56: Joe DiMaggio and the Last Magic Number in Sports (47 page)

“You can try to factor in all those things a batter is going through until you are blue in the face,” said Jim Lackritz an emeritus professor of information and decision systems at San Diego State, whose 1996 paper
Two of Baseball’s Great Marks: Can They Ever Be Broken?
demonstrated that the odds of someone hitting .400 again are much better than the odds of someone hitting in 56 straight games. “But ultimately it won’t have much impact on the probability of a hitting streak.”

That’s where I disagree. It’s certainly true that the best statistical models can work to establish a fair distribution of probability. And it’s also true that many of the myriad in-game factors may mitigate themselves over a period of time, a full season say, meaning that hazarding a rough probability estimate can make sense. That’s why sophisticated stat processors like Bill James can sometimes do a reasonably good job of predicting player performance and why decades-old, dice-and-card board games such as Strat-O-Matic and APBA can sometimes come fairly close to replicating a player’s statistics over a given year.

But trying to estimate hitting streaks doesn’t follow. First of all, even an extraordinary streak of 40 or 50 games is a very small sample size and thus very likely to have departed from any underlying probability. More relevant: The conditions of a streak are far less knowable or predictable than the conditions in “regular games.” There is no such thing as an “ordinary” at bat when a hitting streak is on the line. These are highly charged and highly unusual events. The batter himself, the pitcher, the runners on base, the fielders, the managers and the fans are all to some larger or smaller degree impacted by the fact that a streak is in progress. There is simply no way to gauge this impact or its consequences.

Consider another result of Arbesman and Strogatz’s simulation. It revealed the players who most often had the longest hitting streak during those 10,000 baseball histories. The list—headed by 19th century ballplayers such as Hugh Duffy and Wee Willie Keeler—is much like one that Michael Freiman produced in his paper six years earlier and also similar to one published by LSU finance professor Don M. Chance in the October 2009 issue of
Chance
. (Now what are the Chances of that combination?) Chance ranked the top 100 hitters of all time in terms of who was most likely to have had a long hitting streak. In short, he figured the list by determining his own version of streak average
⁴
and also factoring in the length of a player’s career. Obviously, the longer the career went on, the greater was the opportunity for a streak to occur.

Chance’s list in some regards feels spot on. Ty Cobb, Keeler and George Sisler were each ranked among the top five most likely to have a long hitting streak and each does in fact have one of the five longest hitting streaks of alltime. But of the other top 20 most-likely on Chance’s list, 15 have never had a streak of even 30 games, and none but the three mentioned have hit in more than 31 straight. DiMaggio was 28th on his list; Pete Rose was 53rd. These inconsistencies hardly render the list wrong or without relevance—no one would expect real life results to exactly mimic probabilistic estimates—but it does seem far enough off from actual events to at least give pause. Maybe guys who go on hitting streaks have something about them that guys who don’t don’t.

Other recent work more pointedly addresses the disparity between probability guesses and actual player performance. Jim Albert, a math professor at Bowling Green, concluded in a 2008 study that while his probability model “explains most of the streaky hitting in baseball,” it also made clear that “there are some players that appear to exhibit more streakiness than one would predict.” Then there’s the 2008 paper by Trent McCotter, then a student at North Carolina, titled
Hitting Streaks Don’t Obey Your Rules
. McCotter took every batter’s game log from 1957 through 2006 and randomly shuffled these game logs 10,000 times to see what hitting streaks would materialize. His results revealed that there were
more
actual hitting streaks than were predicted by chance. (More or less is not really the issue here. The main point, for our purposes, is that reality did not match up with probability theory.) McCotter’s study, as he summarized, “seems to provide some strong evidence that players’ games are not independent, identically distributed trials, as statisticians have assumed all these years and may even provide evidence that things like hot hands are a part of baseball streaks.” So, might some hitters be more streak prone than others who produce hits at a similar rate?

“From a statistical standpoint you’d like to say that it’s simply a reasonable fluke that of all the .325 hitters DiMaggio was the one to put together the longest streak, but there is a very serious stumbling block to that thinking,” says Bill James. “And that is the 61-game hitting streak that DiMaggio had in the Pacific Coast League. How do you account for for the fact that there was one player having two streaks of that length? You can’t. It makes you think that other things must be in play.”

WAS THERE SOMETHING
about Joe DiMaggio that suited him to hitting streaks? If so, was it tied to his unwavering style of play, an approach and commitment to every game that made him, according to peers, the most consistent player they were ever around? Was there something relevant to DiMaggio’s unflagging hustle, a trait shared by Pete Rose, history’s other great hit-streaker? And what to make of DiMaggio’s extraordinary combination of power and a propensity to make contact—an ability that appears to have some usefulness in maintaining hitting streaks. Home runs cannot be fielded after all, while strikeouts have no chance of worming their way to a fluke hit.
⁵
Maybe DiMaggio’s acute self-consciousness helped him. Behavioral research has suggested that people who are generally self-conscious, as DiMaggio clearly seemed to be, are more easily able to thrive in situations that cause a high level of self-consciousness (such as a hitting streak) because those people are more accustomed to being in that frame of mind. Undoubtedly DiMaggio had a keen understanding of the need to seize important moments on the baseball field and also had the ability to seize them.

One factor that leads many players, as well as most math professors, to say that the streak will not be broken is the extent to which it lords above all others. This is baseball’s ultimate statistical outlier. No one has gotten to within even 80% of the record. Having the single-season streak record at 56 and the next highest streak at 44 is analogous to Roger Maris’s single-season home run record of 61 being followed by a runner-up at 48. In fact there have been 28 player seasons of between 48 and 61 homers.
⁶
Hank Aaron’s career home run record of 755 would be followed not by Babe Ruth’s 714 and Willie Mays’s 660, but by some player’s 593. Hack Wilson’s single-season standard of 191 RBIs would be seconded by 149, while in fact the RBI totals of 45 player seasons have fallen between those numbers. All other major records—Orel Hershiser’s stretch of scoreless innings (49), Pete Rose’s career hits (4,256) etc.—have a next-best that, relative to DiMaggio’s lead, is breathing down their necks.

“DiMaggio’s is a number that just doesn’t seem like it can be explained,” says Hall of Famer and career .338 hitter Tony Gwynn. Ed Purcell, the late, great physicist whose work engendered much of the hitting streak analysis and debate, agreed. In Purcell’s evaluation, DiMaggio’s streak was the only event in baseball history that defied probabilistic explanation.

In the end, The DiMaggio Enigma persists. The scads of probability studies are intriguing and useful in providing a framework for thought. They confirm the intuitive understanding that the likelihood of anyone at any time having reeled off a streak of 56 games is much higher than the likelihood of Joe DiMaggio in particular having done so. And they confirm in a general sense that some players—by statistics alone—are more likely than others to go on a hitting streak. But ultimately we get few solid answers.

If there is life on Earth but none yet observed on any of the other planets in our solar system, can we make a guess as to the probability that alien life is thriving somewhere out there in the cosmos? Who could possibly say? We only know that there is life on Earth. And when it comes to baseball and to hitting streaks, there is at least one thing that we can say for sure: Through the end of the 2010 season 17,290 players were known to have appeared in the major leagues. Only one of them had ever hit in 56 straight games.

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¹
DiMaggio, hobbled by an ankle injury in late August and September, played in just 139 games that year.

²
Based on our assumption of DiMaggio getting 4.54 at bats per game, McGill used an 81.61% per-game hit probability to derive these figures. Also, seeking to more closely replicate reality, he ran the same numbers a second time but instead of 4.54 at bats, which is an impossible number for a batter to have in a game, he applied a formula in which he assumed four at bats in half of the games and five at bats in the other half. In this latter model the probabilities for a hitting streak of the various lengths were all very slightly smaller than those listed above.

³
There are some nicely laid out examples of Bayesian analysis, named for its progenitor, the 18th century mathematician and Presbyterian minister Thomas Bayes, as well as many other intriguing thoughts on randomness and chance in Leonard Mlodinow’s 2008 book,
The Drunkard’s Walk: How Randomness Rules Our Lives
. Mlodinow examines some sports occurrences in the book and very briefly touches on DiMaggio’s streak.

⁴
Chance didn’t exactly use total plate appearances to derive this average. He argued that appearances that result in intentional walks or sacrifice bunts should be left out and not held against the hitter in computing his streak average (again, my term) because these aren’t true opportunities to get a hit. That, in my mind, is a mistake on his part. A sacrifice bunt might sneak through two fielders or die on a swatch of wet grass and go as an infield single; a batter could reach out over the plate during an intentional walk and smack the ball for a hit—as Kelly Leak did for the Bad News Bears in 1976 and as Miguel Cabrera did for the Florida Marlins in 2006. Any time that a batter steps into the box he has an opportunity to get a hit.

⁵
Not only is DiMaggio’s career rate of 1.02 strikeouts per home run by far the lowest of any player with 350 or more home runs, during his streak in 1941 he struck out only five times while hitting 15 homers. Nobody hits like that.

⁶
I am excluding from all home run discussion the dubious achievements of the Steroid Era, 1996 through 2004. In that time there were an additional 23 player seasons that eclipsed 48 home runs, including six that surpassed 61, polluting the record book.

At Yankee Stadium, DiMaggio leaving the field after Game 48

Photograph by Daily News Archive/Getty Images

DiMaggio with Les Brown as he plays “Joltin’ Joe DiMaggio”