Jim Albert looks to improve the runs expectancy table.

This table provides the foundation for the development of many measures of performance such as wOBA. However, it always has seemed a bit unsatisfying to me since it provides an incomplete view of run scoring potential. For example, when there is a single out and runners on 2nd and 3rd, we see from the table that teams will score an average of 1.42 runs. But this is only an average and does not directly inform us on the probability of not scoring or the probability of scoring 2 or 3 runs. It seems better to describe runs potential in a way that would say more about the future distribution of runs scored than just the mean.

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Albert produces the runs expectancy table for 2022, but also shows the runs advantage table for the same year, based on the probabilities of score a certain integer number of runs compared to a given starting state (in this case, bases empty, none out).

When evaluating strategy, it seems that the sacrifice bunt would be more advantageous in the situation with men on first and second and none out than with a man on first and none out, as a team should be more likely to score two runs. The runs expectancy table, however, shows a team is likely to score 1.55 runs in the 120-0 (occupied-outs) situation, 1.42 runs in 023-1 situation. So a successful sacrifice bunt lowers the expected number of runs score in an inning.

The runs advantage table tells a different story, however. The advantage over the start start in the 120-0 situation is 1.58 comparted to 1.64 in the 023-1 situation. I interpret this as on average a team scores fewer runs (fewer big innings), but scores some runs more often. In other words, it’s a two-run strategy!

This does not hold for the 100-0 situation versus the 020-1 situation. In that case advantage drop from 0.75 to 0.55.