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Thursday, April 17, 2008
Loss Shares and Win Advancements
Studes has a little program as to how to calculate WPA Above Baseline. He actually taught himself PHP so that we have a simple calculator. Sweet. I think the algorithm needs modification though. He says:
Here’s how the math works:
- Combine Win Advancements and Loss Advancements (for a total of 27).
- Calculate the factor, which is .411 plus .178571 times the replacement level (in this example, 0.4824284).
- Multiply the combined win and loss advancements times by (1-(2*the factor)), or 0.9.
- Add the original WPA (9.0).
This was based on your standard league-leader season of 18 Win Advancements (WA) and 9 Loss Advancements (LA)
Let’s figure out how we should do it. The average team will have roughly 1.4 WA and 1.4 LA per game. WA minus LA is ALWAYS equal to a team’s (W minus L)/2.
Anyway, if you set the team baseline level at .300, that means W-L = .4 per game. That would mean that a baseline team would have 1.3 WA and 1.5 LA. Game Advancements (GA) = WA+LA. So, we can see that the baseline level of WA/GA = 1.3/2.8= .464
If the team baseline level is .300, then that means that the offense and defense is each at around .400 (which is what I used in Studes’ program).
Anyway, you take the 27 GA (which is 18 WA and 9 LA), and multiply that by .464 to get you your WA of 12.5 and LA of 14.5, or -2 WPA. With a WPA of 18-9=9, then this player’s WPA above baseline is 9 minus -2 = 11.
So, I think that studes has a little bug about the “*2” part.
***
Studes makes a similar type of problem when he says:
Smith is 94 Win Shares above average (Win Shares minus Loss Shares) while Trammell is 106 Win Shares above average.
As I wrote to studes, actually, you have to do (WS-LS)/2 to do “above average”. This is easily proven that if a team has 300 WS (100 wins) and 186 LS (62 losses), then they are +19 wins above average (+57 win shares above
average).
Update: studes replied with
Well, I would say they’re 19 games above average and 38 wins above average. We run into this all the time when talking about number of games a team is above average (different people do it different ways), and I’ve settled on the different definition between games and wins as a way of navigating the disconnect.
So, we have to be very careful in knowing whether we are talking about “games above .500” and “wins above .500”.
In both cases, what you’re advocating is at odds with how 90% of baseball fans think about baseball. In the latter case, most fans say “games” when they look at the absolute difference between wins and losses. I agree that this is wrong in a technical sense, but I also like to communicate in a way that can be understood. So I use “wins” by keep the scale the same.
I don’t differentiate between a .300 replacement team having a .400 replacement level set of offensive and defensive skills because I think this is also a nuance that 99% of fans won’t get, and I think it’s just as valid to think in terms of team replacement level instead of worrying about components.
If you input .300 into my PHP script instead of .400, you’ll see that it works fine.