A single, for example, is worth almost twice as much with a runner on first than it is with the bases empty. These events, based on when they occur, are compared through the use of linear weights (or relative valuation).
The linear weight system is interesting because it lets us see what would happen to run-scoring in theory if we substituted one event for another. For example, what happens to run creation if a hitter improves his patience at the plate by also increasing the number of times strike three is called. According to Tom Tango's Men On Base Linear Weight System (MOBLWTS), a base on balls is, on average across all possible events, worth +0.35 runs, while a strikeout is comparably worth -0.31 runs. Thus, a player who improves his walk rate at the expense of a comparable decline in strikeout rate is actually improving his run-creation output.
A few years ago, Ichiro Suzuki said that he intentionally sacrifices power for batting average. When asked how many home runs he was capable of hitting if he focused on his power strong, Ichiro replied: "If I'm allowed to bat .220, I could probably hit 40. But nobody wants that.” For Ichiro, a .220 batting average would be a significant dropoff from his career average, which is a hair above .330. Nonetheless, I ask this: Would hitting 40 home runs at the expense of a lower batting average, and thus on base percentage, really hurt Ichiro's run-creation output? Let us examine.
Under that linear system, the average home run is worth +1.42 runs, while the average single is worth +0.49 runs. This means that a home run is roughly equivalent to 2.9 singles. Ichiro has averaged about 8.5 home runs in his nine-year major league career. If we assume that Ichiro could hit 40 homers, that means that he would need to increase his home run output by 31.5 to match his claimed ability.
Using the relative weight of home runs to singles and singles to outs (assuming all non-home run hits sacrificed by Ichiro would be outs), we get a proportion of 1.42(Y)-.3X=.49X, where X equals the number of singles Ichiro would have to hit to "break even" in regard to his run-creation output. Thus, to "break even," he would need to hit these additional 31.5 home runs at the expense of 56 or fewer singles.
Ichiro averages about 678 at-bats per season with a batting average of .331 (~224 hits). The loss of 56 singles (again, we are pessimistically assuming that all of Ichiro's forgone singles would become outs) would cause Ichiro's batting average to plummet to approximately .248.
If, as Ichiro claims, he could hit 40 home runs at the cost of a .220 batting average, then he should not do it. However, if he can hit at least as much for average as Adam Dunn (a career .250 hitter) does, then perhaps Ichiro should re-evaluate his approach at the plate.
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