THE BOOK--Playing The Percentages In Baseball

Tango, how important or how accurate is changing WPA into wins and losses. I mean, is this something I can calculate and show to someone that X player is more or less valuable than they appear?
Thanks ^^

Wow.  Cannot follow that.  In this…

Now, at the team level, this makes the average team worth 40.5 WA and 40.5 LA.

Where does the 40.5 come from?

Since each game the adjusted WPA will have 0.50 WA and 0 LA for the winning team and 0 WA and 0.50 LA for the losing team, 81 wins and 81 losses will give you 40.5 and 40.5.

Another (simpler, I think) approach:

There is a constant relationship between WPA% and Win% (WPA% being WA divided by (WA+abs(LA)).  That is:

Win% = (WPA% minus .411)/.1786

Multiply that times GA/1.4 and you have a player’s wins.  Subtract that from GA/1.4 to get losses.

Greg Maddux, who has a 351-222 record in “real life”, has a 353-137 W/L record by this methodology.  And it’s off for extreme players like Mariano Rivera, who is 175/-1 by this methodology.

But what do you think?

81 wins and 81 losses will give you 40.5 and 40.5.

Got it.  Thanks.

I just played with my formula and got a better one.  I was using 2.8 GA per game and should have used 1.4.  The better formula is…

Win%=(WPA%-.321)/.3571

That will give Mo a 131-43 lifetime record, and Maddux gets a 299-191 lifetime record, which seems reasonable, too.

Here’s the reasoning:

- An 0-10 team will accrue 4.5 WA and 9.5 LA, for a WPA% of .321.

- Each loss turned into a win increases the WPA% .0357 points, so that a 10-0 team has a .679 WPA%.  This increase is a straight line.  Each increase in win% of .1 increase WPA% .03571, from .000 to 1.000.

- So you take the .321 as equal to a .000 winning percentage, and scale the difference by .3571 (which is .03571 divided by .100).

By the way, when I plus this into your 2004 Mo example, I get the exact same answer.  I had no idea Mo Vaughn had such a good year.

Gotta give my kid a bath… let me think about it.  Maddux in your case ends up with +54 wins above the average player and Mo is +44 wins.

That’s what Fangraphs is pretty much showing.

I recognize the .321 number you have (as .45/1.40) and I imagine if you shorten my whole process, you’ll probably end up with what you have.

Let me give it the once over to make sure that your formula ends up being the same as mine.

Note: we really want to do this at the game level, but we’ll probably end up with the same thing anyway.

Mo=Mariano Rivera

Mo=Mariano Rivera

Really??? 

Note: we really want to do this at the game level, but we’ll probably end up with the same thing anyway.

That I understand.  My approach is probably best for careers instead of seasons, though it’s not really terrible for seasons.

I recognize the .321 number you have (as .45/1.40) and I imagine if you shorten my whole process, you’ll probably end up with what you have.

Right.  That’s another way of explaining how it’s defined.

Ok, I will redo my wiki post, but these time use variables instead of examples, and let’s see if we can get a quick equation, and if it matches studes.

Let’s go…

W = (WA - .45/1.40*(WA+LA))*2
L = (LA - .45/1.40*(WA+LA))*2

W+L
= (WA+LA - 2*.45/1.40*(WA+LA))*2
= .357*(WA+LA)*2

WA%
= WA/(WA+LA)

win%
= W
/(W+L)

= (WA - .45/1.40*(WA+LA))*2
/ .357*(WA+LA)*2

= (WA - .45/1.40*(WA+LA))
/ .357*(WA+LA)

= WA/(.357*(WA+LA))
- .45/1.40/.357

= WA%/.357
- .90

= (WA%-.321)/.357

Cool, it works.

That’s the most confused I’ve ever been after reading a Tango post… the comments section cleared it up though.

Awesome, Tango.  This…

Win% = WA%/.357 - .90

... is probably an easier formula to communicate.

Note that:
win%
= (WA%-.321)/.357

is really:
= (WA%-.321) * 2.8
= (WA%-.321) * 1.4 * 2
= (WA%-.45/1.4) * 1.4 * 2
= (1.4*WA%-.45)*2

The 1.4 is the total WA+LA for that game (or the average for the league per game if you need something quick).

1.4 = WA+LA
0.5 = WA-LA

Add up the two, and you get:
1.9 = 2*WA
0.95=WA
making
0.45=LA

So, the 0.45 is really: (GA+.5)/2-.5, or (GA-.5)/2

So, this:
= (1.4*WA%-.45)*2

is really:
= (tGA*WA%-(tGA-.5)/2)*2

which is:
= 2*tGA*WA% - (tGA-.5)
= tGA * (2*WA% - 1) + .5

I would recommend therefore that we present it as:
win% = tGA * (2*WA% - 1) + .5

where tGA is the number of game advancement for that team in the game.  The average is around 1.4, but it could be 1.1 or 1.9 or whatever. 

If David were to ever implement this at Fangraphs, that would be real quick to do.

Albert Pujols: career WA% is .611.  That converts into .812 win%.

Barry Bonds: .629 career WA% translates to .861 win%

Adam Everett: .436 career WA% is .322 win%

Mariano: .589 WA% is .750 win%

Roger Clemens: .555 WA% is .653 win%

Pedro: .571 WA% is .697 win%

Looks good to me…

***

Now, what happens if we eventually add fielding?  Well, the Game Advancements will go up from 1.4 for each team game to say 1.6 or 1.8 or something.  That increases the multiplier.  However, an average fielder would add as many personal WA as he would add personal LA, thereby reducing his WA%.

Overall, I think, the translation would work out to exactly the same (for average fielders).

Also, I think an easier version of the generic form would be:

WPA% * 2.8 - 0.9

Just turned around the division.

I was trying to think through the impact of adding fielding.  You know, if you just look at WPA, then individual pitchers and batters are about even (for example, both Maddux and Schmidt have 54 WPA).  But if you look at WPAR (I set a replacement level of .350) then Maddux outranks Schmidt by 128 to 95.  Which makes sense, cause Maddux participates in more GA.

Now what happens when you add fielding?  As you say, it increases the GA for everyday players because you’re essentially adding two “plays” for each in-park batted ball.  And perhaps it brings players like Maddux and Schmidt back to an “even” ranking in WPAR?

It would be interesting to track a few games using a better allocation for fielding model and then compare it to the Fangraphs result.  Maybe I should pull out that old spreadsheet again and try it.

All numbers for illustration.

Suppose that, in some situation, a ground ball out is worth .05 win advancements. In a fielding-aware WPA model, would it go something like this?

* Pitcher surrenders ground ball, receives .03 LA.
* Shortstop fields ground ball for out, receives .08 WA.

Yeah, looking over it, the problem is that you need to find somewhere to award fielders LAs as well.

Colin: I refer you to wiki entry #40:

http://www.tangotiger.net/wiki/index.php?title=Mailbags#Defense_-_splitting_credit

Yes, exactly.  I currently have a “split” method in my spreadsheet, but that was only meant to be a placeholder until I put in some better options.  Unfortunately, I haven’t had the time to build those better options.

I knew something was bothering me.  There are 2.8 game advancements per game, not 1.4.

So, my numbers are wrong here.  I think if you change the 1.4 to 2.8, we are ok.

This means that alot of the great players will get a win% over 1.000.

Gotta put my kid to bed now…

I was right the first time?  Dang.

Okay, so my new generic formula for Win% is…

WPA% * 5.6 - 2.3

Clemens is 200-48
Rivera is 87-1
Pedro is 116-14