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

On the last video, we showed the Texans did much better on first-and-ten

when they passed on average, than when they ran.

But there's a price to be paid here.

Passing plays that were much riskier for

the Texans on first-and-ten than running plays.

And the way we'll show that is emulating a standard deviation IF,

like an AVERAGEIF, or a SUMIF, or a COUNTIF.

Basically using array formulas.

So again, a quick so we're going to open an array formula.

Let's list some people on Gossip Girl.

Serena, Blair.

In real life Blair is married to Adam Brody from the OC.

And we'll have Dan and Chuck.

Suppose I want to translate xoxo from Gossip Girl.

Now suppose I want to transpose those peep holes.

Okay.

Well to do an array formula we first select where the answer is going.

That would be these four cells if you want to transpose them.

Then you type the formula, then you point to the range you're looking at and

you hit control key+shift and enter.

And that transposes the name.

So that if I change Dan to Elvis it changes there.

And so the last chapter of the Data Analysis in Business Modeling book

talks about this.

So you select the range, you enter the formula and

then you do Control+Shift+Enter.

Now I think I've tried this three times.

I think being in the package I've recorded

is going to disable my standard deviation IF.

But here's the formula I want to use, and it worked fine as you can see.

But I had to Ctrl+Shift+Enter.

So this one where it says standard deviation, and

if the pass or run column equals pass you keep the points gained.

Otherwise you make it a blank.

And Excel ignores blanks.

So it'll take the standard deviation of the points column

only when the play was a pass.

And that's 1.63.

I had to Ctrl+shift+enter if the curly bracket indicates it's an array formula.

And here when I did an, when the plays are run,

the standard deviation is half as much.

Now let me try and see.

Now this works fine when I'm not in this Powerpoint mix.

But let's see if I can get it to work.

I would say standard deviation.

because I've tried three times.

Okay, and then I would say if

the passed run column equals pass,

then I would keep the expected points game column.

Otherwise I put a blank.

And then I need two right parenthesis, and I'll hit Ctrl+Shift+enter.

Oh it worked this time.

I don't know what I did wrong before.

Okay now if I just want to copy that formula an easier way to do it, Ctrl+c,

and now I'll put it in here and I'll just change pass to run.

Now again you can't see this but

I'm going to be hitting Ctrl+Shift, enter.

Pass or run equals run.

Points gained.

Okay.

Okay, it needs a correction there.

Okay, there. 0.74.

Okay.

And so you can see there's sort of twice as much risk for

the Texans on the first and ten passing play as a running play.

Okay now let's look at from game play index comes the great pro football

reference dot com site.

Let's look at fourth and two plays.

So I've got these here, ours, Wilkin 2, here we go.

All right, so I picked off every play where people went for it.

In other words instead of runner pass and didn't do a punter field goal.

Okay so there are 130 run plays and

they average 1.22 points on runs what it was worth in two or less.

And there were 78 passing plays, they average 0.6 points.

And the standard deviation was about the same on running and passing.

So now if you look at the average points per play,

in other words I took the total points of 204 here divided by 208, that's 0.98.

And the standard deviation over all the plays was 2.84.

You can create what's called the confidence interval.

In other words, we average 0.98 points per play, but we're not sure that

Ii we did thousands of plays on fourth and two that would be the true average.

So the way you do a confidence interval you take the mean plus or

minus two standard deviations divided by the square root of the number of points in

the data set.

So that's what I did here.

I took the average number points per play,

0.98, minus two times 2.84 divided by the square root of 208.

And change minus to a plus.

So given this data I'm 98.5% sure that on fourth and two if a coach goes for

the average points he can expect to get per plays between points 59 and 1.38.

Now I looked at punts and field goals and fourth and two or less also.

Now there were 353 punts and those were probably smart calls,

they added 0.58 points per play and here's the standard deviation.

The 95% confidence interval is I'm pretty sure an average punt will at fourth and

one or two will add 0.48.

It's from 0.48 and point 0.68 points.

[SOUND] And that's less than what we got if we went for it on fourth and two.

But here's where the real kicker is,

but it's not that much less, because this confidence interval,

0.48 to point 0.68, overlaps my conference interval right here.

[INAUDIBLE] Look what happens if you field goal on fourth and two.

A lot of these are just dumb calls.

How do I know that?

The average points added on the 133 field goals on fourth and one or

two, was .08 points.

Now when coaches went for it, it averaged .98 points.

I mean that's ridiculous, you can't average one point more going for

it then when you kick a field goal on fourth and two or less,

if people are kicking field goals in the right situations, and

if you do a 95% confidence interval, I am 95% sure that the average points added by

an NFL coach's field goal attempt in 2014 was between minus 13 and 0.3.

That is just significantly less than what I got over here when coaches went for it.

So coaches are still field goaling way

too much the data shows in terms of expected point target.

I mean it's again, it's easier to field goal than to go for

it because nobody's going to yell at you if your kicker kicks a field goal.

But you're leaving points on the table if you do this in most cases and

that's really sad.