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, you'll recall when we discussed baseball decision making,

we defined the possible stats during an inning, which could be zero, one or

two outs and there were 8 on base situations

And so there were 8 times 3, or 24 different situations.

We had that run expectancy matrix

that told us how many runs we could expect to score in each situation.

Now football's much more complicated.

So what sort of defines the state in football game even

if you ignore the time that's left in the game and the score?

Or you could have four downs.

You could have, let's say one, two, let's say up to 30 yards to go.

Can't have 30 yards to go if you are near the goal line.

And there are 99 different yard lines you could be on.

And so this isn't quite right, but

if you take four downs times up to one to 30 yards to go.

And you have 99 different yard lines, you've got about 11 or

12 thousand possible states.

Now what do you want know, for instance, if you've got, let's take an example,

what it is mean to say value of first and 10 on the 40 yard.

This would mean, basically, if I have the ball, and

I will assume we're identical to the other team,

first in ten on 40 yard line, how much will I out score the other team by?

And basically, people have come up with analysis of this problem.

Let me just copy some of this stuff here.

There's a long history on this.

I think it dates back to Virgil Carter used to play quarterback for the Bengals

and Robert Mackel, a giant of operations research who started at Northwestern.

They had a paper, Operations Research on Football and

the Operations Research Journal in 1971, where they would look at first down and

ten yards to go on different yard lines and

see what was the value of that situation.

Okay, now how might you figure that out?

Well, a simple way, and it's not perfect, but let's suppose you would try and

look at the next score after the ball is in that situation.

So first and ten on the 40, let's suppose there were 100 times that happened,

you'd followed it through.

So let's make up some frequencies here.

So 40 times the team with the ball scored 7 points.

30 times, they scored 3 points, and that was the next score let's say 20 times.

30 times the other team scored 7 points before we did, so we lost 7,

and 10 times the other team kicked a field goal before us assuming no safeties.

Okay, now if you average that up and

divide by a hundred that would sort of be the value of the situation.

So you would take these probabilities of what happen times how many points

I would gain on the next score or lose and

I would divide by a hundred, and I'd get one point, okay?

If that was the way it went then you count possessions near the end of the half or

into the game because they'll run out of time, but roughly that would say first and

ten on the 40 is worth one point.

Now the problem is we've got these 12,000 states.

There's around 40,000 plays in an NFL season.

So how many times were there 3rd and 12 from the 48 yard line?

Well, maybe never.

So it gets really hard to estimate this on situations where it's not first and

ten and you really need to know this.

So the late Victor Cabot, I mean, probably the greatest man

I've ever known in my life, passed away unfortunately of throat cancer,

a professor in Indiana University's Kelly School of Business passed away in 1994.

And you may know his daughter, Meg Cabot,

because she wrote the Princess Diaries series, among other books.

Certainly if you've had a teenage girl,

you'll probably be familiar with his daughter, Meg Cabot.

Okay. And they're just a wonderful family.

And my colleague Jeff Sagger, who you know from USA Today sports radio, and myself,

we in 1983, wrote an unpublished paper trying to figure out the value of a given

state in football for any yard line, yards to go and

down situation and we did this using a board game called Pro Quarterback.

Which seem to duplicate pretty well the scores of NFL games and

basically we had took the probabilities and modeled this as stochastic the game,

the math was fairly complex.

But our values come fairly close to the other values that people have found.

Now let me just give you two more papers that talk about this,

if you're interested.

The most famous paper is by David Romer, Berkeley economics professor.

His wife, Christina Romer, was one of Obama's advisors.

It's called, It's Fourth Down and What Does the Bellman Equation Say?

That comes from something called dynamic programming.

And basically was in the best, one of the most prestigious economic journals,

the Journal of Political Economy.

In April 2006, by the way that's where the black scholes option pricing model

was published and Romer's conclusions are very controversial.

He would say you got to for it almost all the time on fourth down

even if you got fourth and four, fourth and five in your own territory.

I just don't agree with that.

If you look at our numbers, we don't come up with that conclusion.

And then Steven Levitt of Freakonomics fame,

I'm sure many of you have read one of the Freakonomics books, part of a blog.

And Kenneth Covash's colleague wrote a working paper and

I don't know if it got published, Professionals Do Not Play Minimax,

indicating that teams don't go for it enough on fourth down.

And we'll see more on this later.

It is definitely true still.

NFL do not go for it enough on fourth down.

They basically kick the field goal instead of going.

Okay, so that's some history on this but let's talk a little bit

what the values mean and then that'll lead to the idea of expected points,

which is the key to analyzing football plays.

And that's where Brian Burke's website advanced footballanalytics.com comes in.

So like let's suppose you have third and three on the fifty yard line.

And you gain three yards.

That's a good play, right?

How good?

Well you start on the 50 yard line,

I've got a look up here to look up, third and three on the 50.

It's worth 1.39 points.

So we can call that, let's say, value of third and

three on the 50 is 1.39 points.

And if you gain 3 yards, that's a good play, right?

On 33.

So now you would have first and ten on the 53.

We count how many yards you are away from your own goal.

Now what is that?

That's 2.09 points.

So that would say that, that play is worth 0.7 points.

Okay, it was a good play.

Now, suppose it's 3rd and five on the 50.

And you gained three yards.

So that's not going to be that good a play.

So all three runs are not created equal.

But now we look at the value of this situation.

So in this case.

Let's go back to that first situation.

The value of the three yard run was the point situation after

minus the point situation before.

So that was a 0.7 point play.

So what you want to do is assign every play a point by.

So Adrian Peterson runs for 80 yards and he takes it down to the one yard line and

the Viking quarterback throws a touchdown pass,

who should get most of the credit for that touchdown try?

Well, Adrian Peterson, cause he ran the whole 80 yards.

Although if you play fantasy football, that corrupts our values as we know.

Okay, so now let's suppose its third and 5 on the 50.

And we gain three yards.

That should have a negative value.

So if I start with third and 5 from the 50,

that's not going to be as good a situation.

That's 1.26 as the batter.

Okay and if I gain 3 yards, I have 4 and 2 from the 53

Fourth in two with the 53 and that's .75 points so that was a bad play.

That lost me points.

So, afterwards, it was worth this much before this much.

So that was worth minus .51 points.

So I basically lost about half a point on that play, and

that will see this is basically how Bryan Burt assigns points to each play.

And this is how you could rank quarterbacks.

You could look at every pass Tom Brady threw.

How many points did he have on his passes?

Or Paten Manning.

How many points did he have?

Okay, although it's not scheduled, adjust it.

Okay, so that's a quick introduction and again, our point value, we'll be using

our point values in the analysis here, because we've gotta have something that

doesn't just work with first downs and all the other articles have just graphs.

They don't have tables, as far as I know.

So in the next video we'll talk about specific football decision making.

You'll want to know for instance, on fourth down, what does your probability

have to be of making the first down, before you should go for it?

And so we'll talk about a couple of situations, where that occurs.

Okay, we'll see you in the next video.