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August 22, 2007

The Big Picture

Re-calculating the Save

by David Pinto

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Two weeks ago I proposed a new way of defining saves. The save had been instituted to reward the evolving role of the fireman, the reliever who came into a game in a tight situation to save the day. However, today's closer rarely faces a game on the line situation, unless he creates it himself. The rule defined the role over the years, turning saves into relatively passive activities. It's time to refine the rule, or introduce a more active statistic to move the closer back to the role intended, the pitcher who saves the day.

Which is where I came up with my proposal--rather than awarding saves to the person who finishes the game, the reward goes to the pitcher with the best performance in terms of increasing the team's chance of winning while also meeting a threshold increase of 0.1. Unlike the 1970s, when baseball defined the save rule, we now know the probability of a team winning at every point in the game. Given the score, base situation, and inning when the reliever enters and leaves the game, we can tell how much he helped shift the probability toward winning.

That was the theory. This week's column puts the theory into practice to find out how the proposed rule changes the number of saves awarded and which pitchers benefit and decline under this scheme. The play-by-play data used comes from Baseball Info Solutions and covers 2002-2006. William Burke and Keith Woolner supplied the Win Expectancy data, and I'm grateful for their help.

For every game in that time frame, queries determined the last event in a game in which a team was tied or trailing. Relievers entering the game after that point were eligible for a save, provided they did not get the win. For each reliever eligible, the inning, half-inning, outs, base situation, and score difference was recorded both for the event in which he entered the game and the event in which he left the game. Queries then calculated the win expectancies for both points, and the difference became the score for the pitcher for the game. If the score was...

  • greater than 0.1 and the highest score for the game
  • or greater than or equal to 0.3

... then the reliever was credited with a save. Note that the team's chance of winning has to increase by at least 0.1--to spell it out, that means if a team already has better than a 90 percent chance of winning, the reliever can't get a save.

The data shows that the new proposal eliminates about 40 percent of current saves:

Save Stats, 2002-2006
Current Rule6108
New Proposal3623
Difference2485
Pct. Change-40.7%

A much higher percentage of saves under the current rule are eliminated, almost 65 percent. Over one-third of those lost are shifted to other pitchers with the new proposal, however:

Saves gained and lost, 2002-2006
Current Rule, Saves Lost3964
New Proposal, Saves Gained1479

The data shows that a large number of saves are going to pitchers who enter the game in high-probability win situations. This rule shaped strategy and contract negotiations for a generation, and yet it is mostly applied in situations where the probability of winning is already better than nine in ten. The distribution of the various parameters shows us how the new proposal shifts save opportunities. First, the distribution of inning entered:

Distribution of Innings
Inning
Current
New
1-5
2
18
6
34
331
7
99
737
8
811
960
9+
5162
1577

As you can see, many of the ninth inning saves are eliminated. Basically, if you enter the start of the ninth and the lead is two runs or more, there's no save opportunity. Notice, however, that pitchers in the sixth and seventh inning get many more chances to pick up a save.

The next table shows the distribution of outs when entering the game:

Distribution of Outs
Outs
Current
New
0
4922
2467
1
419
576
2
767
580

The distribution is not all that different. A higher percentage of saves comes with outs already recorded in the inning, but the great majority still occur with a pitcher entering with no outs. Pitching a full inning without allowing a run raises the win expectancy by over 0.1, and that gets higher the later in the game a pitcher enters.

Now for the base situation the pitcher faces entering the game:

Distribution of Base Situations
Men on Base
Current
New
0
4901
2187
1
357
408
2
120
162
3
44
43
12
327
392
13
150
133
23
59
97
123
150
201
p>

Again, the number of saves awarded in the relatively easy situation of entering the game with no one on is reduced. But while the number of saves rewarded in tougher base situation goes up, the current rule actually does a pretty good job of rewarding pitchers who enter games with runners on base.

The distribution of the lead a pitcher inherits changes things quite a bit:

Distribution of Score Difference
Lead for Pitcher
Current
New
1
1918
2358
2
2023
903
3
1798
295
4
259
57
5
68
9
6+
42
1

Under the current rule, saves are pretty much evenly distributed over one-, two-, and three-run leads. Again, the rule for awarding a save by starting the ninth with a three-run lead or less shapes the distribution, but under the new proposal, the distribution is heavily weighted to games with a smaller score difference. Another way to look at this is by subtracting inherited runners from the lead, a measure of potential scoring:

Distribution, Lead Minus Base Runners
Lead-Men On
Current
New
-2
11
45
-1
116
260
0
313
615
1
1979
2248
2
2135
399
3
1479
52
4+
75
4

This distribution makes it clear that saves under the new proposal are shifted to much more perilous situations. Under the current rule, the distribution peaks at +2, but with the new proposal, 87 percent of the saves come in situations where this figure using leads minus baserunners is one or less, or the games that are really in jeopardy. It is also clear on examination of the average win expectancy when a pitcher enters a game for a save--the average win expectancy for a pitcher earning a save under the current rule is 0.89, but under the new proposal, 0.77.

The new proposal clearly makes earning a save more difficult. Just how much is evident in the leader board for the new proposal over the five years from 2002-2006:

Most New Proposal Saves, 2002-2006
Pitcher
Saves, New Proposal
Saves, Current Rule
Difference
Pct. Change
Billy Wagner
69
178
-109
-61.24
Mariano Rivera
68
198
-130
-65.66
Eric Gagne
66
161
-95
-59.01
Trevor Hoffman
61
168
-107
-63.69
Jason Isringhausen
54
173
-119
-68.79
Eddie Guardado
51
153
-102
-66.67
Francisco Cordero
51
133
-82
-61.65
Brad Lidge
51
104
-53
-50.96
John Smoltz
48
144
-96
-66.67
Danys Baez
47
111
-64
-57.66
Francisco Rodriguez
47
106
-59
-55.66
Armando Benitez
45
137
-92
-67.15
Joe Nathan
44
123
-79
-64.23
Todd Jones
42
80
-38
-47.50
Braden Looper
40
98
-58
-59.18
Bob Wickman
39
111
-72
-64.86
Robert Ryan
39
78
-39
-50.00
Jose Mesa
37
140
-103
-73.57
Jorge Julio
35
99
-64
-64.65
Troy Percival
35
114
-79
-69.30
Chad Cordero
35
91
-56
-61.54
Flash Gordon
35
52
-17
-32.69
David Weathers
34
34
0
0.00
Keith Foulke
33
101
-68
-67.33
Joe Borowski
32
80
-48
-60.00
Brian Fuentes
32
65
-33
-50.77
Ugueth Urbina
31
103
-72
-69.90
Tim Worrell
31
64
-33
-51.56
Mike Timlin
29
25
4
16.00
Damaso Marte
29
31
-2
-6.45

It seems the quality closers also do very well under the new proposal. What interests me is if this rule change was ever adopted, would managers start using these relievers differently? Would we see them more often in the eighth inning, or even the seventh? Some closers complain if they come in before the start of the ninth. If coming into a key situation in the seventh will earn them a save, are they more likely to want to pitch early? Would they eschew pitching with a two-run lead in the ninth? I'd suggest that closers pitch longer in games less often; better to save them for that tough situation in the eighth, and give someone else the three-run lead in the ninth.

There are, of course, pitchers who do face those early, tough situations. Here are the pitchers who increase their saves by at least ten under the new proposal; you'll recognize a few quality set-up men in that group.

Most New Proposal Saves Gained (10+), 2002-2006
Pitcher
Saves, New Proposal
Saves, Current Rule
Difference
Pct. Change
Juan Romero
20
2
18
900.00
Guillermo Mota
24
7
17
242.86
Rheal Cormier
17
1
16
1600.00
Scott Eyre
15
2
13
650.00
Ricardo Rincon
14
1
13
1300.00
Steve Reed
13
1
12
1200.00
Brendan Donnelly
16
4
12
300.00
Alan Embree
16
4
12
300.00
Chris Hammond
14
2
12
600.00
Chad Qualls
12
1
11
1100.00
Travis Harper
13
2
11
550.00
Scot Shields
25
14
11
78.57
Jason Grimsley
12
1
11
1100.00
Joel Zumaya
11
1
10
1000.00
Ryan Wagner
10
0
10
Inf.
Scott Linebrink
13
3
10
333.33
Paul Quantrill
13
3
10
333.33

Among the many excellent comments on the original piece, one person suggested that since the chances of a change to the save rule were thin, perhaps this new proposal should stand by itself. He suggested, "The Rescue" be introduced as a new statistic. I like that idea very much; the difference between a save and a rescue is the difference between catching the person who tripped and rushing into a burning building to pull out the children. If a middle reliever ends up with more rescues than a closer, maybe fans and management will start to question that role more closely.

Related Content:  Saves,  The Who,  Rule Changes,  Save Situations,  Game Theory

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