The Mathematics of Hitting Streaks

By Chris Gorski
Inside Science News Service

The 30-game hitting streak of Washington Nationals third baseman Ryan Zimmerman came to an end Wednesday, after a hitless game against the San Francisco Giants. He is, however, one of only 21 players have hit in 30 straight games in the past 50 years.

The rarity of such a streak means it could be the longest in major league baseball not just for this season, but for years to come.

It’s impossible to predict how long any streak will continue. Many baseball players depend on superstition to keep hitting streaks going - the “lucky socks” theory. Scientists, specifically statisticians, rely on hard numbers to predict the future. Neither group has developed a reliable forecasting method because superstition can’t be quantified and, as it turns out, there is an as-yet unexplained factor in hitting streaks that defies the best statistical models.

Trent McCotter, a baseball historian, published an article in the 2008 Baseball Research Journal explaining that considerably more hitting streaks have actually occurred than statistical models predict. That simple finding is raising questions about both baseball and the field of statistics.

Mathematicians usually compute the chances of a hitting streak by multiplying a player's chance of getting a hit in any given game, about 76 percent for a .300 hitter, by itself repeatedly. McCotter examined the real historical record of hitting streaks. Then, he took each individual season of every player from 1957 to 2006 and pulled out all the games where players did not record at bats. He used a computer to reorder the remaining games 10,000 times and calculated the average number of streaks.

He counted far more hitting streaks in real life than in his model. McCotter couldn't find any numerical explanation for the discrepancy.

"We've kind of gotten rid of all these obvious things that might explain it, so what else is there?,” he said. “[A player's] probability of a hitting streak isn't what it might seem given the final batting average at the end of the year.”

This leaves statisticians with a number of possibilities that are difficult to study mathematically. A hitting streak could affect the behavior of the hitter, the pitcher, managers, or even the official scorer, who determines if plays are hits or errors.

Steven Strogatz, a professor of applied mathematics at Cornell University in Ithaca, New York, said "first the dogma was that players are hot, players have streaks. Then the dogma was, no that's not right, everything is just coin flipping. And so, McCotter is saying, no, that's not right either. It's not just coin-flipping, there is some correlation from game to game, that players do something to keep their streaks going."

The longest hitting streak in baseball history is Joe DiMaggio's legendary 56 gamer in 1941. Strogatz investigated the probability that anyone in baseball history would have achieved a similar record. What he found indicates that, no matter the underlying reason, the odds of anyone challenging DiMaggio are long indeed, as Zimmerman can now testify. Though not as unlikely as many had previously suggested, statistically speaking streaks longer than 55 games should happen about once every 500 years.