Hitting Streak Probability...How's my math?

[oysterboy22]

I was thinking about it...
According to wikipedia the average hitter of all time has hit about .260 to .275 and the average in 2004 was .266. So assuming the average average is about .270 for a starting player:

A player gets an average of about 3.5 at bats per game, so he has a 1 - (.730)^3.5 chance of getting a hit which comes up to .667 or about 2/3. Therefore, the chance that the average hitter will get a hitting streak of x number of games, starting today, is (2/3)(2/3)...(2/3) x times, or (2/3)^x.
So for example, the chance that the average hitter will get a 5 game hitting streak starting today is (2/3)^5 or about 13/100. So chances are, out of the 250 or so starting MLB players, about 25 of them will hit in their next 5 games.

But for a 56-game hitting streak....
(2/3)^56 = 1.3769 x 10^-10 or about 1.3 / 1 BILLION! However, that's just the chance that a random player, let's say Dustin Pedroia, is gonna hit in his next 56 games (haha). In fact, this streak could start in any of the games in his career, so let's say the average starting player plays 10 seasons, with 150 games started in each season, he has 1,500 career games. The chance that he WON'T get a 56-game hitting streak in that time is (999,999,998.7/ 1 Billion) ^ 1,500 or 0.999998039. The chance that he will is 1 minus that, which is about 1.9 / 1 million, which is approximately 1 in 500,000. Have there been 500,000 baseball players in history who we can consider starters over their careers? I don't know, but if there have been, one of them should have done it.

Any flaws in this math? Any comments?
Of course this doesn't factor in any of the human element, sorry! :p

[Second Base Coach]

Have there been 500,000 baseball players in history who we can consider starters over their careers? I don't know, but if there have been, one of them should have done it.

Any flaws in this math? Any comments?
Of course this doesn't factor in any of the human element, sorry! :p

Even if there were 32 major league teams every year since 1876, then we would have had:

2008-1876=132 seasons
132 times 32 = 4224 teams (we could be close to that, with multiple leagues early on in baseball history, but probably not)
4224 times eight spots in the linep = 33792
Even if every job was split between two men: 67584

So you have no more than that many in realistic terms. Not 500,000. I doubt someone like Rusty Staub playing three times a week could run up a historic streak.

Looking at it for all of about 24.8 seconds, I think your math is ok, forgiving you for a lack of grouping symbols...

And to answer your question, I think one player DID hit in 56 straight games.

Joe DiMaggio :bowdown:

[abolishthedh]

I was thinking about it...

A player gets an average of about 3.5 at bats per game, so he has a 1 - (.730)^3.5 chance of getting a hit which comes up to .667 or about 2/3.
Any flaws in this math? Any comments?
Of course this doesn't factor in any of the human element, sorry! :p

I do not have a calculator handy here at the public library. But the chance should be worked out as:

(1 - 0.73)^3.5.

You have 1 - (0.73)^3.5

This will affect the calculation significantly, although your logic is sound. It affects the calculation because the exponent must apply to the batting average you are using of 0.270. As it is done, the exponent is applied only to 0.73.

Again, your logic is sound. As a SABR member, I have articles which have explored this exact topic using probability theory. Two published articles by separate authors have been done in the SABR Research Journal, each several years back. I'll try to find them.

[digglahhh]

Stephen Jay Gould has done a ton of work on this type of modeling, and putting the Dimaggio streak into mathematical, probabilistic context.

Check it out.

Or, if csh strolls by, I'm pretty sure he's got a bunch of them saved on his computer and maybe he'll post some of it.

[tinseltown]

But the chance should be worked out as:

(1 - 0.73)^3.5.

You have 1 - (0.73)^3.5 (0.73)^3.5 is the probability of going hitless in a game; 1-(0.73)^3.5 is therefore the probability of getting at least one hit.

[oysterboy22]

(0.73)^3.5 is the probability of going hitless in a game; 1-(0.73)^3.5 is therefore the probability of getting at least one hit.

That's what I was thinking.

Also yep, DiMaggio sure did it, and his chances were higher since his career batting average was .325. I really think this kind of stuff isn't very helpful when talking about record-setting streaks (56 takes something beyond math, it probably took being completely locked in at the plate). It's more interesting when talking about 5 or 10 game hitting streaks, when they're not really thinking about it.