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 University of Houston System 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

Okay, let's use what we learned about states and

values to solve a real problem with pro football coach Mike Fitz.

Okay, it's 4th and 4 and the opponent's 30 and

we're just trying to maximize expected points here.

Win probability we'll talk about later thanks to Brian Brooks great start.

Okay and so should you kick a field goal?

Well we need some assumptions here.

You really need to know what the chance of making the field goal.

I think looking at recent data it's roughly about a 75% chance of making

a field goal.

I think we'll talk more about how to estimate that more exactly later.

And we'll assume that if you kick it off it's always going to be returned to

the 22 yard line.

I think on average now would these great kickers kicking touch backs

despite them moving back where you kick off from.

The average yard line where teams start is the 22 yard line.

And let's assume if you go for

it on 4th and 4 you'll either make it or you won't obviously.

Let's assume you always gain five yards when you make it,

you gain two yards when you fail.

Okay, and we'll let the questions.

What probably of making your team mean just sort of the break even between

going for the field goal and going for it on 4th down?

So, what are the relevant values do you need from our last file?

The value 27, 27 file and I looked them up, okay.

Well, if you kick off,

the value to the other team would

be point Minus 0.084, okay.

Okay the value of having it on the 22 yard line, let's just take a look at that.

First and ten on the 22 is worth -0.084 points to the other team.

Which means it's worth 0.084 points to you okay?

We also need the value first and ten on the 37 yard line.

because if you kick a field goal and

you miss it let's assume it was kicked from 70 yards behind scrimmage.

Then the other team will get the ball on the 37 yard line.

And that's worth 0.979 points to the other team.

But again,

the value to you is minus that because that's the value to the other team.

So you hear the value to the team that has it.

It's -0.08, but to you, it's plus 0.08.

Now if you make the first end, you'd have the ball the 75 yard line.

You started on the opponent's 30.

So you gain, that's the 70-yard line you gain five.

That's worth 3.88 points.

And if you didn't make it, basically you gain two yards, you're on the, you're 72,

the other team's 28, and the other team would have a value of 0.336.

Okay, o now, what's the value to you if you go for

it, given a probability of making it?

So that's in this.

The probability of making it, we don't know.

It actually turns out if you look back at past data on 4th and 2,

teams make it 44% of the time.

Which that may surprise you, it may not.

But what's the value if go for it?

Okay, with the probability that you make it, okay.

You would have first intent on the 75 and get this, and then you take

the probability you wouldn't make it times the value to you of that situation.

Okay the other team would have the ball under 28.

The value to them would be 0.33,

but to you it'd be minus .033 because it's good for them.

Okay, I've got the formula right here but let's just do it again.

Now what's the value of the field goal?

Okay, well we said there's a 75% chance you'll make that variable.

And if you make the field goal, it's worth 3 to you.

We should make the 3 points- oay.

And then they're going to have the ball here, which is on the average negative.

So they're going to have the ball, which has a value -0.08,

which has a value to U of plus 0.08.

Okay and then if they don't make the field goal

Then the value to you is going to be unfortunately, they'll have the ball on

the 37 which is worth this and to you it's worth minus that.

Which is 2.06 points.

Okay now we've got the right answer here, but you want to set the value.

Let's post this 0.5.

You had a 50% chance for going for it, okay.

Let me just copy this difference.

Well, we'll just do it right here.

The value of going for it minus the value of not kicking the field.

Okay now here you have a 50% chance of making it, you're worse off going for it.

So we'd have to raise this probability to make us indifferent.

So we want to change the yellow so

that the red equals zero, we can use Goal Seek cause we've done several times.

What if analysis > Goal Seek, okay I want to set this cell to

zero By changing the probability.

So I get 50, you need a 57% chance to make it to make it worthwhile.

We have only a 44% chance to make it so you wouldn't go for it.

Okay, now let's take another situation where actually you should go for it.

And we'll look at the empirical evidence and see coaches don't go for it enough.

So we have 4th and 2 on the opponent's 20.

Should we go for it?

Now teams made it 62% of the time in 2014, if they went for it.

Which may surprise you how easy that was.

Okay, I just did 4th and 2 on any yard line, not the 20.

Just looking at all the times teams went for it on fourth and two.

And the chance of making the field goal is higher let's suppose it's 85%.

So we need the following values.

What's the value of first and ten on the 22?

Because of the kick-off they'll have minus, that's the value to the other team.

They'll get it on the 22.

It's -0.08 to them, 0.08 to us.

Okay now if we don't make the field goal they'll get the ball

seven yards where we attempted it from, they'll get it on 27.

That's worth a positive value to them, a negative to us.

Let's again assume it's worth two on the opponents twenty.

And again, assume yo make it you gain 5 yards.

You fail, oh fail, we should gain one yard.

So gain two yards, we would have made it okay.

So if we make it, we'd have first and 10 on the 85,

because we were 80 yards away from our own goal line.

Now we're 85 away.

That's worth 4.9 points.

If we fail to make it then they'll have first and

ten on their own 19 because we were on the 20.

That's worth -0.298 but negative that is plus.

Okay, so now what's the value to us if we go for it?

The probability we would make it times, we'd have first and ten on the 85.

One minus problem you don't make it and then we would take minus this,

we would take minus the 0.298 it's not that bad of a situation for

us because they're taking over on a bad yard line, so that would be times a plus.

In other words we still got positive value if we don't make it

because they're getting the ball in a bad field position.

Okay, now what's the value of the field goal?

Well the chance of making the field goal, we get three points minus the -0.08 which

makes it a plus, because that's not good field position for them.

Chance of field goal we get 3.08 times the chance of a field goal, and

if we miss the field goal, one minus chance of making the field goal

the value to they get the ball on the 27 which is pretty good for them so

the value for us would be minus 0.267.

So why don't we take the difference between these and equate them.

Let's suppose we say 0.55.

Well that may going for it would be better there okay.

0.45 going for it would be worse.

So somewhere in the middle we want to change the yellow again

to make the red equal zero to see if we should go for this.

So we go What If Analysis > Goal Seek, set sell is going to be.

The difference between expected points going for it or not.

Now this is not win profitability because I mean if I was down two points and

we're 4th and 4 from the 40.

I'd want to kick the field goal.

And in the previous example we're trying to do expected points.

Bryan Berkley we'll see in a couple of videos

has a fourth down calculator that helps us solve this problem.

We want to set the difference to zero, and we want to change the probability.

So we need a 50% chance to make it to make it worthwhile.

And teams made it 62% of the time.

So we should go for it and we'll see that teams should have gone for

it much more in 4th and 2 than they did when look at some data from the great site

www.profootbalreference.com which we can analyze using text functions.

And we'll get to that in a little while, but

that's an example of football decision making.

We'll give you a homework problem on this and

then we'll give you a test question, to see if you understand how

to use our value 27 file to do basically football decision.