Does Joe DiMaggio's Streak Deserve an Asterisk?

Oct. 7, 2007 — -- October is the month of baseball's World Series, so it is an appropriate time to consider "56*," an article just published in the Canadian magazine Walrus. In it author David Robbeson asks, "Was Joe DiMaggio's fifty-six-game hitting streak the greatest feat in all of sports or merely a product of its time?"

The article strongly suggests that DiMaggio's legendary record might deserve an asterisk similar to that many have attached to Barry Bonds' recent breaking of Henry Aaron's home run record.

Robbeson's Argument

Robbeson's argument, which has been made before but never, I think, so thoroughly, revolves around one Dan Daniel.

Daniel was a baseball writer who had covered the Yankees for a long time, was a personal friend of many of the players, traveled with the team and submitted his expenses to it. He was also the official home-game scorer for the Yankees. He decided, among other things, whether any at-bat should be adjudged a hit by the batter or an error by the fielder, yet he was, in Robbeson's words, "as much a PR man as a reporter."

Specifically, Robbeson cites two games in the middle of the streak, the 30th and 31st, when DiMaggio managed just one hit. In each of these games, the hit was suspect and could well have, and perhaps should have, been deemed an error.

The first involved a bad bounce that hit off the shoulder of shortstop Luke Appling after he reached for it. Hits and errors were not immediately recorded on the scoreboard so, Robbeson writes, some spectators believed the streak had come to an end. Daniel, however, called it a hit.

The 31st game of the streak involved a fielding play that was also arguably an error on the part of Appling, who got his glove on the ball, but dropped it. Again Daniel scored it a hit.

How could this have happened without arousing more controversy? Robbeson argues that despite the present Olympian status of the streak, at the time American involvement in World War II was looming and attention to the then-29-game streak and its fluky extension was not intense and baseball attendance was quite low. Amazingly, the attendance in 22 of the games during the streak was less than 10,000.

In short, the streak wasn't that big a deal then.

Gould's Counter

There is no clip of the fabled streak by the Yankee Clipper on YouTube to decide the matter, so it will never be conclusively settled. There is, however, a counterargument, well stated by Steven Jay Gould.

Gould argues that these two, at best, weak hits as well as a couple of others seem out of place in a record set by a mythical hitter like DiMaggio. The reason is that people tend to believe that streaks are a causal consequence of courage and competence and that their lucky extension is somehow an affront to our conception of them. DiMaggio is too great a figure, people unconsciously think, to have his streak depend on such thin threads.

As psychologists Amos Tversky and Daniel Kahneman demonstrated years ago, however, people fervently mistakenly believe in hot hands, in clutch hitters, in coming through under pressure, and don't want to think of streaks as simply matters of luck. But luck is sometimes just that, and good hitters benefit more from it than do bad hitters. They will generally hit in longer streaks than will bad hitters just as heads-biased coins will result in longer strings of consecutive heads than tails-biased coins will.

In other words, DiMaggio's streak remained intact because of these calls by Daniel, but so what? Some lucky breaks and a dubious call or two are to be expected in a long streak.

Streak Probabilities

Whether the streak was tainted by a biased scorer operating in a different historical context and under much less fierce media scrutiny can't be cleanly judged now. We can, however, understand something of the improbability of DiMaggio's feat by doing a few little calculations. (This is the time for mathphobes to check out.)

His lifetime batting average was .325. If, therefore, we assume as a first approximation that he generally got a hit 32.5 percent of the time he came to bat and hence made an out 67.5 percent of the time and that he came to bat four times per game, then the chances of his not getting a hit in any given game were approximately, assuming independence, (.675)^4 =.2076.

Remember independence means he got hits in the same way a coin that lands heads 32.5 percent of the time gets heads. So the probability DiMaggio would get at least one hit in any given game were 1 - .2076 = .7924.

Thus the chances of his getting a hit in any given sequence of 56 consecutive games was (.7924)^56 = .000 002 192, a minuscule probability indeed.

The number of times in a season that a hitter with a .325 batting average might expect to hit successfully in exactly 56 consecutive games is still tiny - .000 010. This number is determined by adding up the ways in which he might hit safely in some string of exactly 56 consecutive games.

The probability and expected number of streaks of length at least 56 straight games is about five times higher, but DiMaggio hit in only 139 games so his chances were somewhat less than this multiple of 5.

The conclusion is that such an extraordinary achievement "should not," probabilistically speaking, have yet occurred in the history of baseball.

There are many differences and a few similarities between Bonds' record and DiMaggio's. I leave them for readers to ponder.

Essential links:

http://www.walrusmagazine.com/articles/2007.10-joe-dimaggio-56-games/

http://www.nybooks.com/articles/4337

John Allen Paulos, a professor of mathematics at Temple University, is the author of the best-sellers "Innumeracy" and "A Mathematician Reads the Newspaper," as well as of the forthcoming (in December) "Irreligion." His "Who's Counting?" column on ABCNEWS.com appears the first weekend of every month.