The Tao of Gaming

Boardgames and lesser pursuits

The Hot Hand

Kevin Drum has a discussion of the hot hand effect (“players who have recently made a streak of baskets are more likely to make the next basket”), which has been thoroughly debunked. I recommend reading Gilovich’s “How we know what isn’t so” for more background. I read the book a decade (or two, sigh) ago and I’m convinced that the stastics are solid. Kevin, meanwhile, is arguing with Paul Waldman, who agrees with the bball boys over the scientists:

After spending a few hundred hours in pick-up games, I’d say that real hot and cold streaks happened around one out of every eight or 10 games I played. Some games were better and some worse, but every once in a while, I’d have a game where I just couldn’t find the basket, and every once in a while, I’d have a game when I couldn’t miss.

Drum doesn’t buy it. (And I suspect that most of those hot and cold games aren’t nearly as hot/cold as Paul remembers them … a big factor). But then Drum backs off :

But why did I say “most streakiness” can be explained this way? Why not “all streakiness”? Because there’s always Joe DiMaggio.

Look, there’s a lot going on here. But just because I believe statistics doesn’t mean I’m a cold unfeeling monster. You can have a bad day. Suppose that I’m an 80% free throw shooter (ha!). If I have a cold, or a bad day and my mind isn’t in the game because I’ve had a tough day at the office, then I may be a 70% free throw shooter on that day. But it would be tough to just look at my stats for that game and tell. I’m likely to only go to the line a few times. If I play “hundreds of hours” of games (which, to a pro, is a few seasons of games but less than a season if you include practice games, drills, etc) then you have good and bad days and they average out … in the long run. Sometimes when you miss you double your effort, concentrate and make the next shot because you’ve improved your technique. Sometimes when you miss you double your effort, concentrate and miss the next shot anyway, despite improving your technique. Improving your technique made your chances of hitting the shot go back up, but hey. Sometimes when you miss, you just clock out and go through the motions until you hit the showers.

The fact that there’s no statistical proof of “the hot hand” doesn’t mean people don’t have good and bad days. It just means that these aren’t visible on a big scale. Nobody can really prove or disprove them on a minor scale (I guess scientists could get players to record how they felt on a given day prior to a game, then compare the results). Does hitting three in a row prove you are having a good day? Not really. That’s probably just mostly lucky, whether you are having a good (80%) day or a bad (70%) day. Presumably if you were having a terrible (20%) day coach is going to pull you.

Let’s look at DiMaggio. Joltin Joe had a career average of .325 (Yes, yes, I should use OBP. But the point is basically the same, and since we’re talking about the streak, Batting Average is reasonably correct). It moved around a bit, year to year, mainly due to random chance. But his 1951 average was .263. Was that random chance? Of course not. DiMaggio was 37 … at that age we don’t call it a cold streak. His career was ending.

But in ’41, could DiMaggio have been on a hot streak? Sure. He batted .357 for the year. But the numbers don’t tell the whole story. Maybe he was thinking “If I can just set a huge record, I’ll get to sleep with the world’s foremost supermodel next decade.” (I’m not sure if access to supermodels will improve my work performance, but I’m willing to suffer the experiments).

Consider DiMaggio could be in the middle of the streak  — Some pitchers will go right at him, trying to end it and prove their worth. In that case, he’s got his typical chances of getting a hit. However, the pitcher might start overthinking it, get inside their own head, and then lob a juicy target. (I prove it thus — Bull Durham). So, not only may be DiMaggio may legitimately have raised his expected average to .400 during the streak (which helps greatly), but he’ll now get a gift or two from pitchers who overthink. And that’s not even considering some pitcher who knows DiMaggio has his number and is just trying to avoid a homer then put the next few guys out.

Turning back to Basketball — if you are in the finals against a good, MVP caliber player and he just starts unleashing bombs, ferocious dunks and even his slips and should-be-airballs hit nothing but net, at some point you may just say “He’s too hot” or “Game Over, Man” and switch your goal from winning to “conserving energy for the next game” and “Not being the guy that Michael Jordan is dunking on in his next poster.” (You know, the guy with the Nike smashed into his nose). Even if you fight past that response, it probably lingers in the back of your mind, lowering your effectiveness slightly … which ups MJs effectiveness (slightly). [I’m reminded of the … uh, ‘91 US Open, where Jimmy Connors decided to just give up in the 3rd(?) set to play hard for the remainder of the match, then seemed to feed off the crowd’s energy and pulled it out. Amazing Television.]

Drum writes:

I believe the hot hands study is correct. Really. And yet….even I have to admit that it’s hard to accept that players don’t have good and bad games quite aside from their statistical chance of randomly doing well once in a while. It’s just….hard.

Good news, Kevin! You don’t have to. Players do have good and bad games. In the long run, these average out. In the very short run, no.  But in the middle? DiMaggio was, by the stats, a .408 batter during the streak and he undoubtedly got very lucky. But he was presumably healthy the whole time (instead of suffering from aches and pains … like during his ‘51 season). So that helps. Maybe he was performing as a .450 batter during the core of the streak (a mere two months), due to being free of minor injuries. The Binomial distribution tells you that the streak is fantastically rare, but it assumes that each at bat is independent of the ones around it. And if a pitcher tells you that facing DiMaggio during the streak (or Jordan during the finals) is just another routine at-bat (or defensive setup) then you can wake up, snap your fingers, and say “Hey, maybe these aren’t really independent.” Look at the mental stress Roger Maris went through.

In our (mental) games  it’s easy to be “cold”. You just give up and check out (or chat up the hot red head, a valid strategy). And it’s easy to be on a hot streak, where you “see the cards well” and don’t make stupid mistakes, and the red head pouts because you are ignoring her. Maybe the cards aren’t giving you problem hands you normally screwup, maybe you are just concentrating. Maybe you intimidate the opponents, but somedays it works.

Just don’t expect it to show up in the stats.

PS — When playing Kakerlaken on Monday, I felt en fuego. One opponent got a card most people had passed, decided not to challenge, looked at it, and then started thinking about who to pass it to. He glanced at me, and I said “Get that weak-ass shit out of here.” (If you can’t talk trash during a bluffing game, what’s the point of playing?) He passed the card to someone else. At the end of the game, I’ve lost one challenge, most people have lost ~5, and the loser has lost around 10. A good result, but not all skill. All luck? Perhaps. It didn’t feel like it. (Knowing cognitive biases doesn’t mean I don’t feel them).

PS — I’m tempted to write a book on Kakerlaken poker, just to see how many copies I could sell to confused poker players, and to amuse myself.


Written by taogaming

May 6, 2011 at 5:19 pm

Posted in Ramblings

Tagged with ,

4 Responses

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  1. I’ve been told that DiMaggio actually lost ground in the batting title race to Ted Williams over the course of his 56-game hitting streak. I haven’t checked this, but if it’s true, it’s another amazing fact about that season.

    Eric Brosius

    May 6, 2011 at 7:13 pm

  2. I believe in sabremetrics and I believe in statistics. I am also no athelete. But even mere observation will force you to agree with what anyone who’s ever played a game will tell you: that there are times when a player is performing extremely well and times when they are a dog. And it’s not the ramifications of a statistical distribution, but rather something physical or mental in the player. Look at a batter’s swing when he’s hot or when he’s in a slump–very often, the swing is radically different. Look at Tiger Woods when he was winning everything in sight and look at his swing now; this is not a statistical anomaly, but practically a different player.

    Do these hot and cold streaks follow statistical laws? Quite possibly. But there is a difference: in many, if not most cases, the hot player is a *better* player than when he is cold, not merely unlucky. I’d put more money on him to succeed in the former case than in the latter case, which I’d never do if it was just the result of a statistical distribution.

    One of the most maddening recent trends in baseball sabremetrics are analysts who come up with a theory of how a player should perform and then declare that he’s “lucky” if he exceeds the prediction and “unlucky” if he falls short of it. It’s conceivable that they’re correct, but what an astoundingly convenient excuse that is!


    May 6, 2011 at 9:44 pm

    • Yes, it’s like the doctor that tells an expecting mother that the baby is late! This implies that the baby’s job is to show up when the doctor predicted it would come. Shouldn’t the doctor try to predict when the baby will arrive?

      Eric Brosius

      May 7, 2011 at 8:18 am

  3. Did you watch the Mavs-Lakers game 4? Things like that really make it hard to not believe in hot streaks. Jason Terry and Peja were a combined 15 for 16 from 3. Almost all of these were open shots but still! And from two bench players, albeit very good scorers. I certainly was believing those shots were going to go in after a while far beyond their normal percentages.

    Aaron Fuegi

    May 9, 2011 at 8:53 am

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