Racial Bias and the Free Agent Market

Orlando Hudson Believes Racism Is Why Jermaine Dye's Unemployed | MLB Fanhouse

Though, if you were to ask Minnesota Twins second baseman Orlando Hudson why [Jermaine] Dye is sitting at home right now, he'd tell you there's another reason for it. Well, he'd hint at another reason for it, but he wouldn't actually come out and say it. Hudson believes that the reason Dye doesn't have a job has nothing to do with his declining skills, but rather his skin color.

"You see guys like Jermaine Dye without a job," Hudson told Yahoo's Jeff Passan. "Guy with [27 home runs and 81 RBIs] and can't get a job. Pretty much sums it up right there, no? You've got some guys who miss a year who can come back and get $5, $6 million, and a guy like Jermaine Dye can't get a job. A guy like Gary Sheffield, a first-ballot Hall of Famer, can't get a job. ...

"We both know what it is. You'll get it right. You'll figure it out."

First of all, I think the reason Jermaine Dye is unemployed is Jermaine Dye and his agent don't understand how valuable he is. In case you were wondering, that's not very, seeing as Jermaine Dye is a right-handed DH who hit .179/.293/.297 in the second half of 2009. The list of things Jermaine Dye brings to the table is very short and mostly has to do with his reputation and nothing that actually happens on the baseball field.

Regardless, rather than discussing this specific case, I'd prefer to examine the problem through a different zoom lens and ask the question, "Were minorities compensated differently on the 2009 free agent market?".

Using the data from baseballprojection.com's Free Agent Tracker, I've come up with the following chart* of the free agent contract information by race (WAR = 2010 CHONE projection, $ = total guaranteed money, Years = total guaranteed years, $/W = average implied $/W, n = number of contracts):

*Note: this chart does not include relievers.

First impression, outside the Hideki Matsui aberration, Black free agents were given more money ($3.72 million) per projected WAR (by CHONE) than any other race. If any group has a legitimate complaint, it's Hispanic players, who were compensated only $2.96 million per projected WAR.

But the question has never been "which group got the most?" or "is there an observed difference?". We're only observing samples, not populations, here, so the appropriate question is, "is the difference statistically significant?".

I ran four T-tests to see if there's any numerical evidence of racial bias. I compared the $/W of Black FA's to White FA's, Black FA's to non-Black FA's, Hispanic FA's to White FA's, and Hispanic FA's to non-Hispanic FA's. The following represents the results of the four tests (Δμ = difference in mean $/W, σ2 = Standard Deviation, Var(Δμ) = Variance of Δμ, T = T-value, DF = Degrees of Freedom, P = 1-tailed P-value):

None of these sample sizes is as big as I'd like, but given the data we have, I can't comfortably say there was any racial bias in the free agent market this off season. At the 0.05 level, none of these T-values are statistically significant. In essence, the differences can all be attributed to random variation.

As for Dye, well, my conclusion hasn't changed. He's probably unemployed for the same reason Joe Crede and Bartolo Colon are--the market has a different idea of what their services are worth than the FA does.

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