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

Let's talk in this video about the famous NFL quarterback rating

that you see whenever you watch an NFL game.

So they might say,

Peyton Manning's quarterback rating in the first half was 120, or it was 80.

And the higher quarterback rating is generally considered better.

So what is a quarterback rating based on?

It's based on four quantities, your completion percentage, your yards per pass

attempt, your touchdowns per pass attempt, in other words what percentage of your

passes result in touchdown passes, and your interceptions per pass attempt.

And so on Wikipedia there's this complicated explanation,

the NCAA in college has a different formula, just slightly different.

But basically, Perfect passing rating would be 158.3.

In other words, it basically again Wikipedia explains exactly how this works.

But basically, we can sort of deconstruct the quarterback rating for

the NFL using regression.

And it's a really good example how regression can get to the bottom of

what's going on with this.

Okay, so from espn.com for the 2014 season, I've got the quarterback ratings.

And then I downloaded all these stats on the right, and what we need to know is

completion percentage, yards per pass attempt, percentage of passes that were

touchdowns, or percentage of passes were interceptions.

So Drew Brees, 5% of his passes were touchdowns, and 2.5% were interceptions.

And the idea is can we with these four columns,

in orange, predict the rating.

So we simply run a regression, which we know how to do by now.

And it pops up over here the results.

The R squared is 0.999999, I don't know how many more nines you want there.

And the standard error is 0.04, which means 95% of the time,

we can predict the quarterback's passer rating within 0.08, okay.

And usually the average rating is what it's about.

70 or 80, I'll bet.

Let's see.

And so if we can predict something that tends to be around 70 or 86,

or 87 at 95% of the time within 0.08, we've basically got the formula.

So in other words, if you want to predict a guy's quarterback rating, okay, and

all the P values are fantastically low here, look at this 10 to the 90th.

It's obvious they all matter, and this is basically a winner, your formula.

Well nobody really puts it that way, okay.

So you would take 2.06,

Plus 0.84 times completions percentage.

And then the next one is 4.16 times yards per pass,

Plus 3.33 times Touchdown percentage.

And then interception should be negative, and it is.

Minus 417 times Interception percentage.

And that will pretty much give you somebody's quarterback rating.

So the question is, what do these coefficients mean?

Okay, so if you can have a 1% increase in your completion percentage,

that means completion percentage goes up by 1.

Quarterback rating goes up by 0.84.

Again, all good things being equal, or

the other three variables in quarterback rating being equal.

And if you can increase your yards per pass attempt by one,

I think I got that wrong.

Yards per, 4.16, decimal point's in the wrong place.

That would really mess things up.

Okay, if you could gain one more yard per pass attempt,

your rating would go up by about 4.17, 4.16 points.

And in the homework problems and a test question, we'll talk about how you would

interpret the other two coefficients in this equation.

But basically the quarterback rating is not that complicated.

But what you have to understand with the quarterback rating,

it's based on the quarterback statistics with the offensive line he has,

with the receivers he has, and the running backs he has.

So if you trade the quarterback to another team, you can't expect the same

quarterback rating because he'd have a different offensive line,

different receivers etc.

Also, it doesn't really measure how much you help the team, think about it.

It counts a 1 yard touchdown pass almost the same as a 50 yard touchdown pass.

You get credit for the yards, but that doesn't make much sense.

And if the interception is run back for a touchdown,

that counts the same as the interception is run back for one yard.

And we know that yards per pass attempt is the most important statistic, and

completion percentage just really for team performance.

And completion percentage just doesn't really correlate well with team

performance after you adjust for yards per pass attempt.

You could run a regression to show that.

So if a quarterback reading is purporting to show how a quarterback helps a team,

or how good a team's passing offense is, I don't think it does the job.

And we go to Brian Burke's great site, advancedfootballanalytics.com in a few

videos, I think we'll see a better way to rate quarterbacks.

And I should mention ESPN has a total QBR,

which we're not ready quite to understand yet, but which really tries to

address the shortcomings in the NFL's quarterback rating.

And we may talk a little bit about that, but first we have

to talk about the concept of states in football and then the value of the state.

Because that's really the key to the concept of expected points,

which is really the key to understanding football at any level,

from Pop Warner or Pee Wee football to the great NFL.