One of my favorite non-sports blogs, CoyoteBlog, linked me to this little gem the other day: a breakdown of expected runs given runners on base and outs already scored.

RE 99-02 0 1 2
Empty 0.555 0.297 0.117
1st 0.953 0.573 0.251
2nd 1.189 0.725 0.344
3rd 1.482 0.983 0.387
1st_2nd 1.573 0.971 0.466
1st_3rd 1.904 1.243 0.538
2nd_3rd 2.052 1.467 0.634
Loaded 2.417 1.65 0.815

So, for instance, if you have a runner on third and 1 out, you can expect 0.983 runs in this inning. Runner on 1st and 2 outs, you only have a 25.1% chance of scoring.This kind of data can occupy me for hours. It looks relatively unimpressive – such a small table! – but there’s so much implied in those numbers.

calculate THIS!There’s a line in The Hunt for Red October where the Russian sub’s navigator boasts about being able to “fly a plane in the Alps with no windows” with a compass and a map. Well, I could manage a professional baseball team in an underground bunker with no windows given a spreadsheet with the team’s stats, and this table.

Here’s an example, taken from the Coyote himself:

You can actually calculate what percentage chance of success you need to justify stealing second. Lets again take man on first, no outs. The RE is 0.953. If he steals successfully, the RE goes to 1.189. If he gets thrown out, the RE goes to 0.297 (bases empty, one out). If X is the probability of stealing success, then 1.189X+0.297(1-X)>0.953. X must be about 74% or greater.

I open it up to the forum. What other exciting facts or predictions does this matrix make for you?

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  • Tom D.

    I can tell you roughly when a sacrifice bunt is a good idea. For example, runner on first, no outs. Assume batter can sacrifice bunt with 100% efficiency, for a payoff of .725 expected runs (runner on 2nd, 1 out). Further assume that the batter if allowed to swing away will either hit a single or make an out, leaving us with either 1st and 2nd with no outs (1.573 expected runs), or a runner on 1st with 1 out (.573 ER)

    Thus, a it makes sense to let the batter hit if 1.573x + .573(1-x) is greater than .725, or where the batter’s OBP is above a staggeringly low .152!

    Of course my assumptions aren’t perfect, but the clear implication is that under normal circumstances, a manager who has anybody other than the pitcher sacrifice bunt in this situation should be fired.

  • I agree re:firing, Tom.

  • BedelBlitz

    This chart makes my head explode.
    And I love it.

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