have come to an end running into a couple tough GMs to finish the event, he still had a hot hand.
I’d also mention the female player that was wrongfully accused of cheating a while back, she had a hot hand, and then of course all that mess started and she went cold.
Then of course there are situations where for whatever reason a higher rated player routinely struggles against someone clearly under him. Lower player has a hot hand there.