Shin-Soo Choo, Logarithms, and the 2010 NL Rookie of the Year

The 2010 National League Rookie of the Year race was the subject of much spirited debate. After giving all due respect to Neil Walker and Jose Tabata, most folks agreed it was a two man race between Giants catcher(/first baseman) Buster Posey and Braves right fielder Jason Heyward. While the Heyward supporters won me over with their razzamatazz algebra and their free vouchers, there is one thing they missed—not in their analysis so much as their analysis of the analysis: why was it in this world where a guy like Felix Hernandez who has no idea “how to win” ™ can win a Cy Young that so many folks couldn’t see the difference between a 3.0 WAR player and a 4.4 WAR player?  Sure, part of it was those elusive, intangible intangibles and part of it was (mis?)valuing their defensive contributions, but there was something else going on.

Speaking of Wins Above Replacement, at the end of the year I browsed the major league leaders, working upward through the top ten: Wainwright, Beltre (yeah, I knew he had a good year), Gonzalez, Halladay, Jimenez (what a year for pitching in the NL, eh?), Cabrera, Pujols (good old dependable Albert), Choo—what the?! Choo? The second most valuable player in the major leagues? But then sometimes, I have to confess, I neglect Indians baseball.  I went in to see what he’d been up to, expecting to be blown away only to find 22 home runs, 22 stolen bases, .300 average—oh, but he did have a .401 OBP…but still, second most valuable player in baseball in 2010? Shin-Soo Choo?

To understand why Heyward was not the 2010 NL Rookie of the Year, you might want to look at Shin-Soo Choo. You might ask why is it so hard for some folks to believe, even for a real-facts/WAR kind of a guy like me to believe, that Choo could be the second most valuable player in the majors. And you might need logarithms.

That’s almost certainly a lie, the part about needing logarithms, but on the other hand if there is one thing we do here at the Juglandaceous Porthole it is making sure we cover all the angles. As an erstwhile math professor, I can tell you by the time we get to logarithms in my College Algebra class there are two camps. First, there are those who stare at the definition and see a bit of abstract mathematical esoterica completely removed from the real world and those—wait, how many camps did I say? I meant one camp.

Early in the semester, long before we enter the logarithmic wastelands, I throw in the following question at the end of a quiz: “Name three locations, one that is near to your house, one that is a medium distance away, and one that is far away.” Having not had much of a chance to let their creative juices flow while using the quadratic formula on the preceding question, and given a question which seems impossible to get wrong, most of them are enthusiastic in their responses. Answers vary from conservative to bordering on philosophical, but a fairly common type of answer is along the lines of “My friend Steve’s house, my friend Shin-Soo’s house in Cleveland, Neptune.”

Does that sound like a reasonable answer? I think to most of us it would, but the thing that (most of) most of us don’t realize is the only way it could possibly be considered reasonable is using a logarithmic scale—in other words, many people use logarithms all the time without knowing it. In fact, everyone is using all sorts of math all the time without knowing it. Much of what we call “math” is a formalization of what we do informally dozens of times a day without thinking about it.

Why then, you might ask, do we need to bother with the formal part? The answer is in part that most of the time we don’t.  I could work out, with a bit of observational data thrown in, the equations to help me decide how to handle the hundreds of decisions I face on the drive in to work—but of course that would be silly. The rough math I do after just eyeing it up works fine, as it does for hundreds of other situations. But sometimes things are more subtle and this sort of math doesn’t give us an answer. Worse yet, sometimes it makes us think we have an answer when we are actually wrong.

Which brings us back to the alleged second most valuable player in the major leagues last year. Certainly, one possible answer is simply that WAR is not accurate. Advocates of the newer more ambitious stats are usually the first to point out that there is still a lot of work to do. But in this case in particular, this case of WAR versus my gut feeling, I notice that it seems to be for a particular type of player that WAR doesn’t seem quite right. Players like Shin-Soo Choo. Players like J.D. Drew, who I thought was nuts for opting out of his contract with the Dodgers but who some pretty sharp folks in Boston thought was worth even more. Players who make a defensive contribution but not in a position where it seems to really matter, who have some power and some speed but not enough of either to really impress anyone, who have a great on base percentage that is easy to miss if you are looking at average instead. Players like Jason Heyward.

Maybe WAR is not accurately valuing this type of player, but it seems more likely to me that I am making an error when I run through the numbers and try to weigh everything according to the rough math in my head. When Bill at the Platoon Advantage tells me that Jason Heyward didn’t simply have a good rookie year he had a great one, I believe him—at least in my head. But there is another part of me that is still looking at his baseball card stats and doing the rough math in my head and seeing another Ben Oglivie.

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