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As we chronicled in Baseball Prospectus 2000, the current thinking
on how to build and run a major-league bullpen may be changing. For 20
years, teams have used their "closer"–a term originally used to
designate a team’s best reliever–more and more exclusively in what we call
"save situations:" the ninth inning with a lead of one to three
runs. Implicit in this thinking is that the most important situations are
the ones that qualify a reliever for a save if he does his job.

Over time, the design of the save rule led teams to use their best reliever
to pitch exclusively in save situations, presuming that those situations
are the ones in which a top reliever will do his team the most good by
guaranteeing victory in a close game.

But is that really the case? Is bringing Mariano Rivera in to pitch
with a three-run lead in the ninth inning really the best way to maximize
his value? Last year, the Reds under Jack McKeon started using their best
relievers, Scott Williamson and Danny Graves, late in the
game even if the score was tied. This year, teams like the White Sox and
Red Sox have been bringing Keith Foulke and Derek Lowe in to
pitch the eighth inning as well as the ninth to protect a late-inning lead.

These developments are a move back towards 1970s-style relief usage, when
the term "closer" still competed with the term
"fireman" to describe a team’s best reliever. Guys like Rich
Gossage
and Rollie Fingers weren’t being used solely to finish
games. They were brought in to extinguish rallies under whatever
circumstances their managers felt they would have the most impact on the
game’s final outcome.

We’ve gone on record many times as being critical of 1990s-style
hyperspecialization, the clustering of 45 or more saves on one reliever
even though many of those saves may come in games whose outcome was not in
serious doubt even before Dennis Eckersley or Bryan Harvey
trotted in from the bullpen. But until now we’ve never done a comprehensive
study to determine the potential impact a great reliever can have in
different situations. It’s easy to say that a three-run lead in the ninth
should be a lower priority than a one-run lead in the ninth. But how about
a two-run lead in the ninth versus a tie ballgame? A three-run lead in the
ninth or a one-run lead in the eighth? Should a closer ever be used when
his team is losing?

It is possible to answer such questions, using complex baseball simulations
like the one Keith Woolner has designed. Woolner’s model takes a team’s
average scoring level–say, five runs per game–and determines, with
remarkable precision, the likelihood that such a team would score no runs
or 1 run or 2 runs, etc., in an inning. The distribution for just such a
five-run-per-game team:

0 runs: 70.7%
1 run: 15.45%
2 runs: 7.3%
3 runs: 3.45%
4 runs: 1.65%
5+ runs: 1.45%

Using that distribution, the simulation can simulate all the innings in a
baseball game and determine, say, the probability that the home team will
win when they are losing by three runs in the bottom of the seventh inning,
given that the home team scores 5.5 runs per game and the visitors 4.75
runs per game (actual answer: 15.747%).

We can use this simulation to calculate the impact a closer can have in any
given situation. For example, when the home team leads by one after eight
innings, and both teams score an average of five runs per game, then their
estimated winning percentage would be .830. Hence, an infallible closer (a
theoretical pitcher who automatically throws one scoreless inning) would
increase the home team’s chances of winning by .170. Therefore, given these
scoring levels for both teams, the potential impact of a closer in this
situation (top of the ninth, leading by one run), is .170.

Let’s look at the impact on winning percentage that an infallible closer
for the home team in the ninth inning has, depending on the score
differential. We’ll assume the visiting team scores 5.10 R/G and the home
team scores 5.40 R/G (the average AL team scored 5.23 R/G last season). The
chart below examines eight different situations, from a lead of four runs
to deficit of three runs:

Situation             Win Pct.   Win Pct. with closer    Closer Impact

Top 9th, lead by 1 .830 1.000 .170 Top 9th, tied .509 .669 .160 Top 9th, lead by 2 .920 1.000 .080 Top 9th, trail by 1 .184 .233 .049 Top 9th, lead by 3 .962 1.000 .038 Top 9th, trail by 2 .088 .113 .025 Top 9th, lead by 4 .981 1.000 .019 Top 9th, trail by 3 .042 .055 .013

A one-run lead is the situation in which a perfect closer has the most
impact on his team’s chances to win, which is not surprising at all. What
is surprising is that using a closer in a tie game increases your chance to
win by 16%, just slightly behind a one-run lead and well ahead of any other
situation! In fact, using your closer when losing by one run is actually
more beneficial than using him when leading by three runs, the rulebook
"save situation."

Let’s look at the same chart for the same two teams, only this time
evaluating the impact of a closer on the visiting team in the bottom of the
ninth inning:

Situation                Win Pct.  Win Pct. with closer  Closer Impact

Bottom 9th, lead by 1 .767 1.000 .233 Bottom 9th, tied .331 .491 .160 Bottom 9th, lead by 2 .887 1.000 .113 Bottom 9th, lead by 3 .945 1.000 .055 Bottom 9th, lead by 4 .973 1.000 .027

A similar pattern emerges. A tie game proves to be a higher priority than
any situation other than a one-run lead. However, note that for every
situation with a lead, a closer’s impact is greater than in the
corresponding situation in the top of the ninth inning. Since the visiting
team does not have the luxury of an extra at-bat should the home team tie
the game (and doesn’t get to bat at all if the home team takes the lead),
their overall winning percentage is lower and the impact of a perfect
closer therefore greater.

That establishes the pecking order for the ninth inning. But how about an
earlier point in the game? Does it make sense to use your closer in the
eighth inning? Earlier?

The closer impact for the home team in the top of the eighth inning:

Situation                Win Pct.  Win Pct. with closer  Closer Impact

Top 8th, lead by 1 .741 .864 .123 Top 8th, tied .517 .632 .115 Top 8th, lead by 2 .858 .933 .075 Top 8th, trail by 1 .280 .342 .062 Top 8th, lead by 3 .924 .967 .053

It’s the exact same pecking order as in the top of the ninth. in
particular, the impact of a closer in a tie game is almost identical to his
impact with a one-run lead. Although the overall impacts are smaller for
those two situations, the impact of a closer when trailing by a run, or
leading by three runs, is actually higher than in the ninth inning! Holding
the visiting team scoreless in the top of the eighth gives the home team
two chances to tie, which presumably makes the difference.

The same chart for the bottom of the eighth:

Situation                Win Pct.  Win Pct. with closer  Closer Impact

Bottom 8th, lead by 1 .658 .816 .158 Bottom 8th, tied .369 .491 .122 Bottom 8th, lead by 2 .804 .912 .108 Bottom 8th, lead by 3 .888 .958 .070 Bottom 8th, trail by 1 .136 .170 .034

Again, the impact of a closer in the eighth inning is greater for the
visiting team than for the home team. The only major difference to note
here is that a three-run lead is a higher-impact situation than a one-run
deficit, because in this case, even if the closer throws a scoreless
inning, the visiting team has to come back in the ninth and hold the
home team scoreless again in the bottom of the ninth. (We didn’t run any
examples of the closer’s impact when trailing in the bottom of the ninth,
for obvious reasons.)

How about even earlier situations? The Reds frequently used Williamson and
Graves as early as the sixth inning last year. Let’s collect all of the
above data into one chart, and add the data for earlier situations. The
following charts present the closer impact for a variety of innings and
scores.

The chart for the home team:

Score        Top 6th      Top 7th     Top 8th      Top 9th

Lead by 3 .050 .052 .053 .038 Lead by 2 .068 .074 .075 .080 Lead by 1 .079 .096 .123 .170 Tied .073 .092 .115 .160 Trail by 1 .059 .059 .062 .049 Trail by 2 .048 .034 .039 .025

And the chart for the visiting team:

Score        Top 6th      Top 7th     Top 8th      Top 9th

Lead by 3 .066 .060 .070 .055 Lead by 2 .084 .086 .108 .113 Lead by 1 .096 .111 .158 .233 Tied .082 .089 .122 .155 Trail by 1 .055 .051 .034 N/A Trail by 2 .035 .031 .013 N/A

There’s a lot of information to digest there, but the major points are:

  • A closer has more impact for his team when they’re on the road than when
    they’re at home. With just one exception, every situation in which the
    closer’s team has the lead has a higher impact for the visiting team than
    the home team.

  • While a closer has the greatest potential impact with a one-run lead in
    every inning, a tie-game situation is not far behind. In particular,
    closers have almost as much impact in tie games as they do with one-run
    leads when at home. Remember the expression, "play for a tie at home,
    play for a win on the road? " In this case, it’s true. If a closer is
    used to keep the game tied for the home team, the strategy will pay off
    more often than not.

  • And most important of all: the practice of using a closer to protect a
    three-run lead in the ninth inning is absurd, even in today’s high-offense
    environment. The impact that a closer has in that situation is less than
    the impact he would have protecting a three-run lead in the sixth inning!
    Almost every situation in which the closer’s team is tied or has the lead
    is more important than the simple task of the three-run ninth-inning lead,
    save or no save. In fact, for the home team, the impact of protecting a
    three-run lead in the 9th (.038) is less than the impact of throwing a
    scoreless top of the first inning (.046).

So how should a team prioritize the use of its best reliever?

            Home                                 Away

1) Top 9th, lead by 1 (.170) 1) Bottom 9th, lead by 1 (.223) 2) Top 9th, tied (.160) 2) Bottom 8th, lead by 1 (.158) 3) Top 8th, lead by 1 (.123) 3) Bottom 9th, tied (.155) 4) Top 8th, tied (.115) 4) Bottom 8th, tied (.122) 5) Top 7th, lead by 1 (.096) 5) Bottom 9th, lead by 2 (.113) 6) Top 7th, tied (.092) 6) Bottom 7th, lead by 1 (.111) 7) Top 9th, lead by 2 (.080) 7) Bottom 8th, lead by 2 (.108)

Keep in mind that all of these numbers have been generated in a neutral
ballpark setting (5.1 R/G for the visitors, 5.4 R/G for the home team). In
a future article, we’ll look at how the offensive context changes the
priorities for using a closer. Should Buddy Bell use Jose Jimenez
with a three-run lead in Coors Field? Does it make even more sense to use
your closer in a tie game in a pitchers’ park like Dodger Stadium, where
one run is harder to overcome? Stay tuned.

Rany Jazayerli, M.D., can be reached at ranyj@baseballprospectus.com.