It sounds like all you need is Hugh Duffy, the right computer, and maybe 100,000,000,000 at bats.
Arbesman, a PhD candidate at Cornell University, recently tackled an issue that didn't necessarily need tackling, but is nonetheless interesting: the likelihood that anyone, ever, would have a 56-game hitting streak.
The following quote is from a NY Times Op-Ed piece he co-authored with Steven Strogatz, a Cornell professor of applied mathematics:
In a fit of scientific skepticism, we decided to calculate how unlikely Joltin’ Joe’s achievement really was. Using a comprehensive collection of baseball statistics from 1871 to 2005, we simulated the entire history of baseball 10,000 times in a computer. In essence, we programmed the computer to construct an enormous set of parallel baseball universes, all with the same players but subject to the vagaries of chance in each one.
It turns out that if you give it 134 years, you usually end up with at least one remarkable streak. "Two-thirds of the time," they write, "the best streak was between 50 and 64 games." The 19th century seems to be when most of the simulated streaks take place, and Duffy and Willie Keeler were most likely to own them.
In an email exchange, Arbesman wrote, "The general point is that long streaks are simply much more likely in baseball history than you might expect, at least using our way of thinking about the problem."
The longest sim streak -- which he didn't think we should dwell on because it's an outlier, but c'mon -- belonged to Jack Tobin in 1921. It was 109 (fake) games. Tobin's real-life 1921 wasn't so bad, either: 132 runs, 236 hits, 31 doubles, 18 triples, 8 HR, 59 RBI, .352/.395/.487. For a few seasons, Tobin was basically Ichiro without the steals.
And now, more than 38 years after his death, he pretty much owns DiMaggio.
(Thanks to The Deadball Era for the image, cropped badly by me).