Friday, September 26, 2008

Modal's Sporting Goods; The Best Value For Your Alternate Universe Dollar

'If Buckner had fielder that grounder, then he would have beaten Wilson to the bag.' Maybe, maybe not. Usually, statements are true when they tell it like it is, false otherwise. But how is it with something that never happened?

Answering such counterfactual questions- so called because the first clause is counter to fact- is difficult not just because we don't know how it is, or could have been, but because, being counter to reality, there may not be anything at all to know.

One of the neat things about philosophy is how a little problem like this has cosmic implications. The philosopher David Lewis argued that any possible state of affairs actually exists, but at another possible universe, different from ours in just such ways. For Lewis, there exists a world where Buckner makes the play to retire the side, forcing another extra inning (remember, the tying run scored on the wild pitch), and there's a world where Buckner makes the play but Wilson beats the throw, and on the next play a grounder goes through Boggs' legs, and so forth. (There's also a world where Tampa wins the division and the Yankees finish third. Crazy, I know.)

The reason for this infinite explosion of universes is to provide grounds for the truth of counterfactual statements. Without such universes, there simply is nothing- nothing exists- that makes counterfactuals true or false; there'd be nothing to know. So according to Lewis, 'if Buckner had made the play, Wilson would have been out' is true if the existent possible world where that happens is closer to this one than a world where he makes the play and he's safe.

Don't worry, I'm not going to explain what makes one world closer than another. (Though it is pretty crucial for the plausibility of all this craziness. For more, here's the wikipedia on "modal realism.")

The point of all this, as I so often have to say to my class, is the Most Valuable Player award.

For some reason, the MVP has to play for a contending team. Now, there might be many different definitions of 'valuable', or, 'most' or 'player', I imagine, but its best to be on the same page with these things. If I say "yankees suck," and some yankees fan says "sure, if by 'suck' you mean 'awesome'", besides from forgetting to conjugate properly, this would be a pretty superficial, if short lived, agreement.

I think the definition of the sort of V that one finds in MVP is best put in counterfactual terms- I think the MVP is the player who answers this question: The hypothetical absence of which player would cause that player's team the greatest loss? Or, in other words and letters, if a player x was absent, then which team y would suffer the most? Player X is your MVP. That is, the most valuable thing is the thing which, if taken away, would harm whatever it was taken away from the most.

So if you can live without your hair, as some of us must, but not without your liver, then your liver is more valuable than your hair. And if your team can win without Manny Ramirez, then Manny ain't that valuable.

Now, what does this have to do with contending? As the Manny example indicates, the better a team is, the more able that team is to withstand the loss of any one player, even if that player is great; I'd say there's an inverse relationship between a players' value and the competence of his team. It's the worst teams, not the best, that can least withstand the hypothetical absence of their best player. The closest possible worlds are those where a bad team loses its best player and plays even worser...

'Well now,' one might say, especially if that one is you, 'take away a great player from a last place team, and they're still last.' Well, yes. But take Manny away from a wild card leading team, and they're still a wild card leading team, even though he's put up monster numbers. And standings are relative to the other teams- you can win close to 95 games and not win a division (stupid tampa), so I think its the number of wins that counts. A last place team may win 65 games with a star player, but, who knows, 50 without him. A first place team may win 96 games with a star player, 94 without him, as they are better able to absorb the blow.

Pedroia is getting a lot of MVP attention, and there's no doubt that he's a kick ass ballplayer, and the heart of this team. But if players on noncontending teams or the Twins are counted, as they should be, he doesn't really stand out. Only on the assumption that only a contending non-Minnesota team is worthy of MVP consideration puts him at the top (even though, of course, Mourneau won in '06.)

Pedroia does well in some traditional and count stats, and not in others. The top 3 in BA: Mauer .327, Pedroia .325, and Bradley .324. But Bradley is far and away ahead on OBP: .439, Mauer second at .413, and Pedey's 17th, at .375. Bradley is 3rd in slugging (behind Arod and Quentin), Youkilis 4th, Pedroia 18th at .493. Bradley leads in OPS, Youkilis is 4th, Pedroia's 18th at .868

Bradley has only played in 124 games, which hurts, whereas Pedroia is tied for third in games (and is 3rd in plate appearances, which helps his count stats.) Pedey leads in runs with 118, with the other contenders not in the top 5. He leads in hits with 210 and doubles with 54, but Aubrey Huff, of all people, leads with 329 total bases (Dustin is 4th), and Huff is 3rd in doubles with 48. Huff also leads in extra base hits with 82, Youkilis and Mourneau tied for 4th with 74. Pedroia's 6th with 73. And Youkilis has played plenty of games.

But it's not clear how much these tell us about the counterfactual situation. Some fancier stats aren't decisive, either. Bradley is way ahead in adjusted OPS+ with 165, Youkilis is 4th with 143, Pedroia's not in the top 10. Grady Sizemore leads in Runs Created with 132, Josh Hamilton is next with 125, and Pedroia 3rd with 122, Morneau 7th, Mauer 19th.

It seems to me that stats like 'value over replacement player' (VORP) are in effect counterfactual- if player x were absent and was replaced by an average player, how many 'value points' would the team lose?- in which case such a stat would be the best indicator for MVP. In this category, Pedroia is 3rd, behind Sizemore and ARod. Huff is 4th, Bradley 5th. Youk 8, Mauer 9, Mourneau 12.

But VORP is relative to a position- its easier to have a high VORP at 2nd than at 1st, and also it doesn't count defense. And particularly relevant to my conception of MVP is that it doesn't take into account the idea that a player's value is inversely proportional to his teams awesomeness, as discussed above. (The Indians would probably be more worse without Sizemore than the Sox without Pedey. And of course, as everyone knows, the Yankees would be even better without ARod and with a 42 year old Scott Brosius instead.)

But it's right about here where the fancy numbers exceed my present state of knowledge, so I have nowhere else to go. And there being another me in another possible world who knows this stuff doesn't help. As a philosopher, I'll simply say I think this is the right direction, and let the guys in the lab coats make the call...

That, and far be it for me to argue against the man. Pedey's 20/21 in stolen bases are remarkable, his f yeah attitude is f'in awesome, he curses and gets dirty, and he hits line drives like they were giving him lip.

I'm sure Pedroia is saving no-hitters in other possible worlds, and that if he were gone, and the Sox had to play Cora or Mark Bellhorn at second, they'd be a lot worse. Because they have a 7 game lead on the Yankees. (Ha), they'd probably would be the wild card without him, though of course it would have been a lot less fun. But just Pedey's swing, let alone the defense, speed, and attitude, for now, at least, make me glad I live in this world.... to the extent that I do, of course.


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Leonard said...

Hi Blogger,

It brings joy to my heart to see you devote the entirety of your discussion of counterfactuals to modal realism. Take that, Kripke! Lewis FTW!

Thanks and Regards,
A Philosopher