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RE+: Factoring Player & Team Hitting Ability Into Run Expectancy and the True Value of a Stolen Base

There are 24 different “states” in baseball. The three bases can be filled in eight different ways, and there can be 0, 1, or 2 outs at any given moment. Each of these 24 base-out states has an expected run value associated with them. Each value represents the average number of runs that the team is expected to score by the end of the inning. These values change each season depending on the run environment, but they generally don’t vary much.

2019 Average Run Expectancy by State
STATE 0 outs 1 out 2 outs
000 0.53 0.29 0.11
100 0.94 0.56 0.24
010 1.17 0.72 0.33
001 1.43 1.00 0.38
110 1.55 1.00 0.46
101 1.80 1.23 0.54
011 2.04 1.42 0.60
111 2.32 1.63 0.77

Consider the following situation: Lorenzo Cain is on first base with two outs. Now consider two possible hitters, one being Christian Yelich and the other being Ryan Braun. According to the 2019 averages, the run expectancy in this base-out state was 0.24, regardless of the hitter. While both players had impressive seasons, Yelich is unquestionably the superior player at this point in time.

2019 Player Comparison
Player wOBA ISO
Ryan Braun .354 .220
Christian Yelich .442 .342

As a result of their differences, the run expectancy should be higher when Yelich is at the plate. Consequently, the benefit Milwaukee gets from Cain attempting to steal second base should be adjusted as well. Why is this the case? Given Braun’s inferior power and hitting ability, there is more to gain from Cain putting himself in scoring position, but more importantly, there is less to lose if he were to get caught. On the other hand, Yelich is much more likely to drive the ball. With Yelich at the plate, the increase in run expectancy from a stolen base is slightly smaller than if Braun were hitting. However, the decrease in run expectancy from being caught is significantly greater. This is why we need RE+. Read the rest of this entry »