THE BOOK--Playing The Percentages In Baseball

Oooh, a Bayesian exercise!

If you really have to choose, it’s obviously #1, right?

"If you can only pick one player to start at a position...”

That’s kind of a strange condition to have to explicitly specify.

I’ll pick door 1 only if I can change it to door 3 after they reveal the player behind door 2.

Do you mean for one game against the pitcher against whom he has great numbers?  I also assume that everything else is equal between the two batters (their lifetime stats or their projections).

Obviously it depends on how many PA those numbers are based on.  But since I found zero predictive value for hitter hot streaks, I’d have to go with the player with great batter/pitcher numbers, although I don’t think it matters much either way.

Now, if you don’t know anything else about the two batters (and they are not necessarily equal players otherwise), then the player with the 15 game hitting streak is likely an above average player.  The player with the good batter/pitcher numbers is also likely an above average player, but if he is 3 for 4 or 2 for 3, he is only a marginally above average player.  If he is 15 for 20 lifetime against that pitcher, then he is more of an above average player (against all pitchers).  So basically you choose whomever has the better wOBA of the hitting streak or the batter/pitcher sample.  Again, that assumes that the players are not necessarily otherwise equal and you know nothing else about the batters and the pitcher.

Here’s a related problem from Steven E. Landsburg.

It’s related in the sense that ... the two questions remind me of each other, they both involve Bayesian thinking, and they both require you to make a hidden assumption explicit.  (In the above link, the question does explictly give you the assumption).