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.
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.
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.