# Ivars Peterson's MathTrek

April 11, 2005

## Sosa's Corked Bat

On June 3, 2003, in the first inning of a baseball game between the Chicago Cubs and the Tampa Bay Devil Rays, slugger Sammy Sosa hit a ground ball toward second base. The impact split Sosa's bat. The Devil Rays catcher picked up one of the fragments and tossed it over to the home plate umpire, who found a cylindrical piece of cork embedded in the wood.

Sosa was thrown out of the game for using a corked bat and was subsequently suspended for seven games as a punishment.

The rules of Major League Baseball specify that any player who "uses or attempts to use a bat that, in the umpire's judgment, has been altered or tampered with in such a way to improve the distance factor or cause an unusual reaction on the baseball" be called out and ejected from the game. This includes bats that are "filled, flat-surfaced, nailed, hollowed, grooved."

How does a corked bat help a hitter? Drilling out the center of a wooden bat and replacing the wood with cork reduces the bat's weight and changes its center of mass, shifting it toward the bat's handle. Such changes suggest that the bat could become easier to swing and that it could be swung faster. Presumably, hitters could send a ball farther by using a corked bat.

Sosa himself, now with the Baltimore Orioles, admitted that he sometimes used a corked bat in practice just to put on a show for any admiring fans who might be present. He denied ever using such a bat in a game—except by accident on this one occasion.

In fact, tests on 76 bats that belonged to Sosa and were seized by officials after the incident, revealed no evidence of tampering.

Is there any evidence in Sosa's hitting statistics that might reveal that he had been using a corked bat?

Economist Paul M. Sommers of Middlebury College and a team of students took a look at the data, comparing Sosa's hitting before and after the corked-bat incident. Their findings appear in the current issue of the Journal of Recreational Mathematics.

Selected hitting statistics for Sammy Sosa, 2003:

 Category Before Incident After Incident At Bats 138 379 Hits 39 105 Extra Base Hits 18 44 Home Runs 6 34

In the case of "hits" and "extra base hits," the statistical analysis showed that there was no discernible difference in Sosa's prowess at the plate before and after the incident. And, a higher proportion of "at bats" produced homes runs after the incident than before. Maybe Sosa felt a need to prove himself at the plate and tried harder.

"If Sammy Sosa did indeed use a corked bat throughout the first part of the 2003 season, there is no statistical evidence that he enjoyed an advantage in any of the most obvious hitting categories," Sommers and his coworkers conclude.

"These results should silence (put a cork in?) his critics," they add. "They suggest that the Chicago Cubs' slugger is Slamming Sammy, not Scammin' Sammy."

Of course, there's little evidence that corking a bat actually makes much of a difference. In his book The Physics of Baseball, Robert K. Adair notes that the same effects achieved by drilling out a wooden bat and filling it with extraneous material can be obtained legally in several ways—by choking up on a bat, using a bat made from a slightly lighter wood, sawing a modest slice off the end of a bat, or trimming a bat's barrel to a slightly smaller diameter.

Indeed, the rules of Major League Baseball merely specify that a bat be no longer than 42 inches and no wider than 2.75 inches. There's no maximum or minimum bat weight.

This still doesn't stop hitters from using various subterfuges to try to gain an advantage. Players have been caught using bats doctored with not only cork but also rubber and other materials. Maybe, in the end, it's all in the mind.