Baseball Logic & Probability Question

[steddie]

Most coaches, scorekeepers, and others i know who understand baseball, have a very good understanding of probability and logic. So, put on your thinking cap and see if you can answer the following probability question.

Here it is:
As you approach home plate to flip a coin to determine who will be home team, the umpire decides he is tired of using the coin toss to decide this, tosses 3 identical hats on the ground. He has you look away, while he puts a baseball under one of the hats. He asks you to chose the hat which is covering the ball. You choose hat #1.
The umpire then lifts up one of the other 2 hats and tosses it aside. (since he knows where the ball is, he shows you the hat that does NOT have the ball). He then asks if you would like to switch your choice from hat#1 to the remaining hat?

To give yourself the best chance to pick the hat with the ball, do you:
1. Stay with your first choice?
2. Switch your choice to the other hat?

[real green]

Monty Hall problem.

[Jake Patterson]

First proposed by Stephen Selvin (sp?) 1975.

[bbrages]

The umpire then lifts up one of the other 2 hats and tosses it aside.

Maybe he only lifts up one of the other hats whenever he knows that you guessed right...? :P That would be pretty tricky.

I have a probability question rattling around my head; it's not a brain-teaser, though, just math:

Here it is:

Assume a batter that takes every pitch.

If a pitcher throws 80% strikes, what is the probability that the batter will draw a walk rather than strike out? What about 70% strikes? 60%? 50%?

[MLBFutureProspect44]

well, does he throw his strikes all clumped together or strike-ball-strike-ball?

[bbrages]

Assume the probability of each pitch isn't affected by the previous pitches. Just like flipping a coin or rolling dice...

[bbrages]

Correct me if I'm wrong, but here's the numbers I get:

80% strikes: 1.7% chance of a walk
70% strikes: 7.0% chance of a walk
60% strikes: 17.9% chance of a walk
50% strikes: 34.3% chance of a walk
42.1% strikes: 50% chance of a walk

This is assuming the batter doesn't swing. Which isn't all that rare at the very young levels.

[steddie]

I knew this thing had been around for a while, but had no idea how long. One thing that did amaze me about it, was the responses received from top physicists working in various universities across the country. A MAJORITY of the professors gave an incorrect answer when this question was posed in Parade magazine in the early 90s.

This past week we did a 8 hour drive down to the global world series near Gulf Shores, so I had plenty of time to kill.

[JJA]

First proposed by Stephen Selvin (sp?) 1975.

Nice memory Jake. Spot on, correct name (even the spelling!) and the year! real green also got it right. Some pretty educated folks around here that would know something so esoteric.

It's an interesting little problem, at first a little surprising but once you think about it the answer is pretty easy to understand. That said, the vast majority of folks get fooled by the answer, and as steddie points out, even a bunch of Ph.D.'s.

[pthawaii]

Most coaches, scorekeepers, and others i know who understand baseball, have a very good understanding of probability and logic. So, put on your thinking cap and see if you can answer the following probability question.

Here it is:
As you approach home plate to flip a coin to determine who will be home team, the umpire decides he is tired of using the coin toss to decide this, tosses 3 identical hats on the ground. He has you look away, while he puts a baseball under one of the hats. He asks you to chose the hat which is covering the ball. You choose hat #1.
The umpire then lifts up one of the other 2 hats and tosses it aside. (since he knows where the ball is, he shows you the hat that does NOT have the ball). He then asks if you would like to switch your choice from hat#1 to the remaining hat?

To give yourself the best chance to pick the hat with the ball, do you:
1. Stay with your first choice?
2. Switch your choice to the other hat?

2. Switch your choice to the other hat.

[dominik]

Most coaches, scorekeepers, and others i know who understand baseball, have a very good understanding of probability and logic. So, put on your thinking cap and see if you can answer the following probability question.

Here it is:
As you approach home plate to flip a coin to determine who will be home team, the umpire decides he is tired of using the coin toss to decide this, tosses 3 identical hats on the ground. He has you look away, while he puts a baseball under one of the hats. He asks you to chose the hat which is covering the ball. You choose hat #1.
The umpire then lifts up one of the other 2 hats and tosses it aside. (since he knows where the ball is, he shows you the hat that does NOT have the ball). He then asks if you would like to switch your choice from hat#1 to the remaining hat?

To give yourself the best chance to pick the hat with the ball, do you:
1. Stay with your first choice?
2. Switch your choice to the other hat?

I had this problem explained by our maths professor in university. It's several years ago though.

when I remember it correctly changing does increase the chance here however I have forgotten why. maybe brett or matt in the stats section could help you here more.

[Jackaroo Dave]

I had this problem explained by our maths professor in university. It's several years ago though.

when I remember it correctly changing does increase the chance here however I have forgotten why. maybe brett or matt in the stats section could help you here more.

The key is that the umpire knows what's under the hats and the umpire always chooses a hat the coach did not choose but is not the right hat. (And the coach realizes this is the situation.) Try it yourself with 3 cups and a coin. Try different scenarios and note how you are constrained as the umpire and how the second choice shakes down. I think it will make complete sense then.

[Jake Patterson]

How the problem is explained and the sequence of choices is very important when proving Selvin correct.

[JJA]

steddie,

I'll take a crack at explaining the answer to the peanut gallery when you want, but I don't want to spoil the answer yet until folks get a chance to try their luck. It's a fun little problem.

-JJA

[JJA]

Correct me if I'm wrong, but here's the numbers I get:

80% strikes: 1.7% chance of a walk
70% strikes: 7.0% chance of a walk
60% strikes: 17.9% chance of a walk
50% strikes: 34.3% chance of a walk
42.1% strikes: 50% chance of a walk

This is assuming the batter doesn't swing. Which isn't all that rare at the very young levels.

Yes, I get the same numbers. Good calculation.