from Amazon
Friday, March 20, 2009
How to split
Apparently, this isn’t clear as to how not to apportion credit:
Ok, now let me tell you why this splitting-issue is not the right way to proceed. And I’m going to use hockey as an example. In hockey, everyone on the ice for the scoring team gets a “plus 1”, and the players on the ice for the opposing team gets a “minus 1”. This means that every goal has five pluses and five minuses. If we follow the logic in this paper, this would entail taking this one goal, and somehow splitting it up among the players on the ice. Perhaps giving the five guys on the scoring team a total of +.5 goals, and the give guys on the opposing team a total of -.5. And then, among the scoring team, deciding who gets the share of the +.5, like maybe +.25 for the goal scorer, +.10 for the playmaker, and +.05 for the other guys on the ice.
Assume you have a player, which I’ll call Obby Borr. He’s a +120 for the Bruins, and when he’s not on the ice, his teammates are +0. Also assume that Borr plays with everyone on the team. If you proceed with a “splitting” arrangement, Borr will end up being credited for something like +60 goals, if he’s lucky. Likely, under the splitting-system, he’ll be even lower. However, in my system, he gets +120.
You see, Borr plus his teammates is +120. All of his teammates are zero. Therefore, Borr plus zero is +120, making Borr equal to +120.
You have to treat each player as if he’s his own universe, and you adjust for the extra parameters. The same logic applies to strength of schedule, or how to credit the DP between the 2B and SS, and several other concepts.
Splitting doesn’t work.
Let’s think about it in baseball terms then. Let’s say that you have Pedro v Pujols, and Pujols gets on base 4 times out of 10. So, that’s +0.6 above average. Would you split that, and give +0.3 to Pujols and +0.3 to Pedro. (Plus is good for the hitter and bad for the pitcher)? Let’s say we have Pedro v Chipper and Chipper gets on base 0 times out of 20. So, that’s -6.8 relative to average. Would you split that as -3.4 for Pedro and -3.4 for Chipper?
Suppose you say that “yes! that IS what I want to do”. Well, then you’ll end up with let’s say Pedro allowing 250 baserunners to 1000 batters faced. That total is -90 relative to average. In the 50/50 split, that means that if you add up each of the individual matchups (Pujols and Chipper and everyone else), then you end up with Pedro only being -45. Does that make sense? Well, no. His competition was already an average batter. He faced, as a group, hitters who get an OBP of .340. There’s no reason to try to do any kind of splitting the difference here.
Strat-O-Matic, for example, realizes this. (In Strat, they give 50% of the outcome to the batter’s card, and 50% to the pitcher’s card.) So, they give Pedro a rate of 80 baserunners per 500 batters faced, because they know in the other 500 batters faced that he has “no influence” on, he’s 170 / 500 (i.e., .340 OBP). The total is 250 baserunners per 1000 batters faced. If you focus on his 80/500, you realize that this is -90 relative to average.
This is why you can’t just “split the difference” IF AND ONLY IF the universe of your competition is indeed average to begin with. This is the idea behind WOWY (With Or Without You), and why it works well with pitchers/catchers at a career level, or pitchers/SS at a career level or in hockey or basketball on a seasonal level: those players face a diverse enough context that they can be said to be the sole driver to their performance (with some minor adjustments).
It fails in the case of say Mark Howe and Brad McCrimmon when they were +85 players that year, because they were defense partners on practically every shift. It fails for Dionne/Taylor/Simmer because they were out there as one unit for the Kings. It fails for Trammell/Whitaker, because they are always together.
This is why you have to be very careful. In some cases, you can do the 50/50, and in most cases, you should not.
Is this any clearer?
Works for me, but then I understood it the first time too.