collision detection: Math proves the baseball season should be 256 games long

August 23, 2007

Math proves the baseball season should be 256 games long

Many sports fans know that a short season leads to unfairness and chaos. The shorter the season of their favorite sport, the more likely it is that a comparatively weak team will ascend up the ladder -- merely by luckily winning a few key games.

So a couple of physicists recently decided to calculate precisely how long the major-league baseball seasons would need to last to be genuinely fair. They began with this assumption: To truly control for random outcomes -- for the slim chance that, in any given game, the lesser team will accidentally beat the better one -- you'd need to play a total of games equal to the cube of the teams involved. With 16 National League teams, that's 4096 games, and 2744 for the 14-team American League.

Of course, there ain't no way anyone's going to sit through that much baseball. So they decided to scale back the pursuit of perfection, and calculate how many games would result in a situation that was not perfect, but way more fair than the current system. Their number? A full 256 games -- much more than the 162 each team plays in the current National League season. As they put it in a press release:

By adding a preliminary round to the season, and eliminating the weakest teams before regular league play begins, the physicists showed that the best team in the National League would be virtually guaranteed to be among the top two or three teams with the best records, even with a significantly reduced number of games. Although the very best team may not always end up in the lead, a preliminary round or two would at least ensure that the top teams aren't eliminated from the playoffs through simple bad luck.

I confess I know so little about pro sports that I cannot even begin to figure out whether their assumptions hold water, but it seemed like a pretty fun little finding to me.

Posted by Clive Thompson at August 23, 2007 02:20 PM

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Comments

I haven't read the paper, but it seems to be that the preliminary rounds which eliminate weaker teams are small samples and therefore a weak team may get lucky etc.

Posted by: sgt.turmeric at August 23, 2007 5:17 PM

I also haven't read the paper, but wouldn't midseason trades completely invalidate that sort of "proof"? I mean, the August 2007 New York Yankees are better than the May 2007 New York Yankees, right? Not just because some people are playing better, but because of actual roster changes. So when you "prove" that the Yankees, let's say, would only win the 2,744-game Pennant Season if they were the Best Team, which Yankees would those be?

Actually, the point of the article, I'm sure, is to reverse the whole thing and point out that in any league the Champion Team is not always the best team, where best has any criteria other than winning a championship. And to underline that it would be actually impossible in any large league to make sure that the best team wins.

Thanks,
-V.

Posted by: Vardibidian at August 23, 2007 5:43 PM

Maybe it should go back to 126 game season, instead.

Posted by: Proto at August 23, 2007 5:57 PM

I'm just charmed by the idea of a baseball season where everyone plays 4096 games, and it lasts for, like, TEN YEARS.

Posted by: Clive at August 24, 2007 3:03 PM

"how many games would result in a situation that was not perfect, but way more fair than the current system. "

Maybe I'm not fully considering this... but wouldn't ANY number of games MORE than the current be "more fair than the current system"?

I mean, it seems to me that as you increase game, up to 4096, it would get progressively more fair. Why stop at 256? Or why go that high for that matter? Who determines what "fair enough" is?

Mind you.. if it were up to me, I'd say that they should really just toss a coin at the beginning of the game to determine the winner and free up all that precious TV time. :P

-j

Posted by: digital_blue at August 25, 2007 2:21 PM

Ahahaha!

Yeah, I think I'm probably describing their intent poorly ... it's not merely to create a number of games that's more fair, but *optimally* fair given time constraints: I.e. they have some reason for believing that 256 games is actually *doable*.

Posted by: Clive at August 25, 2007 5:41 PM

http://arstechnica.com/journals/science.ars/2007/07/30/ensuring-the-best-team-wins

Posted by: kenny at August 27, 2007 4:23 AM

Awesome link -- a great write-up of this research!

Posted by: Clive at August 27, 2007 10:14 AM