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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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.

From the lesson

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

In the next two videos, we'll talk about the important concept of

Wins Above Replacement, which I am sure a lot of you have heard about.

We'll try and go through detail Mike Trout 2014, trying to compute that.

So, Wins Above Replacement, the idea is you look at how much a better hitter than

average the player is, how much better or worse a fielder the player is,

and then you get replacement values, we'll see in the next video, for

the fact that even if you're just an average hitter or average fielder or

average base running, also it counts.

Even if you're just average in everything, you're better than a replacement player,

which I guess is defined, everybody has a different definition, but

fan graphs were used,

somebody who generates 20 runs below an average hitter for 600 plate appearances.

So, if you're an average hitter, you're basically 20 runs better than that

replacement player, which is two wins per 600 plate appearances.

In other words, even if you're not an above average hitter, you create value for

the teams because there's not a sort of a replacement player in the lineup, and

this can be used to compute salaries.

I don't think we'll go into that because that's fairly controversial,

and people have differing ways of figuring that out.

Let's try and talk about how we figure out, let's say, for Mike Trout 2014,

how many runs hitting did he generate better than an average hitter?

Now, I get pretty much what Van Graffs gets.

They get 50 runs above average for Mike Trout's batting.

I get 55.

It's probably because I use a different set of linear weights, or

a slightly different method, but my result's pretty close to theirs.

Okay.

So, what I do is I look at an average team in Mike Trouts 2014 league,

which is the American League.

I found out, Baseball Reference has it pretty simple, how many singles,

doubles, triples, homeruns hit by pitch that an average team has, and

then I have how many outs, which we know pretty much is 26.72 times 162 games.

Then I use the linear weights, we got earlier in the class and

I'm sure FanGraphs has slightly different because these are based on older years,

the steroid era.

I mean, I don't know what's the right set of years to use for the linear weights.

Then I predict the runs scored for an average team.

I take minus 556, and I multiply single weight times singles plus double

weight times doubles, et cetera, and then walks and hit by pitch.

Okay, so this should be walks plus hit by pitch.

I don't know why it's not showing up here.

There we go.

All right. So, I predict that an average hit,

team would score 674 runs, which is pretty close to what they got.

Per game, what is that, about 4.16?

I think they got to 4.18 runs, so that's not there.

Then I looked up Mike Trout's stats.

He got 89 singles, 39 doubles, nine triples, 36 home runs,

87 walks plus hit by pitches, and I don't include intentional walks there.

Okay.

So, basically, how many outs did Mike Trout create?

Then I can say, basically, we'll see in a minute he

used up 436 outs, and so then we can see how many outs were left for

the rest of the team, 4329 minus 436 which is 89% of the outs.

So I can say, basically, when you put Mike Trout on an average team,

you take Mike Trout's stats, and make the rest of the team,

the 89.9% times the average stats, and that creates a new team.

Okay.

Then basically you figure out how many runs by win your weight

stat team would score, and that's what Mike Trout did in to an average team.

I'll get 55 runs by that.

So, how many outs did Mike Trout create?

Well, we had 602 at bats, and

18 double grounded double plays extra outs from these special things,

double play, sacrifice fly, sacrifice hits and caught stealing.

Okay.

So, then remember you've got 98.2% of the at bats that hit.

You take 98.2% basically of the at bats.

Okay.

Were out, all at bats that weren't hits.

Okay.

You take 98.2% of those, the at bats.

Okay.

They're 98.2% of the at bats will not be errors.

Okay, and then you take away the hits,

in order words this is basically, if you think about it,

this is going to be total at bats, minus 0.018.

This is the errors, and then basically if you would take away

the hits, and that's probably a better way to look at it.

In other words, the outs created by Mike Trout would be total at-bats, and

take away the hits and the errors, and those are outs.

Okay. Then add on these extra.

So he created 436 outs,

which turns out to be almost about 10% of the outs that by a team.

So, that leaves 90% of the outs.

So, I scale down the average American league team to be 90% of this,

what the average was, and I add that to Mike Trout.

So that's 90 percent of an average American league team the second term, and

that's Mike Trout.

So, I have a composite team consisting where everybody else was average

American League player with Mike Trout on there, and

I get that they would score 729 runs and the difference is 55 runs.

So, that's pretty close to what Dan Graphs gets,

which is 50 runs better than average.

Okay.

So, in the next video we can talk about how this

feeds into Wins Above Replacement from Mike Trout,

and he was eight Wins Above Replacement, which is really, really good.

I mean, we could look at the leaders in Wins Above Replacement,

and we will in the next video.

Okay. So, we'll get down and

dirty with the Wins Above Replacement in the next video.

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