# New Baseball Stat: Reliever Rating

May 6, 2010For the next month I will be watching every Met game and recording numbers on the relief pitching to mold them into a statistic called reliever rating. The premise of this stat is trying to create a way to more effectively judge the performance of a relief pitcher. Right now the stats that are available are saves, WHIP, ERA and win loss record. Although these are good they do not tell the whole story. For example, lets say that the Mets are in a one run game in the bottom of the eighth inning. Manny Acosta comes in and gives up a single to the first batter and then a double to the next making it second and third. The Mets now bring in Feliciano who as he usually does(except for last night) lets the other team out 1-2-3. K-Rod comes in for the ninth and closes the door. Now according to conventional statistics K-Rod would get the save and Acosta would have the same ERA as Feliciano and K-Rod. Whereas to anyone who knows anything knows that Felicianos three outs in the eighth were far more valuable than K-Rods three in the ninth. Hopefully my statistic will provide a better look at relief pitching.

The way the stat works is based on numbers given in the Leverage Table and Expected Runs Matrix from Baseball Between the Numbers. The stat is

(Expected Runs for rest of game)-(Runs allowed+Expected Runs for rest of game when leaving)

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Score Differential +1.

And that whole thing multiplied by a constant that varies for whatever inning the reliever leaves the game in based on the leverage table in baseball between the numbers.

Although it sound complicated lets consider the situation listed above. Basically every inning with no-one on and no outs the hitting team is expected to score .454 runs in that inning.

So when Acosta enters the opposing team is expected to score .454 runs in the 8th and .454 runs in the 9th for a total of .908 runs. Acosta allows 0 runs but when he leaves he leaves runners on second and third with no outs so now the hitting team is expected to score 1.946 runs in the 8th plus .454 in the 9th, for a total of 2.4. Now the Mets are up 1 at the time so the denominator becomes 1+1 which is 2. The inning constant for the 8th inning is 2.05. So the final equation becomes {.908-(0+2.4) over 2}X2.08. But in Acostas case the quantity of runs allowed+runs expected for rest of game is higher than his runs expected when entering the game. So instead of dividing by the score differential you multiply by it, otherwise in this situation the reliever would benefit from the game being a blow out. After all of this math Acostas rating is **-6.12**

Now onto Feliciano, Pedro enters the game, because of Acostas poor performance the team is now expected to score 2.4 runs for the rest of the game. Feliciano shuts them down however, bringing the runs expected after he leaves down to .454 which is the expected runs for the ninth inning with nobody out and nobody on. Pedro also came into the game with a score differential of 1 so his denominator is 2 also. Likewise his inning constant is the same as Acosta's so it is 2.05. Making his rating for the game **1.99.**

K-Rod comes in for the ninth and shuts the door 1-2-3. So his runs expected when entering is .454 and his when leaving is 0 because he ended the game. His inning constant for the ninth is 2.63. Giving him a rating of **.597**

Some other notes about the stat. If by some chance the Mets had scored in between the top of the ninth and Feliciano had come out to pitch the ninth. His run differential denominator would be 1.5 because for half the outs he recorded the differential was 1 and for the other half it was 2. So you simply average those together.