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Alternate Baseball Universes
Jamie found a NYTimes op-ed by a grad student and a professor from Cornell, outlining some research they did into alternate baseball universes. The goal was to find out how unlikely in fact was Joe DiMaggio's 56-game hitting streak, played out in the 1941 season. No one since has even come close to that record. The math guys ran simulations of the entire history of baseball from 1885 on — 10,000 of them. For each simulation they put each player up to the plate for each at-bat in each game in each year, just like it happened; and they rolled the dice on him, based on his actual hitting stats for that season. (Their algorithm sounds far simpler than whatever the Strat-O-Matic guys use.) The result: Joltin' Joe's record is not merely likely, it's basically a sure thing. Every alternate universe produced a streak of 39 games or better; one reached 109 games. Joe DiMaggio was not the likeliest player in the history of the game to accomplish the record, not by a long shot.
The most likely reason is that statistics isn't the appropriate method by which to study this problem.
This sort of a study is really more about curiosity, it doesn't deal with things like changes to the way in which the game is played. For instance early on, and for quite a while later, it was common for a pitcher to pitch 9 innings every game, and in many cases to pitch both games out of a double header. Meaning more opportunity for errors and since batters get time to rest up, there's a bit of an edge under that style of play to the batter which doesn't exist today.
That also doesn't include the variety of pitching which players see today or the fact that a player might get to see 3 different pitchers in a single game.
Even the length of the season has an effect on how players play. None of those things are easily quantified, much less analyzed by statisticians.
From reading the article (which is light on the details) it seems like they used nothing but batting average, at bats, and games played.
The problem is this doesn't control for variances in the quality of pitching. The chances of going that many games without running into a hot pitcher isn't accounted for.
Imagine you average a 75% chance of getting a hit in any individual game. If you face three average pitchers, your chances are (.75)^3 but if you face a good pitcher an average pitcher and a bad pitcher it might be (.5)(.75)(1.0) which gives a different probability, despite the same average number of hits.
In order to be realistic the calculation would need to account for the deviation from average in the ability of the pitchers (which would likely be higher 100 years ago because of fewer player and segregation, and now because of expansion, as compared to the 1950s)
What they don't report is how often there are long (but not record) streaks in their model, so there is no way of knowing how accurately it reproduces reality.
Because baseball players aren't dice?