Probability of randomly predicting the score of a baseball game

Hi there,

I'm writing a novel in which the main character receives the scoreboard to a baseball game from the future. It's right of course. He's a math whiz, and to verify that it's from the future he calculates what the probability of it being a coincidence. Unfortunately it's beyond my simple grasp of permutations.

So here are your constraints: The final score is 7-4. The score during each of the nine innings is known. The losing team had three hits, the winning team had four. Let's assume an upper limit for hits is 10 on both sides. The losing team had one error, and for our sake's we can assume an upper limit on errors of 5 on both sides. Here's the scoreboard:

Innings 1 2 3 4 5 6 7 8 9 R H E

Mariners 0 1 0 0 1 0 2 0 0 4 3 1

Athletics 0 2 0 1 1 0 1 2 0 7 4 0

So what would be the chance that if you knew what the score was, a person could guess, in correct order, how the game would score over 9 innings, and the correct number of hits and errors? I know the number would be astronomical, but that's kind the point for my book. Also, if you can explain how you got your answer that would help a lot! Thank you! ~Chris

Re: Probability of randomly predicting the score of a baseball game

Quote:

Originally Posted by

**chrisaxling** So here are your constraints: The final score is 7-4. The score during each of the nine innings is known. The losing team had three hits, the winning team had four. Let's assume an upper limit for hits is 10 on both sides. The losing team had one error, and for our sake's we can assume an upper limit on errors of 5 on both sides. Here's the scoreboard:

Innings 1 2 3 4 5 6 7 8 9 R H E

Mariners 0 1 0 0 1 0 2 0 0 4 3 1

Athletics 0 2 0 1 1 0 1 2 0 7 4 0

So what would be the chance that if you knew what the score was, a person could guess, in correct order, how the game would score over 9 innings, and the correct number of hits and errors? I know the number would be astronomical, but that's kind the point for my book. Also, if you can explain how you got your answer that would help a lot! Thank you! ~Chris

Knowing very little about baseball, I may not understand your question.

But have a look at this webpage.

It gives you the partitions of 7. As you can see there are 15 ways to get a seven.

A team could score all seven runs in one inning alone. That can be done in nine ways.

A team could score one run in each of seven innings. That can be done in 36 ways.

Or from your example: 2+2+1+1+1. That is scores in five innings. That can be done in $\displaystyle \frac{9!}{(2!)(3!)(4!)}=1260$ ways.

So what you are asking requires a lot of tedious workings.

Moreover, once it is done for seven then its must be done for four.

Multiply the two results together. Here are the partitions of 4. There are only five.