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?

Tom M. Tango said...

“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.

jason said...

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

Tom M. Tango said...

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.

Jeffrey Gross said...

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

Jimmy said...

Great piece. It made me curious—would Ichiro *like* being the kind of guy who hits 40 home runs and isn’t on base much? He seems to be the kind of player who relishes getting on base and being fully engaged at-bat to at-bat. One wonders if that would impair his ability to realize full benefits of the 40-HR season. Might we see Sad Ichiro?

Discussion of the intangibles in no way contradicts the numerical analysis, of course. I just find it interesting to consider how often a player’s personality might lead them to choose which type of game they want to play, as opposed to letting an innate talent make the decision for them. It’s probably rare that a player has a skill set well-rounded enough to allow them to make a conscious choice.

Keith said...

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

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

Jeffrey Gross said...

@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…

pinball1973 said...

More of the very often interesting and useful sort of analysis that somehow sometimes – as is the case here – also DEMAND that Baseball (large ‘B’) is somehow like a business where ONLY the bottom line (wins, therefore runs) matters.

To reference current pop culture, I’m on the side of the Don Draper approach to advertising (and quite aware of the ironies involved, thank you!) where he talks of “creating” something instead of simply being “some accountant trying to make a dollar into a dollar-ten.”*

I, and almost everyone else who loves the game, wants our team simply to always win (a condition that suggests a mental illness, which should be called something like “Yankeefanitus”) but to give us the material to build, both individually and collectively at the same time, an exciting narrative that parallels our everyday lives.

Ichiro, like the greatest players ever (though, no, he is not as great, stat-wise, as Musial, Mays, Ruth, Mantle, etc.) allows fans a fantastic character for our baseball memories by being Ichiro and only Ichiro!

In real fiction, we would see him take the challenge, and hit .218 with 37 HRs one season, or not. That can’t happen in real life, as the writer of this (who I know is being playful, BTW, though too many articles like this show simple a-holishness).

We just MAY be lucky enough to see him become a pinch-hitter and middle reliever when he decides he’s slowing down, though: he wants to give fans a special and utterly unique story, after all.

*pardon if my quote is not exact – I’m working from memory.

roadrider said...

If Ichiro Suzuki can hit for more power and is not doing it he is hurting his team for the sake of boosting his personal statistics. No one is arguing that he should hit in the low .200s to produce power – if that’s his argument than I would say that he’s merely a 5 o’clock slugger – a guy who can put ‘em in the seats off a 60-year old coach throwing 70 mph “fastballs” in the same spot every time. Doing it in a game is a different story. My conclusion – Suzuki is not a legitimate power hitter despite his batting practice prowess – merely a singles hitter (albeit a very,very good one) who doesn’t walk and can’t really hit for power against real pitchers in real games.

Jeffrey Gross said...

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

Arvin Hsu said...

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.

Greg Simons said...

Building on what Jimmy said about the type of hitter Ichiro wants to be, I think he is aware of his uniqueness and how that plays to fans. Also, I think he knows that many hits=HOF, while a .220 average and many HR=Dave Kingman.

The guy may pass Pete Rose for career hits, combining NPB and MLB numbers, and that’s going to be a very big deal. Even if it were true that “slugging Ichiro” could help his team win more games, it’s obviously a close call, so sticking with what works provides an overall benefit (wins, hits, fame, ticket & merch sales, etc.) for Ichiro and the Mariners.

Danmay said...

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

Tom Cavileer said...

You can’t have your cake and eat it, too. You can’t use 1.42 as the value of a HR for a leadoff hitter. A leadoff hitter doesn’t see nearly as many men on base as your “average” HR hitter. So, you must either reduce the 1.42 factor or assume fewer PA for the “slugger” Ichiro, who would be hitting lower in the order.

Then, before you state that Ichiro should adopt the “slugging” strategy, you must consider variance. Ichiro’s average value is what it is, but what is the value that you can be certain he has a 90% probability of providing? It’s not that much lower than his average value – he’s pretty consistent, giving the Mariners at least 30 runs above replacement every season. A “slugging” Ichiro, on the other hand, might have slightly higher peak seasons, but at the cost of a much greater probability of being worth half as much. With almost all his value packed into those 40 HR, his value quickly falls if he only hits 25 instead, or too many of them with the bases empty.

Jeffrey Gross said...

@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”…

John said...

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.