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Adjusted Runs Prevented: Runs prevented from scoring for relief pitchers based on the Run Expectancy Matrix.

Measures a reliever's contribution using the Run Expectancy Matrix. For each base-out situation, the Run Expectancy Matrix tells us how many runs are expected to score in that inning.


ARP = (ER(sS,P) - ER(sF,P) + IF*ER(s0,P) - R) / pe(P)

  • ER(s,P): The expected number of runs that will score in the remainder of an inning starting in base-out state "s" in park "P"
  • sS: The base-out state when the reliever entered the game
  • sF: The base-out state when the reliever left the game
  • IF: The number of innings the reliever finished
  • s0: A special state for the beginning of an inning which is distinct from the state for no outs, none on.
  • R: The number of runs that scored while the reliever was in the game
  • pe(P): The park effect for park "P"

This method was introduced by Michael Wolverton and further explained by Derek Jacques.

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ARP appears in the following BP Statistical Reports:

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