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# Introducing ARJS

The other day on Twitter, Sky, and I were discussing how to value relievers.  The conversation was triggered by a comment from Colin Wyers where he said an average reliever would successfully complete 82% of all save situations a closer finds himself in.  Sky then used Mariano Rivera's save percentage since 2007 to do a quick and dirty WAA calculation.

Somehow that led into how we'd measure reliever success using Win Probability while still keeping in mind bullpen chaining. I tossed out the idea of WPA / Leverage Index for each plate appearance times the chained leverage index value for when the pitcher entered the game.  Sky suggested that we should readjust the chained leverage index for each inning.

All this rehash of our Tweeting leads up to my introduction of ARJS - Another Reliever Junk Stat.  I don't know if it has any meaning beyond WAR or WPA but I told Sky I'd run the numbers.

I'm looking for you guys to tell me whether this is stupid or if you think it has merit.  Results and the formula after the jump.

Here's the top 10 and bottom 10 in ARJS for 2009:

 Jonathan Broxton 4.96 David Aardsma 4.57 Andrew Bailey 4.22 Huston Street 4.15 Joe Nathan 4.01 Mike Wuertz 3.78 Mariano Rivera 3.74 Trevor Hoffman 3.65 Heath Bell 3.61 Jonathan Papelbon 3.61

 Brad Lidge -1.33 Rafael Perez -1.03 Jesus Colome -0.89 Chris Ray -0.89 Brian Wolfe -0.88 Scott Linebrink -0.85 Logan Kensing -0.71 Felipe Paulino -0.66 Luis Ayala -0.62 John Bale -0.53

The method to calculate ARJS is:

1. Determine all relief appearances.
2. For each relief appearance, calculate the leverage index at the time of entry by inning.  That means if a reliever comes in with the bases loaded and two outs in the eighth, and stays in for the ninth, we'll have two data points; the bases loaded, two outs in the eighth and the nobody on, nobody out in the ninth.
3. Account for bullpen chaining using the formula (1 + LI) / 2 = chained LI
4. Calculate WPA / Actual LI (WPA/LI) for each of the plate appearances against the pitcher.
5. Multiply the WPA/LI value by the chained LI value.
6. Sum those values across the entire season.

If anyone's interested in more details or the full result set, let me know in the comments and I'll try to oblige.