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K-Rod, Castillo, and Externalities June 17, 2009

Posted by tomflesher in Baseball.
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On Friday, Luis Castillo committed an error in the bottom of the 9th inning with a one-run lead, two men on base, and two men out. The error was such that had Castillo made the play cleanly, the game would have ended with Francisco Rodriguez notching a save; however, Castillo’s error was directly responsible for two unearned runs scoring, giving Frankie a loss instead of a save.

The question: How much money does Castillo owe Rodriguez? I have a pretty good estimate.

Let’s assume, as usual, that clubs base their contract offers on the results the players create, that teams negotiate by placing roughly the same emphasis on the same statistics, and that the market for baseball players is competitive. It is then the case that when a player is a free agent, his stats will dictate the amount of money he’s offered in his next contract, and therefore we can model (using linear regression) the weight placed on each statistic. In this case, a linear regression model could tell us exactly how much money one save is worth come contract time.

Obviously, this is a complicated procedure, and it would take a lot of work to account for all possible variables, so to simplify matters, I did the following:

  • Using Baseball-Reference.com‘s Play Index, I found all pitchers seven or more years into their careers (to avoid the inefficiencies of arbitration and rookies being locked into negotiating with their own teams and receiving the league minimum salary) who were free agents at the end of the 2007 season (the last free agency season available on Baseball Reference) and who pitched in relief in at least 80% of their appearances. There were 92.
  • I threw out pitchers who did not play in 2008, to avoid distorting the salary output.
  • I found the pitchers’ 2008 salaries and created a data file.
  • Using that data, I ran a linear regression in R with these results.

First, the objections: there are obviously a number of vagaries in the data. We can’t, for example, easily account for popularity or clubhouse leadership, which are important factors in salary negotiations. This model has an R-squared statistic of .4174, meaning it explains 41% of the variation in salaries – not a huge number. The sample of pitchers is small, and it doesn’t account for people who might have had high reserve prices and refused to sign with any team despite having stats that would have helped solidify the model.

However, the SV (saves) statistic is highly statistically significant, and UR (unearned runs) is significant at the 90% level. Thus, we can estimate that if Frankie were to negotiate tomorrow for his contract, the figure that he was offered would be one save less and two unearned runs more than he would have been had Castillo not committed his error.

Since a save is worth $111,727, and an unearned run conceded is worth -$311,517, that would mean that Rodrigues would lose $[111727+2*(311517)] = $734,761 if he were to negotiate his contract tomorrow. Of course, he isn’t – he won’t negotiate until the end of the 2011 season. Thus, we have to discount twice.

Assuming a 20% interest rate, 734716*.8*.8 = 470,218.24 or about $470,000. (We’ll assume that teams discount the prior years’ performance and focus mainly on the immediately preceding year. 20% is a fairly high level of discounting, meaning that Frankie would be able to make up for lost stats by performing well next year and the year after.) Thus, Luis Castillo may have imposed a $470,000 externality on Francisco Rodriguez’ next contract negotiation.

If I were Luis, I’d offer him a steak dinner instead.

Luis Castillo
commits minor league error;
externality.

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Comments»

1. harry - June 18, 2009

ok this rules


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