# Ichiro Suzuki, meet linear weights

Depending on when a given event occurs in a baseball game, it will have a different impact on the runs scoring differential. 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)-.30(X-Y)=.49(X), where X equals the number of singles Ichiro would have to hit to “break even” in regard to his run-creation output.

Simplifying the equation, we get: **X = 2.18Y**. Plugging in the relevant numbers, we find that to “break even,” Ichiro would need to hit these additional 31.5 home runs at the expense of 68.5 (or fewer) singles. Ichiro averages about 678 at-bats per season with a batting average of .331 (~224 hits). The loss of 68.5 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 .229.

Hence, if, as Ichiro claims, he could hit 40 home runs at the cost of a .220 batting average, then he should not do it. Exacerbating the issue, as a commenter points out below, would be that a loss in batting average would also depress Ichiro’s on base and stolen base value, which would further lower his overall wOBA. Still, the issue would be a closer one if “Ichiro with power” was be capable of mustering a batting average that is competitive with the likes of Mike Cameron, Adam Dunn, and Russell Branyan, the trade off may be worth it. As is stands, however, “.220 Ichiro” should keep on slapping singles…

What do you think?

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16 Comments on "Ichiro Suzuki, meet linear weights"

“1.42(Y)-.3X=.49X”

That’s not correct. The .3X would be 1-Y. So, you have:

1.42Y – .3(1-Y) = .49X

1.72Y – .3 = .49X

So, when X=1, you have:

1.72Y = .49 + .3 = .79

Therefore, Y=.79/1.72 = .46That is, .46 HR + .54 outs = 1.00 singles

This lets me bring up wOBA. In wOBA, we have the value of the single at .90 and the HR at around 1.95.

And .90/1.95 = 0.46Basically, the wOBA equation itself has already been setup to answer the question without having to go through the whole setup.

you are forgetting to account for the lower OBA having a effect on the amount of value his base running can contribute.

That is a good point. Instead of a single being worth the standard, you’d bump it up a little to account for the value he brings to singles. At the same time, alot of his singles are infield singles that are worth less than the average single.

Bah, my bad. Thanks for correcting my immutably poor math skills Tango. I shall update accordingly.

Nice article, even if it is about three years too late.

http://baseballevolution.com/asher/ichiro2007.html

@Tango, Jason:

Post/Math updated. Thanks for the input

@Keith:

Thanks. Just read through the link you posted. Interesting corroboration of the idea, though I guess since they technically came first, I am the corroboration…

The numbers should be 100% now. My conclusion seems to vary form Baseball Evolution’s.

@roadrider: Imagine Mike Jacobs. That’s likely what we’d see…but with a lower BA

Bonds did this. He famously decided one year to try and hit .400 the year after he hit 73 home runs. I remember he was hovering around that mark near the AS break, but eventually ended the season at .370. His HR/PA dropped significantly from his 2001 year, though. His wOBA went up, however, as all the extra hits and all the extra IBB compensated for his drop in power.

Has anyone heard of player actually attempting to go from a high average to high power?

@Tom,

I acknowledge the point, but I do not say that Ichiro should be power Ichiro. My initial article did suggest doing so, but that was revised after Tom Tango pointed out I accidentally did the Math wrong. By the time you made your comment, my article suggests Ichiro with power does not make sense, as he would essentially have to hit above .230. I do suggest (implicitly) that a .250+ batting average may make it worthwhile, but I do not say (anymore, at least not when you would have read this) “state that Ichiro should adopt the “slugging” strategy”…

I can’t think of anyone, but it’s been done in reverse. In 1984, Dave Winfield made a conscious choice to hit more line drives and hit for average at the expense of power. He ended up hitting just 19 homers, instead of the 30-plus he usually hit, but he batted .340.