Monday, March 2, 2009

Predictability (cerimonial first pitch)

Can we measure how much a pitcher is predictable in choosing the type of pitch he will deliver?
Today I will introduce the Minimum Level of Predictability.

Let's say Pitcher A has two pitches in his arsenal, e.g a fastball and a slider. He is so confident on both pitches that he delivers fastball 50% of the time and slider the other 50%. Suppose also he is perfectly random in his selection: no matter the count, the on base situation, the score, the hitter, the last pitch he has thrown - every delivery is just like a coin toss.

Pitcher B has a fastball and a slider too, but he chooses the hard one 90% of the time. Though his predilection toward the fastball is huge, he doesn't care the situation either: whatever is happening (or has just happened) on the field, his selection will be absolutely random (though heavily unbalanced).

Now we have Hitter C, who is an extreme guess hitter. Every time he's going to face a pitch he spins a roulette in his head to decide what pitch to look for. He is not entirely devote to Lady Luck: he talks a lot with the advanced scouts and takes notes.
The scouts have told him that Pitcher A throws fastball-slider in a 50-50 proportion and Pitcher B throws the same combination but with a 90-10 ratio.
He sets up his mental roulette accordingly.

How many times will he correctly guess offerings from Pitcher A and from Pitcher B?
Short answer: 50% correct against Pitcher A, 82% correct against Pitcher B.
Long answer: ...will see you tomorrow night!


  1. It should work like that, right?

    P ... Pitch Nr. x
    FB ... Fastball Probability
    SL ... Slider Probability
    AP ... Actual Pitch
    % ... Probability the hitter guesses right

    P FB SL AP %
    1 0,9 0,1 FB 0,9
    2 0,8 0,1 FB 0,88888889
    3 0,7 0,1 FB 0,875
    4 0,6 0,1 FB 0,85714286
    5 0,5 0,1 FB 0,83333333
    6 0,4 0,1 FB 0,8
    7 0,3 0,1 FB 0,75
    8 0,2 0,1 FB 0,66666667
    9 0,1 0,1 FB 0,5
    10 0 1 SL 1
    AVERAGE PROB. 0,80710317

    When I run this over any possibility of rankings of FB/SL I should get 0,82 on average:

    E.g.: When the slider is the first pitch it looks like that:

    P FB SL AP %
    1 0,9 0,1 SL 0,1
    2 0,9 0 FB 1
    3 0,8 0 FB 1
    4 0,7 0 FB 1
    5 0,6 0 FB 1
    6 0,5 0 FB 1
    7 0,4 0 FB 1
    8 0,3 0 FB 1
    9 0,2 0 FB 1
    10 0,1 0 FB 1
    AVERAGE PROB. 0,91

  2. ... sorry that I have "," instead of "."! European style!

  3. BurGi, you're stealing the show.
    I had something less eleborate on my mind: tomorrow I'll post it.
    BTW, where do you live in Eurpoe?

  4. Sorry Max!

    BtW ... My solution is wrong ... so I'm at least not stealing the show in a correct way!

    I'm living in Vienna ... studying Management Science! How about you?

  5. I'm from Italy.
    I have never thought there could be interest in baseball analysis in Austria.

    Well, that's the same thing they usually tell me when I say I'm from Italy.

  6. The same with me!

    Haven't hoped for finding another BB interested analyst in europe ... but glad I have!

    Keep posting ... I'll definitelly read it all and maybe sometimes make some comments!

    By the way: I think your blog is a great idea!