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 4

You will learn how to evaluate baseball fielding, baseball pitchers, and evaluate in game baseball decision-making. The math behind WAR (Wins above Replacement) and Park Factors will also be discussed. Modern developments such as infield shifts and pitch framing will also be discussed.

- Professor Wayne WinstonVisiting Professor

Bauer College of Business

Okay, let's continue with our discussion of baseball decision making.

Suppose there's a man on first, nobody out, and

you're thinking about stealing a second.

Okay, what chance of success is needed to make it sort of a break even situation?

Okay, so you look at expected runs.

Again, we're not looking at the situation near the end of the game where the score

is tied or something.

But in general for most of the game,

you want to maximize your average number of runs at the end.

Okay, so if you do not steal, how many expected runs do you expect to get?

So if you don't steal, you've got a man on first, nobody out,

so you expect 0.1812 runs.

Okay, now let's let p be the probability, p equals the probability of success,

When you steal.

Okay, so if you're safe, of course, the guy could throw in the center field,

the catcher, and you make it to third.

But basically it's between man on second, nobody out.

Or nobody on and one out.

So if I have a man on second and nobody out, it's 1.039, three runs.

And if we're out, I'll have a man on first, I'll have nobody on and one out.

That's really bad, 0.2394 runs, okay.

So as long as you take the expected value of your runs if you steal.

And to do expected value, I think you know,

you multiply each outcome times the probability of that outcome.

So probability of p,

we'd be successful, we'd be in a better place if we get this many.

Be, safe.

Probability 1- p, we'd be unsuccessful, we'd get this many runs.

And as long as that's greater than or

equal to what we would get without stealing, it seems like a good idea.

Now if it's exactly, well it's the break even probability.

So we could use Goal Seek here or use algebra, let's use Goal Seek.

So for p, let's say I use 0.8.

And then I can do the left side here,

and let's give this a range name, let's call it probability.

And we'll give it a range name, prob.

Okay, so if you steal, you'd expect

to get this prob*1.0393+(1-prob)*.2394,

and so I get .87,

which is bigger than .81, 82.

So use goal seek to change p, or

the prob here, I guess we'll use prob here.

So that j28 = 0.8182.

What -If Analysis > Goal Seek.

I want to change the prob.

Sorry, the set cell is this.

I want to set it to 0.8182.

And I want to change that probability.

You haven't checked that it was.

Okay, so I get 72.4%.

You need to have about a 72.4% chance to be successful when

stealing second to make it worthwhile.

Anything better than that will increase your expected runs.

Okay, and if you look at probability success on stealing past years,

I mean it hovers around 70%, which is very similar to this, but

one point I should have made on bunting and stealing,

that people who are Not totally analytics people might make,

and it's a valid point, it basically upsets the defense.

See if you never bunt, they don't have to worry about it,

but if you're going to bunt sometimes, they've got to worry,

they've got to play guys in, and then maybe you get more hits because of that.

And I think that's really tough Idea to analyze.

And if you've got a great base stealer on first,

it probably upsets the pitcher a great deal.

We can look at the batting average,

when there is a really good base stealer on first that hitters have,

versus the batting average if there's not a really great base stealer on first.

And see if it makes a difference after adjusting for the quality of the hitter.

And honestly I haven't done the research to check that, but see,

that might imply that base running has sort of an external benefit that's

not captured by the fact that basically you went from first to second.

You'll score more runs because you're on second, but

maybe the fact that the bunting and

the stealing upsets the defense has a benefit which would be hard to measure.

Okay, so in our next few videos we're going to talk about analyzing fielders.