Did Joel Hanrahan Get A Good Deal?

The Pirates avoided arbitration with closer Joel Hanrahan earlier today by signing him to a one-year $4.1 million deal. I was curious as to whom that deal favored.

I came across this article from baseball analysts.com that gave math equations to figure out what a player should be paid based on his contract status with his team and his previous season's WAR. This data was based on all the contracts in 2008. It doesn't necessarily take into account the WAR changing year-to-year, which includes up and down seasons, so this is certainly not a perfect way to do this, but it's interesting nonetheless. Here's the equations:

When under team control: Salary = .51 + WAR*.001
When Arb eligible: Salary = 2.26 + WAR*.31
When FA eligible: Salary = 5.53 + WAR*1.23

Since Hanrahan is arbitration eligible, we use the second equation. His WAR last season was 2.9, so let's plug it into the equation.

SALARY = 2.26 + (2.9)*(0.31)
SALARY = $3.16 million

So according to that equation, Hanrahan got more money than he deserved. However, the Pirates wanted to avoid arbitration, so that could explain going a little above what their ideal amount would have been.

Again, this is probably a ridiculous way to look at this, and I am not saying that Hanrahan was definitely overpaid, but it's something to keep in mind and it's a good way to try and think about things like this.