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Bullpen Chaining: How Valuable is Rafael Soriano to the Rays?

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Earlier this week, Sky Kalkman published an article on the new ESPN The Max Info blog, detailing the effects of bullpen chaining and why losing Joe Nathan won't destroy the Twins this season.  Since I don't have an Insider account, I couldn't read the article, but Sky was gracious enough to share his workbook over at Beyond the Boxscore.   And so, since I'm dying for the season to begin and for us to have some real news finally, I figured it'd be nifty to use Sky's workbook to look at how Rafael Soriano affects the Rays' pen this season.

Before we get into the numbers, let's quickly rehash the theory behind "bullpen chaining".  If a position player gets injured, it's easy enough to determine who's going to be replacing them and the difference between their productions, right?  That's the concept behind measuring a player's WAR (Wins Above Replacement) since if a player gets injured, they're going to be replaced by a bench player or someone from the minors - a "replacement level" player, if you will.  

With a relief pitcher, though, it's not so easy.  Relievers have specific roles and the best relievers get used in the high-leverage situations, so if a closer gets injured, you won't throw their 5.00 ERA replacement pitcher in to close.  Instead, the second best pitcher in the pen gets moved up to close and everyone else in the pen starts seeing slightly higher leverage situations.  So how then do you determine a closer's value?  Do you measure how more valuable they are than a replacement level pitcher?  Do you measure the difference between them and the second best option in the pen?  Or is it somewhat of a combination? 

What Sky did is calculate the value (as measured by Runs Above Replacement) of the Twins' pen both with and without Nathan, taking into effect a pitcher's ERA, innings pitched, and leverage index.  Let's use his workbook and take a look now at how the Rays pen looks both with and without Rafael Soriano.

Google Docs Workbook

I included the workbook above so if you want to mess around and try your own numbers in there, feel free.  I tried to make this a conservative estimate, using CHONE projections for ERA and IP.  I made my best guess for each pitcher's leverage index, although most players corresponded very neatly to the LI's listed.  The Rays do have a deep pen, which negates some of the effect of gaining a closer like Soriano, but he is still a great addition.  From this analysis, it appears he'll be worth around one win to the Rays this season over what our pen would produce otherwise.  If you bump his ERA down to 2.50, though, it's closer to 2 wins.

Anyway, I thought this was a fun little experiment.  If you have any questions on leverage index or bullpen chaining, feel free to ask and we'll do our best to answer.