Thursday, August 09, 2007

Would legalizing steroids create near-perfect competitive balance?

In a recent article from Slate, Daniel Engber speculates on what would happen if MLB effectively legalized the use of performance enhancing drugs.

According to Stephen Jay Gould, increasing the quality of baseball players reduces the variance of their talent. Since increased steroid use makes players better, Engber argues, the variance will continue to decrease. And so,

"A guy like Ichiro might lead the league while batting .280. A guy who hit .250 might ride the pine ... Teams would regularly take the pennant by winning just 83 or 84 games."

This is obviously absurd, even if you accept Gould’s original argument (which I’m not sure I do).

First, even if every player in baseball was exactly a .265 hitter, there would be lots of variation in batting averages just by luck. Over 500 AB, the standard deviation would be about 8 19 points, which means that one player in 40 would be above .281 .303 or below .249 .227. Assuming 240 regulars, that’s six players above .281 .303. One of those would likely wind up close to .300 .320 or so.

And that’s if every player were identical. The current standard deviation of player batting average talent is about 27 points (according to an estimate here). How much would legal steroids reduce that? Not by the full 27 points, by any means. I’d be astonished if it dropped much at all, but suppose it went down to 20 points. That means that the SD of observed batting average (which is the combination of the 20 points of talent and 8 19 points of luck) would go from 28 33 to 22 28. Instead of the top 2% of the league being at .320 .340, they might be around .310 .330. Not really a big deal.

As for team performance, Engber’s estimate is even more out of line. Even if every team were .500 in talent, the SD of observed wins would be 6.3 wins. One team out of 40 would finish with 93 wins, and another with 93 losses. And, again, that’s the minimum possible, which only happens when every team is exactly equal to every other team . Even under a free-steroid regime, that’ll will never happen.

And why assume that taking steroids would make players and teams so equal to each other anyway? Neifi Perez didn’t turn into Barry Bonds, or even come close. Isn’t it more realistic to assume that steroids make the player a little better than he was, instead of believing that it turns great and poor hitters alike into equal supermen? Is Engber just misunderstanding the implications of Gould’s work?

My intuition, for what it’s worth, is that steroids would indeed increase both home runs and strikeouts. But if you deadened the ball a bit, to bring HRs back to normal, you’d lose a lot of free-swinging power-hitters, which would bring the strikeouts down too. And then you’d barely notice a difference.

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At Friday, August 10, 2007 12:25:00 PM, Anonymous Anonymous said...

My guess is that if steroids were legalized in baseball, the result would be pretty much what we've been seeing in recent years. The really good players will have longer careers. Steroids aren't magic potions. You can't just inject them and expect to get bigger and stronger. Steroids enable the user to recover from workout and exercise more quickly. Hence, older players can workout longer and harder, and retain the muscle tone that diminishes with age.

At Friday, August 10, 2007 2:44:00 PM, Anonymous Anonymous said...

Just ran a quick simulation, set batting average = .265 for all players, used 250 players. Standard deviation was .017 over 575 at bats. Bottom 10 were between .224 and .235. 6 .300 hitters, leader at .330.

Pretty hard to tell a real league from one year where all the difference is completely random.

At Friday, August 10, 2007 2:50:00 PM, Blogger Phil Birnbaum said...

Oh, $#!+, I think I made a mistake calculating the SD for batting average. It's the square root of (pq divided by n), right? That makes it 19 points for 500 AB, 18 points for 575 AB.

Thanks, Rally.


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