The Math and Science of Baseball

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Baseball is well-known as America's pastime. For many mathematicians and scientists, it also passes as class time. Batting average is just an appetizer on the menu of number-crunching options for the avid fan. Statistical models exist to determine everything from the winner of the Cy Young award, pitching's grand prize, to a manager's contribution to the team.

Scientists, too, have a blast on game day. They've used the laws of physics, for example, to explain why a head-first slide is faster than going for the bag feet-first.

Why the best team doesn't always have the best record

Major-league baseball teams play 162 games in the regular season. While that may sound like a lot, it isn't nearly enough to ensure that the best team in the league ends the season with the best record. For the 16-team National League, that would require teams to play 256 games per season, a pair of physicists from the Los Alamos National Laboratory calculated.

Their statistical analysis indicates that for the best team of any league to be assured of having the best win-loss record, the number of games on the schedule should be roughly the number of teams cubed. A schedule with that many games overcomes the randomness that permits a lesser team to prevail in any given matchup, according to the physicists.

Playing fewer games, of course, gives underdogs more of a chance to reach the playoffs and sometimes win the World Series, as the wild-card Florida Marlins did in 2003.

Mathematical model judges fielding ability

Should Alex Rodriguez, the New York Yankees third baseman, go back to playing shortstop as he did for the Texas Rangers? According to a mathematical model developed by Shane Jensen at the Wharton School at the University of Pennsylvania … yes, he should.

The model measures factors such as how many runs a fielder saved or cost his team. It ranked Rodriguez as the best shortstop in the league before he was switched to third base to accommodate Derek Jeter, the Yankees' longtime shortstop. According to the model, Jeter is one of the worst shortstops in the majors.

The statistics of managerial style

Stats let managers keep close tabs on the performance of their players. Steve Wang, a statistician at Swarthmore College and avid Yankees fan, has devised a statistical means to keep tabs on managers as well.

He examined data on everything from how often a manager goes to the bullpen, to the number of lineups used in a season. Such factors went into an algorithm to determine managerial style. Certain styles, he notes, might be more effective with certain kinds of teams.

"A manager who prefers to stay with his starters might be best-suited for a team with veteran starting pitching, whereas a team with fragile young arms might do best with a manager who uses his bullpen aggressively," he said in a news release.

Head-first slide is faster

Every fraction of a second counts when a player rounds third and races to beat the throw at home plate, which raises the question: is it faster to slide feet or head first?

According to David Peters, a physicist at Washington University in St. Louis, head first has the edge. For one, arms are lighter than legs, which means as the body rotates, arms extend out a bit farther than the legs. For another thing, the feet give an extra push.

That said, many players still prefer a foot-first slide. They can pop up easier, instead of sliding by the bag, for starters. They also face less risk of an injury to their hands that could keep them out of the batting lineup for months.

To catch a fly ball, keep an eye on it

It may be the most repeated advice in all of ball sports: "Keep your eye on the ball." It's also what outfielders do to catch a pop-up fly, according to researchers at Brown University, who watched student ballplayers catch virtual fly balls in a virtual reality lab.

The researchers found that good players position themselves so that it appears the fly ball is neither speeding up nor slowing down. If the ball seems to be speeding up, the player should move back. If it’s slowing down, they should head in closer.

The findings, however, fail to explain Willie Mays’ famous grab in Game 1 of the 1954 World Series, shown here. He caught the ball over his shoulder and without even looking at it.

Why hitters take a few pitches

Often the world's best sluggers will watch a pitch or two pass over home plate and into the catcher’s mitt. Some of them are fastballs that could have easily been smacked out of the park. Why do they do it? To calibrate the ball’s track, explained Ken Fuld, a psychologist at the University of New Hampshire.

“The batter purposely leaves eye contact midway through a pitch and makes an anticipatory saccade (an eye movement) to the point just in front of where the ball crosses the plate. If the ball seems to rise (which it physically can't if it was thrown overhand), it is traveling faster than the batter initially thought, but now the batter has calibrated it," he explained in a news release.

The next time the same type of pitch is thrown, the slugger has an advantage and just may knock it out to the cheap seats.