
Relievers' Run Expectation Report Glossary
by Michael Wolverton
Current Reliever Report
o Article

ARP  Adjusted Runs Prevented.
 The number of runs that the reliever
prevented over an average pitcher, given the bases/outs situation when he
entered and left each game, adjusted for league and park. The exact formula
for a reliever's ARP for a game is
(ER(s_{S},P)  ER(s_{F},P) + IF*ER(s_{0},P)  R) / pe(P)
where
 ER(s,P) is the expected number of runs that will score in the remainder
of an inning starting in bases/outs state s in park P,
 s_{S} is the bases/outs state when the reliever entered the game,
 s_{F} is the bases/outs state when the reliever left the game,
 IF is the number of innings the reliever finished,
 s_{0} is a special state for the beginning of an inning (distinct from the
state for no outs, none on),
 R is the number of runs that scored while the reliever was in the game, and
 pe(P) is the park effect for park P.

RRA  Runs Responsible Average.

A rate stat
indicating how well the reliever prevented runs per inning, comparable to
parkadjusted RA. It's derived by using a formula that gives RA from
Adjusted Pitching Runs (APR),except putting ARP in place of APR:
RRA = LgRA  9 * ARP / IP
One major way this stat differs from RA: in extreme situations, it can be
negative.

IRP  Inherited Runs Prevented.

The expected number of inherited
runners the reliever prevented from scoring. If this number is positive,
the reliever is chopping points off his teammates' RAs; if it's negative,
he's adding points to his teammates' RAs. It is calculated by looking at
the runners on base when the reliever enters the game, figuring out how many
would be expected to score given their location on the bases and the number
of outs, and comparing that number to (1) the number of inherited runners
who actually did score, plus (2) if any of those inherited runners were
still on base when the reliever left the game, how many would be expected
to score from that state. The formula for a reliever's IRP for a game is
(EIR(s_{S},P)EIR(s_{F}, P)IR) / pe(P)
where
 EIR(s,P) is the number of runners that (1) the reliever inherited and
(2) are currently on base in state s, who would be expected to score
starting from bases/outs state s in park P,
 s_{S} is the bases/outs state when the reliever entered the game,
 s_{F} is the bases/outs state when the reliever left the game (EIR(s_{F}) is
 automatically 0 if the reliever doesn't leave in the same inning he
started),
 IR is the number of inherited runners that scored while the reliever
was in the game, and
 pe(P) is the park effect for P.

BRS  Bequeathed Runners Saved.

The expected number of the
reliever's Own Bequeathed Runners that were prevented from scoring by the
reliever's successors. If this number is positive, then the reliever's
bullpenmates helped him by chopping points off his RA; if it's negative,
the reliever's bullpenmates added points to his RA. A reliever's own
bequeathed runners are the runners who are on base when the reliever leaves
the game, and who are the reliever's responsibility. The formula for a
reliever's BRS for a game is
(EBR(s_{F},P)BR) / pe(P)
where
 EBR(s_{F},P) is the number of the reliever's own runners on base when he
leaves the game who would be expected to score starting from bases/outs
state s_{F} in park P,
 BR is the number of the reliever's own bequeathed runners who actually
did score (i.e., the number of runs charged to the reliever which
scored after the reliever left the game
 pe(P) is the park effect for P.

APR  Adjusted Pitching Runs.

Pete Palmer's method for calculating a
pitcher's value in runs above average. Included for comparison with ARP.
The exact formula we use differs in a few ways from the one used in Total
Baseball. Our version:
APR = L * IP  R/pf(P)
where L is the average number of runs per inning pitched in the league, and
pf(P) is the park factor for the player's home park P.

ARA  Adjusted Runs Allowed Average.

The number of runs charged to the
reliever per nine innings pitched, adjusted for league and park. The
formula:
ARA = R * 9 / (IP * pf(P))
where pf(P) is the park factor for the player's home park P.

R  Runs.

The number of runs the reliever was charged with.

IP  Innings Pitched.

The number of innings the reliever pitched.

Diff.  ARP  APR.

IRnr  Inherited Runners.

The total number of runners who were on base
when the reliever entered his games.

EIR_{s}  Expected Inherited Runs, Start.

The number of runners inherited by
the reliever over the course of the year who would be expected to score,
given their position on the bases and number of outs when the reliever
entered.

EIR_{f}  Expected Inherited Runs, Finish.

Of those runners inherited by the
reliever who were still on base when he left his games, the number who would
be expected to score, given their position on the bases and number of outs
when the reliever left.

IR  Inherited Runs.

The number of runners inherited by the reliever who
scored while the reliever was in the game.

OBRnr  Own Bequeathed Runners.

The number of runners who were on base
when the reliever left his games, and who were the reliever's
responsibility.

EBR  Expected Bequeathed Runs.

Of the reliever's Own Bequeathed Runners,
the number who would be expected to score, given their position on the bases
and number of outs when the reliever left.

BR  Bequeathed Runs.

Of the reliever's Own Bequeathed Runners, the number
who scored. Put another way: the number of runs charged to the reliever who
crossed the plate after he left the game.

G  Games.

The number of games the reliever appeared in. For a team, this
is the number of pitching changes made during the year.

IRnr/G  Inherited Runners per Game.

The number of runners inherited by
the reliever per appearance he made.

EIR_{s}/G  Expected Inherited Runs per Game.

The number of runners inherited
by the reliever who would be expected to score, divided by the number of
appearances by the reliever. This number gives a sense of the difficulty
(in terms of preventing runs) of the average appearance the reliever made.
Current Reliever Report
o Article
Comments and questions welcome. Copyright © 1999 Michael Wolverton.
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