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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From the course by 休斯敦大学系统

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

Okay, let's see if we can get really into detail about wins above replacement.

So we'll deal with Mike Trout, 2014.

And a lot of where I've got my information on this

is from a great book, Beyond Batting Average.

By Lee Panas, I'm not sure I'm saying it right, 2010 copyright.

You can certainly get this on Amazon.

It's got a lot of detailed discussion of

a lot of baseball stats we just haven't had time to talk about.

And again, baseball stats are changing by the day.

We'll try and talk in a future video about some new stuff.

Big trend towards shifts and

also the idea of measuring catcher's defense through catchers framing pitches.

Okay, so those are two new developments which are just quickly introduced

in one of the videos.

Okay, so how many wins better than a replacement player was Mike Trout in 2014?

Well basically, remember 10 runs is a point.

So you take the batting runs above average for Mike Trout, we got 55, FanGraphs,

that's 49.9, that's fine.

Okay, then you take his ultimate zone rating, which is in runs.

Surprisingly, Mike Trout was 10 runs worse than average as a fielder 2014.

In 2013 he was much better than that, I don't know how that happened.

That's sort of surprising to me.

Then you have a position adjustment.

In other words, catchers are worth a lot because there just aren't many

good catchers.

So you get an adjustment of 12.5 runs for being a catcher.

And if you're a designated hitter and you get an adjustment of -17.5 runs.

I think these are fairly arbitrary.

That clearly designated hitters, there's a lot of people who can play that position.

Catchers, there's just not that many.

And Mike Trout's a centerfielder, so he gets a positive adjustment of 2.5 runs.

That's per 162 games.

And then you need to add on baserunning runs, in other words,

how many runs did the hitter create through his baserunning?

Now, in general that just isn't very many, okay?

Even for a really good baserunner,

it usually is less than ten runs, which is less than one win.

So you add up from fan graphs, UBR, which is base running runs above average,

in other words, that's based on how often you'll go first to third on a single,

second, first to home on a double,

not get thrown out when you're trying to take the extra base.

Then you have stolen base runs above average.

In other words, how did your stolen bases help the team score runs?

And then double plays above average.

Mike Trout didn't hit into many, he hit into very few double plays.

So he's really good at that.

And at the end would be a park adjustment.

In other words,

if you play in a park that's favorable to pitchers, you would raise your WAR.

If you played in a park that's favorable to hitters,

we would lower your WAR based on the fact your batting statistics were inflated.

Mike Trout played in one of the six or seven or eight best pitcher parks.

So his WAR's going to be higher than what our formula indicates.

So I think in a homework problem we'll do Alex Gordon, we'll get a lower WAR than

what FanGraphs has and that's because they would adjust for the park factor.

And we'll talk about adjusting for park factors a couple of videos from now.

Okay, so, what do we have on Mike Trout?

His hitting was 49.9 runs above average.

His fielding was 9.8 runs below average.

Okay, his base running, from FanGraphs, you get 1.6 runs for

his way he ran the bases, 1.8 runs for the way he stole bases, better than average,

3.1 runs in not hitting in the double plays, so that's 6.5 runs.

Now value of replacement player.

It's 200 runs per 600 plate appearance, sorry 20 runs per 600 player appearances.

In other words, basically, it's assumed by avoiding

the replacement player playing you are saving two wins per 600 plate appearances.

Mike Trout has 705 plate appearances.

So you have 705 divided by 600 times 20, or 23.5 runs.

His position adjustment would be 2.5 runs, but

he only played 157 games, so you knock that down.

Okay, so his base running was worth, again, 6.5 runs, so

you add all these numbers up here.

And you're going to get 72.5, divide that, that's runs,

divide it by 10, for wins, it's 7.25.

So that, FanGraphs gets 8, but that's I think because mainly because

he played in the pitcher's ball park, you have to pump up his batting statistics.

And we'll sort of give you an indication of how that would work, a couple videos.

So that's really where the wins above replacement comes from.

Okay, so now I downloaded from,

if you click leaders on FanGraphs you can download the 2014 leaders.

And Mike Trout did win MVP in 2014 and that's, we're glad he did.

And Clayton Kershaw won the Cy Young award, and we're glad he did,

because his wins above replacement was better.

And Cory Kluber won the Cy Young award in the American League, and

he was the best pitcher by wins above replaced, they were by a mile.

You've got to go down a long distance to find another good pitcher, okay,

on wins above replacement.

Now Mike Trout, I don't know who was second in the American League MVP in 2014,

but Mike Trout was the best on wins above replacement, so really I think most

sabermatricians, or people who try and do Moneyball, big wins above replacement is

the way you should define a player who helped his team the most.

Of course, if a team lost a lot of games, you may not want to give it to them.

That's another issue.

Jeff Van Gundy, the great basketball announcer,

says you can't have an MVP on a below .500 team.

And I mean, there's something to that.

But I don't think Lebron's ever going to be on below .500 teams for

a couple of years for example.

Or the great Steph Curry.

Okay, now, wins above replacement really caused a controversy in 2013,

which you probably know.

Miguel Cabrera won the Triple Crown for the first time,

I guess since Carl Yastrzemski, I might be wrong on that.

But that's 47, 46 years.

So he got the MVP because people said God, you won the Triple Crown,

you've got to be the most valuable player in the league.

But if you look at, basically, wins above replacement, and he wasn't even close.

Cabrera was not that good of a fielder.

Trout was a really good fielder in 2013,

and that accounted for a lot of the difference.

But Mike Trout's way above Cabrera on wins above replacement, so Nate Silver had

a nice piece in the New York Times and so did a lot of other people saying hey,

how could you give this MVP to Cabrera even though he won the Triple Crown?

Mike Trout should have got it.

Wins above replacement, and

I think now you can sort of understand where that comes from.

Okay. It's the whole player.

I mean it's the baserunning, it's the fielding,

it's the hitting, and then adjusting for the part that they play in.

I mean, Mike Trout was clearly a better player compared to Miguel Cabrera in 2013,

and he really should have won the MVP, and he did not.

Okay, I hope that's made clear a little bit how wins above replacement,

which is incredibly important concept, works.

Again, the key is to understand when you play,

even if you're not that great a hitter, when you are playing,

there's value in you playing because you're avoiding sort of a replacement

player who's a far inferior player from taking those at-bats.

And that's at estimated 20 runs per 600 plate appearances.

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