[RADIOLAB INTRO]

ROBERT KRULWICH: Hi, I'm Robert Krulwich. This is Radiolab, the podcast. Jad is not here with me right now for a really, really nice reason. He—he just had a baby, he and his wife, so he's sort of blissed out at his house. And so that just leaves me here. But that's just the beginning of my woes. Not only am I alone, but I have to deal with all of you. And I mean, you, you listeners who keep writing in little niggly things that you think we kind of got wrong here and there. Like the last show we did, the statistics show? And well, it just happened that we had all our microphones on and everybody was poised, and then all of a sudden, yeah, this happens.

[phone ringing]

JAD ABUMRAD: Hello?

STEVE STROGATZ: Hey, Jad. This is Steve Strogatz calling.

JAD: Oh hey, Steve. How's it going?

STEVE STROGATZ: Well, you know what? I was just listening, and I have to tell you this isn't quite right, what you're saying about streaks.

JAD: Wait, what do you mean?

ROBERT: I should back in here and explain to you what's going on. We said in our show that if you love sports and you watch an athlete or a team have a brilliant, miraculous, off-the-charts streak of some kind, we mentioned the '82-'83 Philadelphia 76ers, who had an extraordinary time and a great season.

[ARCHIVE CLIP: Dr. J coming underneath. Putting it up and in!]

JONAH LEHRER: So during the playoffs, the 76ers were all incredibly hot.

ROBERT: Jonah Lehrer walked in and told us, if you heard the show, that they really aren't as miraculous as they seem. And in fact, what they did was statistically predictable and not miraculous at all.

JAD: That can't be right.

JONAH LEHRER: Some of these percentages are pretty damning.

ROBERT: Statistics professors counted every single shot—not just the exciting ones, but every shot the athlete took on that exciting night, and found that not just some but all great athletes in the end pretty much perform more or less inside their lifetime averages. So if you hit the basket 60 percent of the time or 50 percent of the time, yeah, you may have an exciting moment, but when you count it all through, you did what you normally do. So I leaned over to Jad, who was looking a little bit crestfallen, and I said to him, "The fact is, Jad, you are—Kobe Bryant even, is more like a coin than any of us had dared to imagine."

JAD: No! Shh! Shh! Stop it!

ROBERT: Kobe has a pattern. In his case, it's what, 60-40? On any given night with Kobe, you think, "Oh, this is—he's spectacular!" But all he's doing is he's just having another night of his very 60-40 life. And that's just the way it plays out.

JAD: Even on a shot-by-shot basis, you're saying.

JONAH LEHRER: Yeah, each shot seems to be kind of a random event.

ROBERT: Exactly. By the way, are you willing to concede that statistically this is a ...

JAD: Not yet!

JONAH LEHRER: It's so counterintuitive. I still, as a basketball fan, I was just watching a game the other night saying, "Pass it to Kobe, [bleep], because he's clearly hot." The only exception to this whole, whole literature of streakiness is—is ...

SOREN WHEELER: Hockey.

JONAH LEHRER: No.

ROBERT: [laughs]

JAD: The sport no one cares about.

JONAH LEHRER: Is it Joe DiMaggio's hitting streak where he hits for 42 games in a row? I've got it in the book somewhere.

JAD: Actually, Joe DiMaggio's hitting streak was 56 games. 56.

JONAH LEHRER: Yes, so Joe DiMaggio is just about the only outlier you can find in professional sports.

SOREN: He's the only real hero.

JONAH LEHRER: Yep.

JAD: Well, at least I got Joe DiMaggio.

[ARCHIVE CLIP, Simon & Garfunkel: Where have you gone, Joe DiMaggio? A nation turns its lonely eyes to you. Hey hey hey]

ROBERT: So that's where we left it. Joe DiMaggio proves that really, at the end of the day, we are not coins, that some people can be truly great, like something from The Iliad or The Odyssey, you know, and do something 56 times in a row and that could just not happen. That's what we told you. That's what we told you. But that's not what Steve Strogatz thinks happened.

STEVE STROGATZ: Well, as a mathematician, I like to run the numbers on these kinds of things, and I once checked with a student of mine, Sam Arbusman, whether it really was that unlikely for someone in the history of baseball to have a streak as long as Joe DiMaggio's. And it turns out it's not really that improbable.

JAD: What do you mean it's not that—you ran the—explain—explain what you mean.

STEVE STROGATZ: [laughs] Well, we did simulations of the entire history of baseball in the computer 10,000 times.

ROBERT: And here's what Steve did: He took every player in baseball history, including the ones who did very, very well, like your Babe Ruths and your Ty Cobbs and the ones who did, you know, very poorly.

STEVE STROGATZ: With each player hitting according to their batting average in a given season. And then you keep doing it 10,000 times and compile all the statistics. And then if you look at what's the longest streak in the history of baseball in one of those simulations, well, one out of every six times, you'll see a streak as long as Joe DiMaggio's streak or longer.

JAD: Really?

ROBERT: So that means out of 10,000 totally imaginary baseball histories, in 1,666.6666 cases, somebody produces a 56-game hitting streak or longer.

STEVE STROGATZ: People used to think it was like a million-to-one shot or something like that. It's not that.

JAD: Oh, man! So you're telling me that Joe DiMaggio, too, is like some version of a coin. He's like a six-sided die, basically. And if you roll a one or a two or a three or whatever, that's the same chance as this streak happening?

STEVE STROGATZ: Yeah, that's right. The numbers are about the same as dice. If you win when you get a six—you know, you're not gonna get a six every time, but once in a while you will get a six. That's about as often as you would see a streak as long as Joe DiMaggio's.

JAD: So you're telling me that even the one, the last guy standing, the last guy, the last hero, you're trying to take that from me now?

STEVE STROGATZ: [laughs] Well I mean, you could take solace in this that I mean, it shouldn't by all rights have been Joe DiMaggio, but it was.

JAD: Huh. I'm not sure how to make sense of that. He is statistically predictable, yet—yet high performing nonetheless?

STEVE STROGATZ: Yeah. We know he was a tremendous player. He had a very high batting average. Obviously he was fantastic. But he's not usually the one who has the streak. It's not usually Joe DiMaggio. It's someone like Ty Cobb or Napoleon Lajoie or someone like that. I mean, DiMaggio is great, and there are a lot of great players in the history of baseball, but it's kind of surprising that he's the one who holds the record. Statistically, it shouldn't have been him. Also his era, you know, he hit that—that streak was 1941. In our simulations, that was one of the most improbable times for the streak to have been set.

JAD: Huh!

STEVE STROGATZ: So in a way you could say DiMaggio really truly was remarkable because by all odds, it shouldn't have been him and it shouldn't have been when he actually did it. So the fact that it was him and that he did it in 1941, you know, maybe there's something really special about the guy.

JAD: [laughs] Well, my consolation, my little piece of real estate here is shrinking, but I'll take it. Okay, I'll take that consolation. Well, let me ask you this: What has been—I can't imagine that baseball fans have been very pleased with your findings.

STEVE STROGATZ: That's right. Yes, we got slapped around quite a bit when our findings were first produced.

JAD: Was it just by mathematicians or did you get baseball fanatics?

STEVE STROGATZ: Oh, absolutely, it's baseball fanatics. The mathematicians are totally gullible, like myself, because, for one thing, a lot of us don't know much about sports. You know, these are the kids that didn't really play baseball. [laughs]

JAD: [laughs]

STEVE STROGATZ: So you're talking to a crowd of wieners to some extent. There were a few other things that have come out since then. You know, when you have to do these simulations, like, you think in terms of flipping a coin or doing what a statistician thinks of as independent events, that is, one game doesn't affect the results of the next game, that's also known to not be correct. And that was recently shown by a young baseball expert named Trent McCotter, who did a careful statistical check on is one game independent of the other games before it, and found that no, they're really not. And this is something all baseball fans will believe that what's happening in a streak is that players are doing something to keep the streak going. They're changing their style, they're changing, you know, which pitches they'll swing at, which ones they will let go. And they're trying to keep the streak alive in some way such that, in fact, they end up having longer streaks than they would have otherwise than their—than their performance would have suggested statistically.

JAD: And you're saying that that is, in fact, true?

STEVE STROGATZ: That is real.

JAD: That's real.

STEVE STROGATZ: That's real, and that was only documented in the past few months by Trent McCotter. And so our assumption in our computer experiment that they were coins? Wrong.

JAD: Yay!

STEVE STROGATZ: Okay, that's good for you, right?

JAD: That's good, because if you're saying that the psychology of the hitter is—can sway the length of the streak, well then yeah, the whole coin analogy is not quite right anymore.

STEVE STROGATZ: It's not quite right. That's the truth. And now can I start crying a little bit?

JAD: [laughs]

STEVE STROGATZ: I mean, you were the crybaby before. Now it has to be me because this makes my life really bad. Now I don't know how to do the calculation.

JAD: Really? That's so interesting!

STEVE STROGATZ: Yeah, so it's become a much harder problem now. If the games are not independent one to the next, all our statistical thinking becomes much, much more difficult. And the real truth as of this phone call is that we don't know what the odds are of Joe DiMaggio's streak. And no one does. It hasn't been figured out yet.

JAD: Now if we were to take the realization you just put forward that psychology matters, does it matter in hot hands as a whole, in the same way it matters in Joe DiMaggio's specific case?

STEVE STROGATZ: It's not something I could really say in terms of evidence. My guess is it probably does matter, although if there is a psychological effect, it's been very hard to find it. But in the case of baseball with hitting streaks, it's really been clearly documented now. In other words, the players are aware of who they're playing on a given day, and if they've got a streak going, they're doing something to make the streak longer than it would have been if it were just in randomized game order.

JAD: Oh my goodness!

STEVE STROGATZ: And teasing out the role of statistics, which is sort of always there and it's rigid and it's hard to escape from, it's not everything, it's a big part of the story, but there is still room for psychology and for human foibles.

JAD: Hmm. Oh man, you made me so happy right now. You took me from the depths of depression to absolute elation. This is fantastic!

ROBERT: So the reason Jad is so happy, not that you really need to know, because we know we are not coins. That's what we've just kind of proven—at least strongly suggested here. We are creatures of will. We are the authors of our own success because we have feelings, and the feelings lead to will. If you make the right move, if you say the right prayer, things can change. And you can change them. I mean, listen to Paul Simon. Paul, tell him what you know.

[ARCHIVE CLIP, Paul Simon: I had a long streak of that bad luck, but I'm prayin' it's gone at last. All gone at last. Gone at last. Gone at last. I had a long streak of that bad luck, but I'm prayin' it's gone at last.]

ROBERT: And that's our lesson, with one unfortunate exception, which begins with the word, "but." Do we really have control over our choices, over our destiny? I mean, do we really believe that? Well, I want you to join me here in playing a little game.

GREGORY WARNER: Schnick, schneck, schnook.

ROBERT: This is our reporter, Gregory Warner, and Paul Glimcher, a neuroscientist at New York University.

PAUL GLIMCHER: Okay, schnick, schnack, schnook is like rock, paper, scissors, but there are four choices. They are rock, paper, scissors and well. When someone plays well, the scissors falls into the well, the rock falls into the well, but the paper covers the well.

GREGORY: So always choose well.

PAUL GLIMCHER: No, then I'm gonna always choose paper and you're doomed. Ready? Oh, how you show it? The well is a little tube made with your hand.

GREGORY: Yeah, that kind of looks like a rock, but open.

PAUL GLIMCHER: Right. Ready? Schnick, schneck, schnook. Oh. Okay, you beat me. I played well because I thought there's no way I'd stick with paper again. Schnick, schneck, schnook. When you stand there and you go, "Uh, uh, uh, uh, paper!" you do not actually, at the instant of making that decision, go, "Oh. Well, let's see. Last time and the time before and the time before and the statistical likelihood of—and if I take the likelihood and derive the maximum—" you know, you stand there, you go, "Uh, uh, paper!" I think that that experience is the randomness in your parietal cortex, those cells chuggling along until one of them randomly jumps up. And that's the one you pick.

JAD: To illustrate this point, Paul does a little experiment which he showed Greg at his lab. He takes a monkey, puts the monkey in a seat, and gives the monkey a choice. Here, you can look at this target, it's red. Or you can look at this one, it's green. This is a meaningless choice. Doesn't really matter. Red, green, it's all the same. That's kind of the point. All the while, as the monkey is deciding where to look, Paul is listening to its brain. That's in fact the sound you're hearing, the sound of individual neurons inside the monkey's brain, chattering away as it's about to make a decision. And this coming up is the sound of it actually deciding right—there.

PAUL GLIMCHER: Each time you hear that stuttering, that's actually the monkey deciding to look at that target. It's him deciding to look straight down. When you actually hear the cell firing away, one of the things you may notice is it doesn't sound like a little clock going, tick, tick, tick, tick tick, tick, tick, tick, tick, tick, tick, tick, tick. It sounds more like whirr-whirr-whirr. You can actually hear the randomness in the way it's behaving. And we think that's not an accident. That, we believe, is the randomness that makes us unpredictable when we're making choices.

PAUL GLIMCHER: One of the things I hear all the time is—often from scientists is, "Why would you think there's randomness in the brain? That seems crazy. You're a material scientist. Surely, what you should believe is that everything in the brain is measurable and predictable." Well, I think the answer to that is you don't actually want in real life to always be predictable. People have to be unpredictable if they are to survive in the natural world. I actually think that the experience we have of actually choosing in these hard, hang fire choices is not the experience of "Well, he's going to and I'm going to, and he's going to." You can feel this hanging moment, this pregnant pause.

GREGORY: We both did paper.

PAUL GLIMCHER: And the decision is constructed by the randomness in your brain.

GREGORY: That's not how it feels to us, and in fact, that's not even how it feels to you. Because when you said, "Oh, I thought you were gonna do—well, I never thought you'd do paper a third time." You were kind of making ...

PAUL GLIMCHER: But I think we make up that story afterwards.

GREGORY: You made up that story?

PAUL GLIMCHER: Yeah, I think we all make up those stories afterwards. Like, I try and—I try and give meaning to my choices, just like you. You know, gosh, why did I pick paper? I picked paper because I thought you were gonna pick—well, that's what I thought. [laughs] But, you know, is there really compelling evidence that at the moment I had to pick I was thinking about that? Yeah, not so compelling.

GREGORY: Well, you know better, because you've looked in the brain.

PAUL GLIMCHER: It doesn't look that way in the brain. But randomness is kind of a nasty thing, right? It's sort of the last thing you can't measure. And what we're arguing is sometimes it's there on purpose. That's anathema to the traditional scientific method, where what we do is try and make our measurements more and more and more and more accurate. And then the stuff we don't understand, the stuff that's unpredictable, will go away. What we're saying is it'll never go away.

ROBERT: Special thanks to Gregory Warner, who I know is dreaming of making the American Schnick Schnack team. They're having their prelims in Waco, Texas coming up, and I don't know if he's gonna make it but, you know, all our best to Gregory Warner. Thanks for the piece. Who else? I got Mike—Jad's not here. I can't remember anything. Who else do I have to thank? Oh, Steve Strogatz. Yes, Steve Strogatz, for bringing us out of the darkness into the light. Thank you, Steve. And it's always nice to say something special about Alfred P. Sloan, who's got this foundation that helps pay for us. And to the National Science Foundation and to the Corporation for Public Broadcasting. And Jad will be back, but, you know, oh, well.

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