We're talking about the hot hand and sports, particularly basketball.

I grew up watching basketball.

The New York Knicks.

We knew whoever was on a shooting streak should get the ball, because the chances are that they would make the next shot.

People are more likely to make a basket, given they made a whole street this week.

What we believed.

From a math perspective, hot hand usually means that you have a higher chance than usual of making a basket.

Given that you just made a whole bunch of in a row, I think about it.

You have some lifetime, si vous an average or some average for your game or some kind of base measurement.

And then all of a sudden you've made ah, whole bunch of shots.

Maybe you think the chances are that the next shot is gonna be a winner are higher than your baseline average because you've got confidence because you're doing great because you're throwing that ball well, that's the hot hand, your design.

Oh yeah, in the zone.

And of course, it has implications for strategy, right, because if the guy's on a streak and if he's really doing better than his own usual.

You're more likely to want to feed that guy the ball.

So this is a tale with a long history.

In 1985 a team of three scholars, including famed psychologist Amos Diversity, published a study to professional teams were involved the Philadelphia 76 Years in the Boston Celtics and also some Cornell varsity and junior varsity players.

And what they did was something that scientists do a lot.

They challenged conventional wisdom.

They looked in shot strings of hits and misses and asked the question from a statistical perspective.

Is there a hot hand?

So what they did specifically imagine you have a string with zeroes representing Mrs and one's representing hits, and you could look and see after a player or a team has made a bunch of shots.

Is the next shot more likely to go in?

Then say, after an equally long string of Mrs That's exactly what they did.

At first he was a very, very big basketball fan, so I'm sure he was brought his passion to the study.

But I think he was looking at the strings of zeros and ones and found no hot hand.

This papers published.

It's got thousands of citations, and it had two very interesting effects.

One was the non effect in the sporting industry.

Those who thought they knew better than scientists struck their shoulders.

This is not right.

We know there's a hot hand.

We see it, we're experienced.

And then there was the field of scholars who thought this was pretty interesting and started doing more studies.

Different teams, different time periods, different sports.

There's a big hot hand.

Literature launched 1000 academic ships but got a shrug of the shoulders from professional sports.

If you search for hot hand fallacy on the Web, you're gonna find tons of hits.

It's not universally agreed because, as usual, with a scientific experiment, there could be lots of different ways to do it.

Maybe use a different data set.

What possible?

Different days that could you use the bowl going in the basket?

Well, you could use a different team.

You could use a different season or you could look for streaks in a different sport.

You can do all sorts of things.

You always make a lot of choices in experiments, and it's easy to forget when you have a conclusion that your conclusion depends not just on the hypothesis you want to test, but also the way you implemented your experiment.

30 years later, to satisfactions.

Josh Miller and Adam Sanders Oh, published a paper.

How did it different from the enormous literature on the subject In a really important way, it challenged the original result not by saying, Maybe we need a different experimental design.

Maybe we need a different idea for what?

Ah, hot hand should be in mathematics, It said.

These guys did their study wrong, so I was really stopped in my tracks when I saw this.

But the equivalent thing they made in addition, mistake or something.

It is like that, and especially when you consider a scholar of the importance of Amos Tversky.

So just a little background on her ski psychologist.

As I said, an Israeli psychologist, his partner of Daniel Kahneman, who went on to win the Nobel Prize for their joint work Diversity, died of melanoma in 1996 and did not then receive the price because it's not awarded posthumously.

But the work was all about how people make mistakes.

So here's diversity.

A connoisseur of human error And he, it seems, has made a mistake.

Or so say, Sandra, Joe and Miller.

This gets to the question of the most basic kind of hypothesis.

Testing that statisticians.

D'oh!

So it always goes pretty much the same way.

There's a concept of the ordinary and statisticians, for better or worse, call this thing I know hypothesis, which may be off putting to some.

But while they mean is what's typical, put a metric of what's typical.

And then you look at your observation.

Maybe it's a drug effect.

Or maybe it's whether you've just made an unusual, uh, your probability of making a shot is unusually high compared to a notion of typical.

And then you say, Well, there is there an effect or not?

In effect, hypothesis, testing works.

And so there's a lot of art and science and deciding what ordinary means.

Maybe not everybody agrees.

But the mistake that was found in this paper that singers oh and Miller noticed was in the concept of saying with the non hypothesis what the ordinary waas.

And it was particularly related to the fact that data, even though mathematicians like to think in terms of infinite strings or infinite number of observations or laws of large numbers very often or dealing in practice with small, finite samples of data and small stuff does not need to behave like big stuff.

It's pretty simple, actually.

If you see three things happen in a row, you think, Wow, maybe a trend.

That's a small sample error, right?

Maybe the fourth one's gonna be going in a different direction, But we're very quick to find reasons for things to find trends to find.

Patterns were wired this way.

Okay, so we know about this, and no one knew it better than Amos Tversky.

Ah, and yet Hey had a small sample of data and he treated that small sample along with his co authors, though it were an infinite set.

Maybe the best way to start is with coin flipping.

Okay, so this is like a toy example of the sort of thing they were doing.

Coin flips could be like hitting or missing shots, heads, tales, hits and misses.

Maybe so.

Here's the kind of thing that we're thinking about because, after all, we're looking at the probability of making a shot, given that you've just made some shots or making a shot after you've just missed some shots.

So we want to look at what's happening after something else happens.

So we could play a game with a coin and we're gonna I think that we have a completely unbiased coin, 50% heads, 50% tails, and we're going to think that my flips of the coin are independent.

So what happens on the next flip has nothing to do with what happened on the previous flip or anything else in history.

We're gonna flip the coin three times and we're thinking we're looking for what happens after something.

So here's the game.

I flipped the coin and then we're going to write down what happens after I flip ahead.

So if I flip tails we don't think about anything, then I flip the heads.

We become alert.

Then flip something else we write down in a Jiff.

It's a heads or a tea.

If it's not heads, we're gonna do this three times.

And so the question is, what do we think before we do?

The experiment is get them given.

This is an unbiased 50 50 coin and my flips air completely independent.

You can ask, What do you expect to see on the piece of paper, like half heads and half tails?

Why not?

Because being cued by ahead shouldn't have any effect on the next on the next flip.

But in fact it did.

I can write down all the outcomes.

There's only eight of them.

So I think I got all eight of them.

And let's look at what we would have written down if we're keeping track of what happened after heads, so T t t is a nonstarter.

T th is also a nonstarter because even though you Scott heads here, we don't know what happened afterwards because we were only looking at streaks of length total and three.

Okay, so t th we don't write anything down.

You could already see something's funny is going wrong because out of my eight cases, two of them have already been problematic.

The next guy is not problematic because here's an H right in the middle so that you flip the T.

Ah, you don't get do anything.

Flip the h, it's right in the middle.

You're alert.

Then you get a t.

C You right down a t in this next string.

H T T H starts off right away.

Gets your attention.

You write down a T here in this string, you start with a T.

Don't write anything.

Then we see an H.

We become alert.

We get an h, we write it down and then we're finished.

This age would have cute us if we were doing strings of length four.

But we aren't here.

H th to the first h tells us to write down the tea.

Uh, the second t tells us to do nothing.

Then we end with an H, which is kind of dangling here.

H h t.

So the first age tells us to write down what happens after, which is an age Second Age tells us to write down what happens, which is a t.

We don't do anything when we see a t.

And here finally we have hhhh So the 1st 2 ages each tell us to write an H and we don't get to do anything after the third.

In the 1st 2 cases, we write nothing.

In the last six cases, we write something.

So let's see what fraction had heads.

So in the 1st 1 the fraction zero And in the 2nd 1 the fraction is zero And the 3rd 1 the fraction is one again we have zero.

Here we have a heads and a tails.

Half the time we saw heads half the time we saw tails.

That's 00.5.

And here 100% of the time we saw heads again.

So we have a one.

So we take these numbers, they're average represents expectation.

So I add them up.

I get one plus 1/2 plus two.

That's 2.5 on the average is equal to 2.5 over six, which is definitely less than 1/2 6 is the number of examples that I'm averaging over snow.

Forget were asked What do you see?

What happens given that you have a head on.

So here we never first when we never had a head at all In the 2nd 1 we had ahead at the end.

But we don't know what happened given that we have that head.

So those things are out of the sample.

This is exactly how you would have treated a sample with heads being make a shot and tails being Mrs shot.

If you were doing this for basketball strings.

So if we were happening toe look at only three shots, bringing this back to basketball, we would have seen that there was a biased downward fromthe 1/2 that we would have expected to see, given the fact that the coin is 50 50 and that the flips are all totally independent now.

Importantly, if we looked at longer strings, that average would have tended toward 1/2.

And if we looked at very long strings, even not all the way infinite, it might have been so close to 1/2 that this difference didn't matter.

But in fact, what we're seeing is that in data in this finite data set, the reversals were more likely than the continuation.

And that is a finite data, a small sample effect.

And this was not considered when the original hot hand scholars made up their sense of what was ordinary.

What we could now ask.

What happens when we look at really high end basketball players of today, take the original experiment, but put in this correction, allow for the fact that we're looking at finite data sets small samples which effectively lowers the bar from 1/2 or whatever is the right number down to what ordinary looks like in a data set and see if we do find hot hands.

So this is an experiment that we did.

So the way we did it, I'll tell you a little bit about our experiment is that we took some basketball players.

I'll tell you about them in a second.

Some well known basketball players over the 16 4017 season and playoff game by game.

And we looked there strings of hits and misses.

And we asked the question in each game where they having a hot hand or not, were they more likely to make a shot after a string of shots than they were after a string of Mrs.

That's the question that we asked following the original researchers.

We have to set up a concept of ordinary no effect and then look at the observed string and see if it's different from ordinary in an important way.

So Steph Curry gets 10 shots in a row.

There's a chance that was just luck.

He just, you know, if he was a 50 50 players get 10 shots in a row sometimes, right?

Could be like somebody's got to be on top, right?

Is that luck or skill?

It's exactly the same sort of question.

It's great to see that people in England know about Steph Curry.

He's one of our star players, one of the featured players of the Golden State Warriors, which is the team we looked at and also one of the featured players in this hot hand study that we did.

We looked at two Warriors, so the Warriors were the champions, eh?

NBA champions last season, and we looked at to actually three of their star players Steph Curry and Klay Thompson, who are known as the Splash Brothers for very good reason.