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To Sacrifice or Not to Sacrifice - Did Ned Yost Make the Right Call?

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Our own Will started a nice argument when he stated that there is no way that Ned Yost should have had Betancourt sacrifice in the top of the ninth to get the runners from 1st and 2nd with 0 outs, to 2nd and 3rd with 1 out. Well, lets look at some numbers to see what was the correct answer.

Breaking out my dog eared copy of "The Book" by Tango, Lichtman and Dolphin, I find that historically teams down by 2 runs in the top of the ninth with runs runners on first and second, won the game 5.2% of the time. With runners on 2nd and 3rd with 1 out, the chance drops to 5.0% of the time. Even though it is not a lot, historically the chances drop by sacrificing the runner over.

The preceding numbers are for all teams and don't take into account the Royal's run scoring environment of a high average/no power team. I used Tom Tango's "The Runs Created, Run Expectancy, Run Frequency, Linear Weights Generator" to see what the would be the best method to deal with the 2 runners on 1st and 2nd in the ninth. Here is the number for Royals and the rest of the AL for 2010:

Run Expectancy
Frequency of Scoring 2 Runs
Frequency of Scoring 3+ Runs
Frequency of Scoring 2+ Runs

12x 0 Outs X23 1 Out 12x 0 Outs X23 1 Out 12x 0 Outs X23 1 Out 12x 0 Outs X23 1 Out
Kansas City 1.573 1.375 0.164 0.274 0.264 0.153 0.428 0.427
All of AL 1.562 1.345 0.151 0.313 0.271 0.097 0.422 0.410

First, it can be seen that the Royals, on average, would score more runs by not sacrificing over the runner.

The next 6 columns tell how the first two columns came to those values. If the runners are moved over to 2nd and 3rd the chances of scoring 2 runs jumps from 16.4% to 27.4%. These values seem great, but they don't tell the whole story. By moving the runners over, the chance of scoring 3+ (i.e. taking the lead), goes from 26.4% to 15.3%. The totals for scoring 2+ runs in the inning are almost the same (42.7% vs 42.8%), but by moving the runners over to 2nd and 3rd, the chances of taking the lead diminish.

Historically and ideally, the sacrifice was not a smart idea.