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Friday, August 18, 2006
More WPA (WA minus LA) calculations
This is pure mechanical stuff. Enter at your own risk.
This was written at Fanhome, and is being reprinted here, unedited.
WPA is what it is. It’s a reflection of the change in win probability, *given* the context. It’s a purely marginal impact. While the differential of WA and LA will be directly related to the differential of W and L, there is no reason whatsoever that the relationship has to be 1:1 with no intercept. That is, there’s no reason to make them perfectly equal.
If you want to attempt the conversion, fine. But, I’m not sure it’s going to show what you intended to show, whatever it is that you wanted to show.
If you want to produce a WPAB (WPA above bench), there’s no reason to do any conversion into something else. If you want to assign a bench level of .300, this is how you do the conversion:
WA-LA = (W-L)/2 ... this is by definition
WA+LA = (W+L)*2.8 ... this is a useful shortcut
So, a .300 win% level translates to what in WPA terms?
WA-LA = (.300-.700)/2 = -.2
WA+LA = 2.8
Add the two equations and you get:
2 WA = 2.6
WA = 1.3
LA = 1.5
WA/(WA+LA)= 1.3/2.8 = .464 ... that corresponds to a .300 win percent level.
As a practical example, let’s take a league average hitter, say Chone Figgins last year.
His WA and LA were both around 13. So, WA=LA=13 for him.
WA+LA=26. If we take .464 of that, we get benchWA=12, and benchLA=14.
So, his WPA is WA-LA=0
The WPbench is 12-14=-2
So, his WPA above bench is +2.
Essentially, the bench level is 2 wins below average (if you take the .300 team level as bench level… meaning a .400 offense and .400 defense).
***
Each teams’ players has an advancement in some direction (WA+LA) of around 2.8 or so per game. If you included fielding, I’d guess it would surpass 3.
Easy enough to see. Just look at one half inning. 3 outs = .08 LA, which of course means that your 1.5 hits or walks will total .08 = WA. So, each half-inning has .16 of advancement, on a PA-by-PA basis. .16 x 18 half-innings = 2.88 per game, for each team.
(Another way: Remember that in Part 1 of LI, I reported the average change per event has .0346. With around 80 events per team, that gives us .0346 x 80 = 2.77)
***
You may also decide that starters and relievers have different “bench” lines.
Remembering again that nine innings has 1.4 movements, then the league average pitcher would have a WA of 0.7 and LA of 0.7.
As we know, it’s easier to relieve than to start. Put a league average pitcher in the role of starter, and he would come in with around -.03 wins relative to all pitchers. So, his WA/LA would be .685/.715 . And as a reliever, this average pitcher would be +.06 wins, or .73/.67
Now, where would you put the bench line? I’d probably put it at around -.08 wins relative to average (.420 pitcher, with average offense and fielding), or reducing the WA by .04 and increasing the LA by .04.
So, our benchlines for each role:
starters: .645/.755
relievers:.690/.710
The WA/(WA+LA) for each one is:
starter: .461
reliever: .493
As a practical example, let’s look at 2003. Eric Gagne was +7.3 in WPA. That was +12.4 and -5.1. A bench reliever would have been -.2, making Gagne +7.5 relative to Bench.
Jason Schmidt was +5.5, or +15.5 and -10. A bench starter would have been -2.0. So, Schmidt above bench is +7.5.
There’s another way to do it, and that’s by using PA*LI*.0346 in place of WA+LA. For example, Schmidt had 819 TBF, and an LI of .94, so his WA+LA would be 26.6, instead of 25.5. Gagne would be 306*1.98*.0346 = 21, instead of 17.5.