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On June 13, Andrew Miller relieved Trevor Bauer with the bases loaded and two outs in the sixth inning of the Indians' game against the Dodgers, tied at 2-2. He struck out Yasiel Puig to end the inning and retired all three batters he faced in the seventh. In the top of the eighth, though, he allowed a home run to Cody Bellinger and a single to Yasmani Grandal. He was pulled in favor of Bryan Shaw. Miller took the loss.

The next day, again in a 2-2 game against the Dodgers, Miller entered in the top of the eighth inning. He got Puig on a fly ball but then allowed home run, a single, two walks, and an RBI grounder before getting pulled. He again was charged with the loss. His manager, Terry Francona, in a display of candor, later admitted, “I think I pitched him too much.”

Now, Andrew Miller has pitched 35 2/3 innings this year. (All 2017 figures are through Tuesday, June 20.) That’s not that many. He’s currently tied for 170th among major-league pitchers for innings. Among relievers, he’s tied for 16th. His workload, contrary to Francona’s mea culpa, doesn’t seem to be excessive, although certainly the manager worked his ace reliever very hard down the stretch and throughout October last year.

Of course, even focusing on this season alone, it’s not just the innings, or the pitches, we increasingly hear on broadcasts. It’s the high-leverage innings. Pitching in garbage time doesn’t take as much out of a hurler as pitching with the game on the line. Yusmeiro Petit of the Angels, for example, has pitched 42 2/3 innings—more than Miller. But in his 27 games, Petit has appeared in 17 (63.0 percent) with Los Angeles trailing. Miller has pitched in 31 games, entering only three (9.7 percent) with Cleveland trailing. That’s more pressure.

We can take a crack at calculating this. We know how many innings pitchers pitch, obviously. Noted sabermetrician Tom Tango created the Leverage Index, which quantifies the leverage of each situation using win expectancy tables. The average Leverage Index, or LI, is 1.0. An LI less than 1.0 is a lower-leverage situation; one greater than 1.0 is higher leverage. In the example above, Petit’s average Leverage Index, throughout all his appearances this year, is 0.85. Miller’s is 1.60. Miller’s been used in high-leverage situations. Petit hasn’t.

By using average LI in relief appearances (available from our friends at FanGraphs) and reliever innings pitched, I calculated a new metric with the stupid acronym of LIP, which stands for Leverage Index times Innings Pitched. Bill James once said something to the effect that a new metric is useful if it mostly confirms what we already know. Here are the 10 relievers who had the highest LIP Index in 2016. See what you think of them.

Pitcher

LI

IP

LIP Index

Sam Dyson

2.10

70 1/3

147.7

David Robertson

2.15

62 1/3

134.0

Steve Cishek

2.02

64

129.3

Dellin Betances

1.77

73

129.2

Ryan Madson

1.99

64 2/3

128.7

Andrew Miller

1.71

74 1/3

127.1

Nate Jones

1.75

70 2/3

123.7

Roberto Osuna

1.66

74

122.8

Zach Britton

1.82

67

121.9

Ken Giles

1.84

65 2/3

120.8

That works for me. It’s a combination of closers and setup guys. The common denominator is that they were all very effective, so their managers didn’t hesitate to bring them in with the game on the line.

That last sentences touches on a key objection to LI: It’s not under the pitcher’s control. That’s a fair criticism. Dave Robertson and Nate Jones were both in the top 10 in large part because of the type of games the White Sox played (i.e., close) and the way manager Robin Ventura deployed them (in tight situations), not because of anything they did. All true. But that doesn’t minimize the fact that both found themselves in a lot of high-leverage situations.

So I’m willing to go the LIP Index for now. Which leads to three questions.

Are pitchers today really "softer"?

Back when Goose Gossage was getting 25 multi-inning saves every year (actually, the most he ever got was 21, but never mind), relievers threw more innings, so even if the leverage wasn’t always high, the LIP Index was higher, right? It turns out this is true. Here’s a table of the 15 highest LIP Indices since 1974, the first year for which LIs are available.

Season

Pitcher

LI

IP

LIP Index

1974

John Hiller

1.92

150

288.0

1980

Dan Quisenberry

2.14

128 1/3

274.6

1975

Rich Gossage

1.91

141 2/3

270.6

1976

Rollie Fingers

1.98

134 2/3

266.6

1977

Bill Campbell

1.87

140

261.8

1974

Terry Forster

1.97

131

258.1

1983

Bob Stanley

1.74

145 1/3

252.9

1974

Tom Murphy

2.05

123

252.2

1976

Bill Campbell

1.47

167 2/3

246.5

1980

Doug Corbett

1.76

136 1/3

239.9

1979

Sid Monge

1.82

131

238.4

1979

Mike Marshall

1.68

140 2/3

236.3

1985

Dan Quisenberry

1.83

129

236.1

1978

Rich Gossage

1.75

134 1/3

235.1

1977

Sparky Lyle

1.71

137

234.3

Well, yeah, OK, so Gossage had a point. Those leverage indices aren’t meaningfully different from the ones in 2016. The innings are, though. The highest-ranked pitcher from the 21st century is Billy Koch of the 2002 A’s: 2.09 LI, 93 2/3 IP, 195.8 LIP, 43rd since 1974. The highest-ranked pitcher from the current decade is Dellin "Not A Closer" Betances of the 2015 Yankees: 1.87 LI, 84 IP, 157.1 LIP, 114th since 1974.

So let’s accept that relievers today don’t compile the same leveraged workloads as their predecessors. That’s interesting, but there’s nowhere we can go with it. Nothing’s going to change.

Here’s the same list, just for the 30-team era since 1998:

Season

Pitcher

LI

IP

LIP Index

2002

Billy Koch

2.09

93 2/3

195.8

2005

Scot Shields

2.08

91 2/3

190.7

2008

Francisco Rodriguez

2.53

68 1/3

172.9

2004

Mariano Rivera

2.17

78 2/3

170.7

2000

Derek Lowe

1.86

91 1/3

169.9

2000

Shigetoshi Hasegawa

1.75

95 2.3

167.4

2004

Francisco Cordero

2.29

71 2/3

164.1

1998

Rick Aguilera

2.19

74 1/3

162.8

2001

Mariano Rivera

2.01

80 2/3

162.1

1999

Roberto Hernandez

2.21

73 1/3

162.1

1998

Tom Gordon

1.99

79 1/3

157.9

2015

Dellin Betances

1.87

84

157.1

2005

Francisco Rodriguez

2.33

67 1/3

156.9

2013

Jim Johnson

2.21

70 1/3

155.4

2006

Francisco Rodriguez

2.11

73

154.0

Which 2017 teams and relievers may be overworked?

How about the current game, though? Which bullpens may be overtaxed? I’m going to skip the LI and IP details and just list team LIPs so far this season.

Team

LIP

Team

LIP

Rays

296.9

Red Sox

228.3

Brewers

295.3

Phillies

228.0

Blue Jays

287.3

Rangers

227.9

Cardinals

267.2

Royals

226.7

Mets

260.6

Yankees

225.3

Orioles

260.3

Twins

213.6

Pirates

257.2

Dodgers

213.5

Cubs

247.3

Giants

212.8

Rockies

246.1

Padres

210.5

Angels

244.0

Tigers

209.5

Astros

243.0

Braves

208.6

Diamondbacks

241.8

Reds

201.6

Nationals

232.1

Indians

198.1

Mariners

229.9

Athletics

195.3

Marlins

229.3

White Sox

190.6

And here are the highest-LIP pitchers so far in 2017:

Pitcher

LI

IP

LIP Index

Alex Colome

2.32

33 1/3

77.3

Seung Hwan Oh

2.26

32

72.3

Chris Devenski

1.70

41 2/3

70.8

Corey Knebel

1.95

35 2/3

69.6

Addison Reed

1.87

36 1/3

67.9

Tony Watson

2.11

31 2/3

66.8

Brad Hand

1.74

38 1/3

66.7

Greg Holland

2.32

27 2/3

64.2

Jim Johnson

2.11

29 2/3

62.6

Cody Allen

2.21

27

59.7

Felipe Rivero

1.53

38 1/3

58.7

Brad Brach

1.83

31 1/3

57.3

Andrew Miller

1.60

35 2/3

57.1

Fernando Rodney

2.07

26 2/3

55.2

Brandon Kintzler

1.80

30 1/3

54.6

What does a high LIP index portend?

Well and good, but what does it all mean? Is Francona right that too many high-leverage innings affect a pitcher? Are the Rays, Brewers, and Blue Jays wearing down their bullpens, or are their high LIP Indices just a product of near-.500 teams playing a lot of close games? Are Cleveland and Pittsburgh—both with two relievers in the top 15—wearing its best relievers to a nub?

To check, below is a table that shows the 15 pitchers with the highest LIP Index at the All-Star break last year. In the following three columns, I’ve listed their change in ERA, strikeout percentage, and walk percentage after the break. Positive changes are good, negative changes are bad.

For example, Jeurys Familia had a 2.55 ERA, 24.0 percent strikeout rate, and 8.8 percent walk rate at the All-Star break. After the break, he had a 2.55 ERA, 28.7 percent strikeout rate, and 10.7 percent walk rate. That works out to a +0.00 change in ERA, a +4.7 percent (favorable) change in strikeout rate, and a -1.9 percent (unfavorable) change in walk rate.

Here’s how it worked out last year for the LIP leaders at the break.

Pitcher

LIP

Change in ERA

Change in K%

Change in BB%

Jeurys Familia

89.3

0.00

4.7

(1.9)

Jeanmar Gomez

88.8

(5.74)

0.4

(3.1)

Sam Dyson

87.9

0.39

0.7

(4.5)

Brad Ziegler

87.3

1.18

6.7

(0.2)

Erasmo Ramirez

84.3

1.34

(2.8)

(0.3)

Steve Cishek

84.0

0.90

(4.5)

1.1

Santiago Casilla

82.9

(1.77)

(8.5)

1.0

Jeremy Jeffress

77.8

0.06

1.8

(6.6)

David Phelps

74.5

0.89

5.3

(11.8)

David Robertson

74.1

(0.59)

2.1

1.6

Nate Jones

73.4

0.38

5.7

(0.9)

Dellin Betances

72.2

(1.07)

(7.0)

(8.5)

Luke Gregerson

72.0

0.49

(5.6)

(2.2)

Cody Allen

71.5

0.65

8.5

3.2

Alex Colome

70.7

(0.50)

1.6

4.6

MEDIAN

0.38

1.6

(0.9)

That’s not what I was expecting, either. Of the 15 pitchers with the highest LIP Index at last year’s All-Star break, all but five had a better ERA and a higher strikeout rate after the break. All but five had a higher walk rate, but that didn’t do much damage. (And yes, those figures all easily exceeded the league averages of a 0.12 improvement in ERA, 0.3 percent increase in strikeout rate, and 0.1 percent increase in walk rate in the second half.) Overall, working a reliever hard, at least given last year’s results, does not appear to be well-correlated to a breakdown during that same season.

Unless, as in the cases of Jeanmar Gomez, Santiago Casilla, and, yes, Betances, last year, it does.

Thank you for reading

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ErikBFlom
6/22
It would be interesting to see the same thing for starters in the 1-2 inning before their removal. Which ones are getting the hook, and which are being put through the wringer? Is it pitcher-by-pitcher, or is it just fast-hook managers? Who is really earning his pay out there?
mainsr
6/22
Good idea, ChicagoOriole, thanks. (I'd guess that regularly leaving a starter in high-leverage situations after the fifth inning or so is probably dumb.) This would require more work than the reliever stuff did, but I'll add it to my ideas list.
lichtman
6/22
Good work, Rob. Can you believe another conventional wisdom blown up? What is this world coming to?
mainsr
6/22
Thanks! This was one of those cases in which I was going along, doing my research, when I figured, "Hey, I better check to be sure this means anything," and BOOM! My editor-in-chief suggested another line of inquiry I'll pursue soon. My methodology will draw from some of things you've showed me.
BeplerP
6/22
This is excellent, outstanding. Proving once again that if you do some heavt lifting, you find out stuff! This has really improved my understanding of reliever (abuse). Terry Collins, I have my eye on you.
mainsr
6/22
Well, the last table calls into question whether reliever overuse is really a thing. But certainly, bullpen usage is a major tenet in the People of Queens v. T. Collins litigation.