Dark Bilious Vapors

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Home » Archives » September 2004 » Of asterisks and edges....

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09/13/2004: Of asterisks and edges....

A popular baseball legend is that supposedly Commissioner Ford Frick placed an "asterisk" next to the line in the record books next to Roger Maris's single season home run record of 61 homers in 1961, on the grounds that Babe Ruth, the previous record holder, hit his then record 60 homers in a 154 game season, whereas Maris had the advantage of 8 extra games, the major league season having been expanded to 162 games since the Era of Ruth. (That legend is false, by the way, but that doesn't keep people from stating it as gospel, though most claim that the asterisk has since been "removed".)

The assault that Seattle Mariners rightfielder Ichiro Suzuki is making on the single season hits record (set in 1920 by St. Louis Browns first baseman George Sisler, currently 257) has re-raised, at least among baseball "statheads", the question of what, if any, "edge" does a modern player get with respect to breaking a single season record by playing more games than the "old-timer" like Rurth or Sisler. In today's Hardball Times, baseball statistical übergeek (and Boston Red Sox advisor) Bill James has an astonishing article calculating Ichiro's 8 game edge; that is the extra advantage he receives in breaking Sisler's record by playing 8 more games than Sisler did. Interestingly enough, the edge that Ichiro has in breaking the hit record is much, much more significant than the edge given Maris by playing 8 more games in a season than Ruth did.

What James did was run a Monte Carlo simulation of two hypothetical players (who he calls "Marix" and "Ichirox"):

Suppose that there is a hitter who, in a typical season, given his real level of ability, can be expected to play 150 games (out of 154), bat 570 times, and hit 42 home runs. We will call this player “Roger Marix”. What is the chance that that player, given a 154-game schedule, will hit 60 or more home runs? What is the chance that that player, given a 162-game schedule, will hit 60 or more? What is the difference between the two?

I wrote a very simple computer program to run that problem.
James then ran this player through 200,000 simulated seasons:
I ran Marix through 200,000 simulated seasons of 154 games each. In those 200,000 seasons, Marix hit 60 or more home runs 806 times, or once every 248 years.

I then changed just one tiny element of the program, changing the season from 154 games to 162, and repeated the experiment. Marix hit 60 or more home runs 2,229 times, or once every 90 years. The eight extra games increased the number of times Marix hit 60 or more home runs by 177%.
He then proceeded to do the same with Ichirox:
In this study, Ichirox collected 257 or more hits in a 154-game schedule 845 times in 200,000 seasons -- essentially the same as the frequency with which Marix hit 60 or more homers. This was the operating assumption -- I actually had to re-run the study several times and jiggle the numbers to make it come out in that area, so that we would have a basis to compare the effect of the longer schedule on Ichirox vs. Marix. Ichirox had 257 or more hits 845 times, which is once every 237 years.

I then changed one number in the program, changing the season from 154 games to 162, and re-ran the study.

Given the eight extra games, Ichirox tied or broke Sisler’s record 8,462 times in 200,000 seasons, or once every 24 years. Whereas the longer schedule increased Marix’ chance of breaking or tying Ruth’s record by 177%, it increased Ichirox’ chance of breaking or tying Sisler’s record by 901%.

For me to try to tell you how surprised I am by this answer would be a waste of my time and yours, but ... I certainly did not expect this. Heisman speculated that it would be “easier, but not dramatically so.” I would have agreed. In fact, the impact is (about) five times greater on Ichiro than it was on Maris.
Interestingly enough, though, the issue of the extra games is basically unnoticed today:
The irony is that whereas the extra eight games on the schedule created a mega-furor when Maris broke Ruth’s record, the same factor is being almost totally ignored as Ichiro gets set to cruise past Sisler, even though this edge was a hamster for Maris, and is a gorilla for Ichiro. The reason for the muted reaction, of course, is that, when Maris had his moment broiling in the sun, the 162-game schedule was new, and thus controversial. But most of you reading this weren’t even born then, and the 162-game schedule has long since ceased to be a curiosity. On the one hand, the 162-game schedule has been around so long, and so many players have already “had” Ichiro’s advantage, that this no longer seems to be any big deal, while on the other hand, Barry Bonds in the last few years has so thoroughly trashed the record book that we’re all sort of numb to it. Nobody cares about that stuff anymore.
A fascinating article; go read the whole thing if you're even remotely interested in baseball statistics.

Len on 09.13.04 @ 01:39 PM CST

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