So there's a 42% chance that something will happen once in many, many thousands of chances and we're not supposed to be impressed by that? Is anything in baseball history noteworthy then?

Is anything in baseball history noteworthy then?

boggs' beer consumption on a cross-country road trip, for one.

In other words, streaks of 56 games or longer are not at all an unusual occurrence. Forty-two percent of the simulated baseball histories have a streak of DiMaggio’s length or longer.

Hell, in my college dorm I used to have simulated sex with half the babes in Hollywood. I beat that f*gg*t Warren Beatty by 10 to 1.

What's impressive that the 56 game streak was not Joltin Joe's longest.

So there's a 42% chance that something will happen once in many, many thousands of chances and we're not supposed to be impressed by that? Is anything in baseball history noteworthy then?

Seriously, talk about botching the denominator in the calculation. Stuff like this gives statisticians a bad name... I always tell my students that thinking that you know a little bit of statistics and probability is much more dangerous than thinking that you don't know any.

Alexander Pope comes to mind, #5.

It could have been phrased better, but I think you're mis-parsing what's written.

It's certainly impressive that Joe DiMaggio hit in 56 straight games -- the authors of the article are not disputing that. They are claiming that it's not that impressive that a 56-game hitting streak exists.

Alexander Pope comes to mind, #5.

Indeed...

Well I for one am impressed.

Not that unlikely is probably a more accurate term than not that impressive.

Here’s how it works. Think of baseball players’ performances at bat as being like coin tosses. Hitting streaks are like runs of many heads in a row. Suppose a hypothetical player named Joe Coin had a 50-50 chance of getting at least one hit per game, and suppose that he played 154 games during the 1941 season. We could learn something about Coin’s chances of having a 56-game hitting streak in 1941 by flipping a real coin 154 times, recording the series of heads and tails, and observing what his longest streak of heads happened to be.

Our simulations did something very much like this, except instead of a coin, we used random numbers generated by a computer. Also, instead of assuming that a player has a 50 percent chance of hitting successfully in each game, we used baseball statistics to calculate each player’s odds, as determined by his actual batting performance in a given year.

For example, in 1941 Joe DiMaggio had an 81 percent chance of getting at least one hit in each game (this statistic can be calculated using his total number of hits in the season, the number of games he played and his number of plate appearances). We simulated a mock version of his 1941 season, using the computer equivalent of a trick coin that comes up heads 81 percent of the time.

Shouldn't they have taken into account the pitchers he faced, or the game situations he was likely to face? I would feel much more comfortable with this sort of project if it were done using a baseball engine, such as DMB -- something more complex than a single statistic.

OK, I'll bite.

Using a comprehensive collection of baseball statistics from 1871 to 2005, we simulated the entire history of baseball 10,000 times in a computer.

By my count, 1871 to 2005 gives you 135 full seasons.

Forty-two percent of the simulated baseball histories have a streak of DiMaggio’s length or longer.

So that means 58 percent did not.

So that means 58 percent of 10,000 did not.

So that means five thousand, eight hundrend times they simulated the entire history of baseball, from 1871 to 2005, and they could not duplicate DiMaggio's record.

So that means that they simulated seven hundred eighty three thousand (783,000) full seasons without being able to duplicate DiMaggio's record.

That's pretty damn impressive, if you ask me.

That's pretty damn impressive, if you ask me.

That DiMaggio, personally, hit in 56 straight games is impressive. That the major league record hitting streak is 56 games is not impressive.

Though, Dan Evensen makes a great point. The authors are overestimating the chances of a long streak, I think, by putting each game at an equal probability. The biggest issue is the opposing pitcher. If you play two games, both against average pitchers, your chances of a 2-game hitting streak are higher than if you face one ace and one nonentity.

Using a comprehensive collection of baseball statistics from 1871 to 2005, we simulated the entire history of baseball 10,000 times in a computer.

By my count, 1871 to 2005 gives you 135 full seasons.

Forty-two percent of the simulated baseball histories have a streak of DiMaggio’s length or longer.

...

So that means <strike>five thousand, eight hundrend</strike> four thousand, two hundred times they simulated the entire history of baseball, from 1871 to 2005, and they <strike>could not duplicate</strike> duplicated or exceeded DiMaggio's record every single time.

That's pretty damn unimpressive, if you ask me.

Fixed.

Shouldn't they have taken into account the pitchers he faced, or the game situations he was likely to face?

Or (duh) the sort of pressure a real player would have faced as the streak built up. This little exercise may be the best example I've seen between the occasional 100% disconnect between the computer and the baseball diamond.

No question that the authors have a point, but if they comb their hair just right, nobody'll notice.

Note to number 14 - five thousand eight hundred is significantly more than four thousand two hundred.

Obviously, impressive is in the eye of the beholder, but if you try to accomplish something five thousand eight hundred times and fail, then either:

a) the talent is not up to the task; or
b) we're not discussing some run-of-the-mill feat.

Presuming that their simulation is up to par, then the simulated DiMaggio in these tests possessed the same statistical ability as the real DiMaggio. Yet, more often than not (because, again, 58% is more than 42%) not only could the simulated DiMaggio not accomplish the feat, but neither could any other player in the entire history of the game.

And to me, that makes the fifty-six game hitting streak pretty damn impressive.

But to each their own.

Along #13's lines, another big issue is that AB are not equally spread out. Some games a full-time player will have only 2 or 3 AB, other games 5 or 6. And it's more likely that the low AB games will come against a top pitcher. Basically any variation (park factors, platoon advantages, pitcher strength, walks) will make a streak less likely compared to using averages.

As a simple example, consider .300, .325, and .350 hitters playing two games. In game 1, they get 2, 3, or 4 AB, and in game 2, they get 6, 5, or 4 AB, for a total of 8. Here are the percentages that they have a two game hitting streak:
ABs 0.300 0.325 0.350
2*6 45% 49% 53%
3*5 55% 60% 64%
4*4 58% 63% 67%

My friend Wikipedia has an article listing the longest minor-league hitting streaks (scroll down for that list), and it includes not only DiMaggio's 61 in the PCL but one of 55 by Roman Mejias in the low minors in 1954, one of 69 by somebody named Joe Wilhoit in the Western League in 1919, one of 50 by Otto Pahlman in the Three-I League in 1922. In other words, ~56 does happen (in real as well as alternate universes), though the conditions in a minor league are obviously not identical to those in a major league (Wilhoit and Mejias were major-league quality players in low-middle minor leagues, DiMaggio an all-time great in a high minor league, which must have increased their chances to do well).

Most impressive about 56 is not just the mathematical unlikelihood of it, of course, but the social and psychological conditions DiMaggio did it within. It's one thing to put together a long hitting streak in the West Texas- New Mexico League in the 1950s (as somebody named Frosty Kennedy apparently did), quite another to do it in Yankee Stadium with your mug in the newsreels every week and people writing songs about you.