Learn how probability, math, and statistics can be used to help baseball, football and basketball teams improve, player and lineup selection as well as in game strategy.

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来自 休斯敦大学系统 的课程

Math behind Moneyball

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Learn how probability, math, and statistics can be used to help baseball, football and basketball teams improve, player and lineup selection as well as in game strategy.

从本节课中

Module 5

You will learn basic concepts involving random variables (specifically the normal random variable, expected value, variance and standard deviation.) You will learn how regression can be used to analyze what makes NFL teams win and decode the NFL QB rating system. You will also learn that momentum and the “hot hand” is mostly a myth. Finally, you will use Excel text functions and the concept of Expected Points per play to analyze the effectiveness of a football team’s play calling.

- Professor Wayne WinstonVisiting Professor

Bauer College of Business

[COUGH] No course on the math behind Money Bowl would be complete without

an analysis one of the most famous plays in sports analytics history.

The Colts were playing the Patriots Sunday night, November 15, 2009.

You probably watched this.

There are two minutes and eight seconds left.

The Patriots were up by 6 points and they had the ball.

Fourth and two on their own 28 yard line.

Peyton Manning had just completed two long touchdown drives to bring the Colts

within six points.

Bill Belichick went for it on fourth and two.

Every announcer said Bill, you're a great coach, but

you just made a huge mistake here.

Well, the announcers made the huge mistakes.

I hope they apologized to Belichick although I'm not the biggest fan.

Okay so let's see without a computer and

just doing calculations in your head mentally how

could you sort of think about whether you should just go for it in this situation.

People have gone for it lots of times on fourth and two behind,

but this may have been the first time as far as I know that a team went for

it fourth and two when they were ahead by six points.

Well this is a good example of decision making during certainty

where parameters which you don't know but you have this.

Okay so you have to estimate your chance of making the first down.

Well, in 2009 and 2010 it was about 50 50 teams on fourth and

two would make a first down.

But you've got the great Tom Brady, you probably had better than a 50% chance, but

let's keep it at 49% chance.

Then you also have to estimate the chance if you don't make the first down will

the Colts score a touchdown and win the game.

We're trying to simplify this here.

Okay. We're assuming that if you make

the first down, the game is over and you win.

If you don't make the first down the Colts will get a chance to score the touchdown.

And Brian Burke in a post in the New York Times said, historically teams in this

situation, if they had the ball first and ten, let's say on the other team's 28 with

around two minutes to go, would score 53% of the time.

Well, what would happen if you punt it to Peyton Manning?

Well, it would probably go about 40 yards and

in that situation historically Brian Burke said you have about a 30% chance

Peyton Manning would drive the Colts in for the winning touchdown.

So then you try and figure out by simple expected value your chance of winning if

you go for it given these three numbers.

And your chance of winning if you don't go for it.

Well if you don't go for it it's easy, if Peyton doesn't score the touchdown,

you win the game, so it's one minus the chance

long is the chance the Colts would score a touchdown after the punt.

So there's a 70% chance that you'll win if you punt.

Now what about if you go for it?

Well if you go for it and you make the first down the game's over and

you're going to win.

You can run out the clock.

So with that probability you win the game for sure and if you don't

make the first down, there's still a good chance Peyton won't take them in and

in this case it's one minus short, which is the chance the Colts would score a TD

from, let's make that the Patriot's 28 yard line.

And if you do the math there you come out going for

it gives you a 73% chance to win versus punting gives you a 70% chance to win.

But you don't know these parameters.

But let's keep this one fixed at let's say 49%.

Then I get a two way data table to work with where I varied the chance that I'm

short, which is the chance the Colts will win the game if the Patriots

don't make the first down.

And long is the chance that the Colts

would win the game if the Patriots punt it to them.

And I range long from 20 to 70% and short from 40 to 90%.

And then I took the probability of winning if you go for

it minus the probability of winning if you punt it and get a two way data table.

And the row input cell was long.

The chance that Peyton would drive them in after a punt and

the column inputs, you can see right there, was short,

which is the chance the Colts would win if you didn't make the first down.

And then I took the difference and

I highlighted in red when the difference is positive.

And it's almost always positive.

Now if I've got Tom Brady and this will be exacerbated if I change

the chance of making a first down to let's say 60% because I have Tom Brady which is

probably better then, basically the average team.

So I'd make this a 60% and you can see almost everything is pink there.

Really, the only way it's not going to be worthwhile for

me to go for it is that Peyton has

a 60 to 90% chance of making it from the 30 and only a 20% chance or

30% chance of scoring a touchdown if we punt it to him.

So it's almost a slam dunk as Brian Burke says,

it's very hard to come up with a scenario where the Colts shouldn't have gone for

it, so why didn't, Patriots shouldn't have gone for it.

So why do teams rarely go for it in these situations.

They're risk averse.

I mean nobody gets fired for sort of doing the, for taking the expected,

the common path which would be punting in this case since everybody did.

And basically Bill Belichick didn't have to worry about getting fired because,

I mean, his job is secure as any coaches job I believe in any sport except maybe

Greg Popovich's okay, and so he didn't have to worry about this.

But the typical coach is going to be yelled at, and

Belichick was even yelled at even though he made the right move.

You can't judge a decision by its outcome.

You have to judge it by the process.

And it was indeed the right call to go for it there.

And lots of analytics people including myself wrote posts the next day

discussing it.

Now Brian Burke has something really nice called the 4th down calculator

that let's you, in any situation, figure out should you go for it.

Okay, so we could fill this.

So if you go to advanced football, let's just go back to advancedfootballanalytics

.com and we'll come back to this site a lot.

Okay.

Okay so go to TOOLS > 4th Down Calculator.

Okay so you can put your information in here.

So the score difference is we're up by 6.

There's 2 minutes and 8 seconds to go.

It's the 4th quarter.

We have the ball on our own 28 and we have 2 yards to go.

And so you just hit the Calculate button and you can see what is going on here.

And we're interested here in win probability.

WP is win probability, not expected points, I mean you're the end of the game,

you just want to maximize your chance of winning.

Okay, so, Brian says to break even you could punt the ball,

you'd have a 73% chance to win the game.

Okay, now if you go for it and you make it it gives you a 92% chance to win and

if you fail you've still got a 67% chance to win there.

And so the break even we'll see in a minute would be what probability

0.24 times 0.92 plus 0.76 times 0.67 equals the 0.73 break.

Okay, so the break even probably is 24% and

he says you have a 60% chance of making that, and given that,

that's a slam dunk, that case, and the win should probably go for it.

Now if you do it on expected points it's not as good a call.

I mean I'd need a 55% chance to make it a break even.

But I pasted this into our little sheet here, I believe, right here.

And so just to show you, where does this 24% come from?

Probability come from because if you take 24% chance,

the chance that you make the first down, you'd win 90% of the time.

And if you don't make the first down, he says you'd win 67% of the time.

And so if I take that, what do I get?

Besides making a headache?

I get 0.73 and that's equivalent to your,

that's equal to your chance of.

Winning the game if you would punt it.

A field goal is not an option, would be a silly play here.

And so that 4th down calculator is very useful but to summarize things here.

It was a really smart decision by Belichick to go for it.

I mean the math says he had a better chance of winning the game if he went for

it even though he was up 6 points, then if he didn't go for it.

And the announcers were the ones who really didn't understand what's going on.

It's really hard to come up with reasonable scenarios just ask

any announcer.

To fill in their three numbers in yellow and I'm pretty sure you'll see a positive

number right here which means you should go for it.

Okay, we'll go back.

We'll return to Brian Burke's site in the next few videos to discuss

how you can evaluate players at the skill positions, offensive lines.

And defensive players using the concept of points per play.

In other words how many points to you gain or

lose on a play based on the yards you gain on a given down,

which we have discussed when we talked about the value 27 27 [INAUDIBLE].

So we'll see in that next exciting video.