1. sports
2. baseball

MIT Sloan Sports Analytics Conference 2011
March 4-5,
5, 2011, Boston, MA, USA
Paired Pitching: How to Avoid an Arms Race
Greg Rubin
MBA Candidate 2012
New York University – Stern School of Business
New York, NY 10012
Email: [email protected]
Abstract
For every successive time a pitcher faces a batter in a game, that pitcher is more likely to allow runs to that
batter. An analysis of covariance confirms this observation and suggests that by limiting the number of times a
pitcher faces a batter in a game, the pitching team will prevent more ru
runs
ns from being scored. In order to
prevent multiple plate appearances against a pitcher a strategic shift in pitching staff construction must be
made. This paper proposes
oses the Paired Pitching system, in which four pairs of average pitchers are responsible
for innings one through eight, with each member of a pair taking exactly four innings of work. Four bullpen
pitchers would be responsible for all other innings. Through a careful analysis of the data this paper shows that
the Paired Pitching system would significantly increase wins. Furthermore, MLB teams spend a majority of
their player payroll on a five-man
man rotation. This analysis shows that the Paired Pitching system would
significantly decrease the cost of achieving the desired pitching production. Lastly, this paper quantifies
additional benefits
its from the Paired Pitch
Pitching system,, suggests additional research topics, and provides a
suggested implementation technique for this new pitching model.
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MIT Sloan Sports Analytics Conference 2011
March 4-5,
5, 2011, Boston, MA, USA
1 Introduction
Starting pitching is expensive. Off course the Cliff Lee’s, Roy Halladay’s and CC Sabathia’s highlight how expensive
it is, but the overall numbers support these few cases – in 2009 the average MLB team spent 28% of their entire player
payroll on a 5-man rotation [1]. In other words, 12.5% of the 40-man
man roster took up 28% of the payroll.
It might make sense to overspend on starting pitching if starting pitching is a significant attribute of winning, but it
is tending to be less and less of one. Innings pitched per start has declined steadi
steadily over the past twenty years with
starters now leaving about 1 more out per game to the bullpen than in the early 1990’s [2]. This trend
end can be seen in
Figure 1.
6.30
6.20
6.10
6.00
5.90
5.80
5.70
5.60
5.50
Figure 1: IP per Start
This trend shows that not only are starting pitchers less responsible for ending a game but they are also
a
becoming less efficient. In other words, starters are still facing the same number of batters per three outs as they were
twenty years ago. This effect can be seen in Table 2 and is bad for the pitching team since it means more work is being
performed by the less efficient bullpen [2]
[2]. Clearly the return on investment of starting pitchers is diminishing and
finding a way to limit the inefficiencies of starting pitchers would be a valuable asset to a major league team.
4.5
4.45
4.4
4.35
4.3
4.25
4.2
4.15
4.1
4.05
4
Figure 2: Batters Faced per IP by Starters
One mechanism for limiting staarting pitching inefficiency is the number of times opposing batters face starting
pitchers in a game. From the figures aboove it follows that the average MLB starter faced a batter 2.8 times in a game in
2009:
(5.8 IP per Start [Figure 1] x 4.3 batters faced per IP [Figure 2])) / 9 = 2.8 Times Faced
Most baseball fans and analysts would agree that the more often a batter can face a pitcherr in a game, the more
efficient that batter will become. A numbber of reasons have been given to explain this effect, rangingg from pitcher
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MIT Sloan Sports Analytics Conference 2011
March 4-5,
5, 2011, Boston, MA, USA
fatigue to the batter being able to see thee pitcher’s release point better. Regardless of the cause, the ability of the batter
to improve against a pitcher the more hee faces that pitcher in a game has been shown to exist statistically [3]. In
particular, as previous analysis [3] and this analysis show, facing a batter more than twice significantly decreases
decrease a
pitcher’s ability to prevent runs. Therefore, if a team were to reduce the number of times a pitcher faces
face opposing
batters to less than 2.8, runs would be prevented
prevented. As this paper will show, this
his strategy would have additional
additiona benefits
both in terms of cost savings, ROI, and the careers of pitchers.
Ensuring that each pitcher faces opposing batters less than 2.8 times requires a strategic shift in the way a team
builds a pitching staff. This paper proposes that by desi
designing a pitching staff to have 4 pairs of pitchers
pitche (plus 2 closers
and 2 relief pitchers), with each member of a pair pitching exactly four innings per appearance the team would prevent a
significant number of runs and save a significant amount of money in the process. The data set used is from the 83
starters in 2009 who threw at least 150 innings as starters (a full list is in Appendix A). The metric for gauging pitching
success is Runs Allowed per Batter Faced which will be shown to have a significant relationship to Times
Tim Faced.
2 Times Faced
Before the paired pitching model can be statistically tested it is important to show that facing batters fewer
times in a game will significantly improve a pitcher’s ability to prevent runs. In 1996 David Smith performed an analysis
on play-by-play
play data to show that the more a batter faces a pitcher in a game the better that batter performs. While this
study was comprehensive and showed differences in hitting metrics across times facing a ppitcher, the data was not
rigorously tested from a statistical
tatistical standpoint and also could be perceived as outdated.. So the question remains, in the
post “Moneyball” era how much better do we expect a batter to perform the more times he faces a pitcher? For this
analysis, the question can be repositioned as, how many more runs are allowed by a pitcher the more times opposing
batters face him in a game?
To investigate the interaction
nteraction between Times Faced and Runs Allowed
llowed an analysis of covariance (ANCOVA) is
performed on Runs Allowed (RA) using Times Faced (TF) and total Batters Faced (BF) for the sample set of 83
pitchers. This analysis
lysis shows that there is indeed a significant relationship between TF and RA (p
(p-value
value < .0009). In
fact, holding all else constant, an average number of batters faced would yield 19.9 RA the first time facing those batters,
24.8 RA the second time, 25.5 RA the third time, and 13.3 the fourth time (though the sample size for 4th TF is very
small). These results clearly show the importance of limiting the number of times a pitcher must face an individual
batter in a game. It also supports the use of RA / BF as the success metric with almost 75% of the variance in RA
explained by variance in TF and BF. The
he full ANCOVA results can be found in Appendix B.
3 Paired Pitching
Armed with the knowledge that reducing TF will yield fewer RA it is po
possible
ssible to devise a pitching staff model
within the constraints of the game that works to achieve this goal. It might be possible to construct a pitching staff
whereby once a starting pitcher faces every batter twice he is replaced. This could work, but a simpler way to limit TF is
in terms of innings. With 9 lineup spots and the average pitcher facing 4.3 batters per inning (Figure 2) it would take 4.1
innings to face every batter twice. Therefore, if a team carrie
carries 8 pitchers split into 4 pairings (plus 2 closers and 2 relief
pitchers) and each paired pitcher throws exactly 4 innings it would ensure each pitcher only faces a batter twice at most
(on average). For example, the Boston Red Sox could make a pair of Tim Wakefield (19 starts in 2010,
2010 2 less than 4 IP)
and Daisuke Matsuzaka (25 starts in 2010, 0 less than 4 IP) [4].. On a game day for this pair Wakefield would pitch
innings 1-44 and Matsuzaka would pitch 55-8, with a closer pitching 9 if needed and the relief pitcherss responsible for
extra innings. On the next appearance for this pair they could swap innings or ke
keep
ep it the same depending on
preference, warm-up time needed, etc.
One area of concern that arisess naturally is how this system handles the situation that Wakefield faced twice in
2010, where a paired pitcher can’t last fouur innings. First, there are four bullpen pitchers, all of who
om should be trained
and developed to be able to pitch 1 to 2 innings every day. Since onlyy 75% of games in 2010 actually contained a 9th
inning and of the 1,448 innings pitched bby the average team in 2009 (Appendix C), only 28 of them were extra innings,
these bullpen pitchers won’t be used every game [5].. Thus, at least one should be available to pitch on the off chance
that a paired pitcher cannot last 4 innings.
There are obviously issues that arise from such a drastic change to the pitching staff and the will be addressed.
However, it is important to first investigate the impact such a change would have on performance and payroll.
4 Fewer Runs Allowed
It’s clear that minimizing TF prrevents runs. What isn’t clear yet is exactly how many runs would
w
be prevented
in the Paired Pitching system. Previous analysis in this paper has focuse
focused on data segmented by TF however since the
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MIT Sloan Sports Analytics Conference 2011
March 4-5,
5, 2011, Boston, MA, USA
Paired Pitching system is based on starters throwing exactly four innings it is imperative to use data segmented by inning
going forward. Allll data relating to the Paired Pitching system will assume that each paired pitcher’s stats can be
represented by the data from his first four innings of work
work. In other words, the pitcher who throws innings 5 – 8 will
average the same RA per BS as his RA per BS of innings 1 – 4 from the data set. Table 1 shows the difference between
the paired pitching
ng model and MLB averages for 2009 and Appendix C has a more detailed discussio
on on this
assumption.
Table 1: Paired Pitching vs. Standard System
Runs Allowed per BF
Starter Innings
Bullpen Innings*
Bullpen Runs per BF
Paired Pitching System
0.105
8.0
8.00
Standard Pitching System
0.120
5.81
0.9
0.93
3.12
0.09
0.093**
0.115
* - Average game length in 2009 was 8.93 innings [5]
** - Assumes average of 2009 pitchers with at least 10 SVO [2]
he role of the bullpen is minimized in the paired pitching approach and that even with average pitchers the
The
paired pitching model has a lower RA per BF than the current model. What isn’t clear from the data so far is exactly
how this runs savings would translate into wins if applied to a real pitching staff.
Assuming the paired pitchers work 8 innings, an average closer work
works the 9th when applicable, and an average
bullpen pitcher works extra innings, the Runs Allowed for an average team over the course of the season would be 96
fewer than the current pitching model. The breakdown of this number is shown in Table 2.
Table 2: Expected Runs Prevented
Runs Allowed per BF
Expected BF per IP
Avg Innings per Season (per Team)*
Expected RA per Season
2009 Actual RA
Expected Difference in Runs Allowed
Paired Pitchers
0.105
4.31
1,296
587
Closer
Bullpen Pitcher
0.093
0.115
4.35
4.35
124
28
50
14
Team Total
0.104
4.32
1,448
651
747
-96
* - See Appendix C for calculation
The average MLB team allowed 747 runs in 2009. Had a team utilized the Paired Pitching system they would
have prevented about 13% of those runs over the course of the season. 96 fewer Runs Allowed, using the Pythagenpat
method [2], translates to about 9.3 additional wins. It is of lit
little debate that an additional nine wins is desirable.
5 Payroll Savings
Nine additional wins is desirable but as any experienced executive would say, there are always tradeoffs. This
statement is true for Paired Pitching, but the tradeoffs are not in the budget. For the exercise of determining the
financial implications of the Paired Pitchi
Pitchingg model it is best to create a theoretical pitching staff. The pitching staff for
this analysiss will be comprised of purely average pitchers from each role (starters, closers, bullpen) from a RA per BF
standpoint. Table 3 shows the theoretical pitching staff, each pitcher’s RA per BF using 2009 per inning data [5], 2009
salary [5], and number of years of MLB service as of the 2009 season [5].
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MIT Sloan Sports Analytics Conference 2011
March 4-5,
5, 2011, Boston, MA, USA
Table 3: Payroll Cost per Year of Average Paired Pitching Sys
System
Pitcher
Porcello, Rick
Shields, James
Romero, Ricky
Danks, John
Sanchez, Jonathan
Lannan, John
Cueto, Johnny
Wells, Randy
Wilson, Brian
Wilson, CJ
Lowe, Mark
Chavez, Jesse
TOTAL
Role
Paired
Paired
Paired
Paired
Paired
Paired
Paired
Paired
Closer
Closer
Bullpen
Bullpen
Share of Innings
11%
11%
11%
11%
11%
11%
11%
11%
4%
4%
1%
1%
1,448 IP
RA/BF
0.100
0.106
0.110
0.106
0.104
0.097
0.108
0.106
0.089
0.116
0.115
0.115
0.105*
Salary (000)
$
2,095
$
1,500
$
1,450
$
520
$
455
$
425
$
418
$
400
$
480
$
1,850
$
418
$
402
$
10,413
Years of Service
3
1
2
3
2
1
1
3
4
3
1
* - Total RA/BF
BF is weighted by Share of Innings (see Appendix C)
The first important element to recognize about this pitching staff is that given the number of innings
inn
each
pitcher contributes, the overall RA per BF for the staff is at the target of 0.105. The other, and perhaps more striking
element, is that this target is achievable for just under $10.5 million. In 2009 only 2 teams came close to achieving a
pitching payroll of $10.5 million – the Marlins and the Nationals who respectively ranked 20th and 29th for Runs Allowed
[1]. Achieving this level of pitching performance for such little payout is the competitive advantage for which the
t Paired
Pitching model is designed.
6 Tradeoffs
The Paired Pitching system wins more games and costs much less than a standard pitching staff model but
there are inherent concessions that would be made to gain this strategic advantage. The most obvi
obvious
ous one is that the
traditional concept of ace pitcher doesn’t exist and that might be a difficult transition to make for a lot of coaching
staffs, scouts, owners, and fans. Obviouusly a team could not just flip a switch and all of a sudden haave a Paired Pitching
system implemented. A phased approachh would be necessary. Also, Fans would never be treated to a no-hitter
no
or a 20
strikeout performance, and owners
ers who are thinking about the bottom line might desire an ace pitcher for marketing,
media relations, or merchandising purposes. However, spending so little on pitching would allow a team to court top
hitters to hedge the lack of pitching aces. Plus, fo
forr a team who does not have the luxury of a large payroll the Paired
Pitching system would be a competitive advantage
advantage, which would accumulate larger profits over the long term.
The other difficulty teams would have to overcome is the role of the player contract.
ct. A paired pitcher would
not have comparable stats to traditional closers which, when it comes time to negotiate a contract, would make it
difficult for that pitcher
itcher to garner a top contract (and incentive-based bonuses would be different). This discrepancy
relates to a fundamental characteristic of the Paired Pitching system – that the only pitchers to consider for the system
would be young pitchers,, middle relievers, and past
past-their-prime veterans. It is not a coincidence only one pitcher in
Table 3 has more than three years of major league experience.. Pitchers who have already established themselves as
major league starters may not be willing to fforgo their individual statistical achievements, but young pitchers looking for
a chance to move up from the minors or out of a middle relief role might be more willing to tra
trade
de off individual stats for
more innings of work. In addition, veterans who have achieved all of the individual accolades they desire but have lost
the ability to throw 6-7 innings in a rotatiion and aren’t willing to be in the bullpen might be interested in a contract to be
a paired pitcher. In short, at the individual pitcher level there is a tradeoff to be made between statistical achievements
and the chance at more innings of work.
There is one area in which no tradeoff need be made to realize an advantage. Since a paired pitcher would only
face 11% of a team’s innings in a season (Table 3), it can be assumed that the number of pitches thrown over the course
of a season would be significantly below the average number thrown by traditional starters. Since every rotation
ro
spot is
responsible for between 30 and 35 games [2], the average number of pitches thrown per inning by a starter in 2009 was
16.2 (for pitchers with at least 90% of appearances as starts) [2], and since the average number of innings per start was
5.98 (for the same sample) [2],, the average number of pitches thrown by a rotation spot was:
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MIT Sloan Sports Analytics Conference 2011
March 4-5,
5, 2011, Boston, MA, USA
32.5 games x 5.98 IP per GS x 16.2 pitches per IP = 3,142 pitches per season
The difference is in the number of IP per GS for paire
paired pitchers since paired pitchers are accountable
ntable for 11% of the
team’s innings (Table 3). The
he pitch savings over the course of the season is:
1,296 IP per season x 11% share of IP x 16.2 pitches per IP = 2,307 pitches per season 835 fewer pitches
Saving over 25%
% of the pitches thrown would in theory lengthen the careers
rs of a vast number of pitchers and reduce the
incidence of throwing related injuries. Thhis reduction would therefore reduce medical costs for the team
t
and create an
attractive selling point with which to sign pitchers.
7 Additional Research
The analysis done here to quantify the run and cost savings of the Paired Pitching model is comprehensive but
by no means exhaustive. First, the analysis on runs savings does not account for batting order, platoon effect, league,
lea
or
home field effects.. Devising an analysis that discounts the per inning data by these factors might be necessary for a team
seriously considering the Paired Pitching model. Second, a pitching coach running this model would have a considerably
different dynamic
namic to deal with in terms of game preparation, side sessions, gauging closer and bullpen fatigue, 2nd paired
pitcher warm-ups, and a whole host of other aspects of managing a pitching staff. Qualitative research should be
performed with managers and pitching
ching coaches to identify potential pain points and coaching advantages of Paired
Pitching. Also, while this study uses RA per BF to quantify the advantages of the Paired Pitching model,
model RA per BF is
admittedly a very high level statistic and might be tough to use in target
targeting
ing potential pitchers for this system. Studies
could be done with pitching statistics more commonly used in evaluating pitchers. Lastly, this model would obviously
benefit from more than four pairs of pitcchers.. Having five pairs of pitchers instead of four would significantly
signific
benefit
each pair with more rest but additional pitchers would be required to handle bullpen situations
situations.. An analysis should be
performed that quantifies the elasticity of Runs Scored and Runs Allowed when a position player is exchanged for a
pitcher (and how that elasticity changes depending on type or level of player/pitcher) on the 40
40-man
man roster.
8 Conclusion
To summarize, this
his analysis first shows a significant relationship between the number of times a pitcher faces a
batter in a game and thee average number of runs allowed per plate appearance. The analysis then proposes that the ideal
way to exploit this relationship is, in a practical sense
sense, to have pairs of pitchers, with each pitcher in a pair appearing in
the game for exactly four innings.
Using this Paired Pitcher system
m with the limit of exactly four inningss for each paired pitcher would, on
average, result in the savings of 96 runs, or about nine additional wins per season. Furthermore, to achieve this average
runs savings it would
d cost the average MLB team about $10.5 million per year for their entire pitching staff. An
important point to remember is that thesse are average runs and cost savings. The price elasticity of pitching is such that
additional runs presented could most likeely be bought in the Paired Pitching system. Lastly, even with only 4 pairs of
starters instead of 5 rotational pitchers each pi
pitcher
tcher would throw about 835 fewer pitches over the course of a season.
Additional work on the effects of this sysstem could greatly increase the runs and/or cost savings. Further research is
suggested to improve and more accurately quantify the effects of this pitching model.
This study suggests that the ideal implementation of the Paired Pitching system would be to maintain the
current number of pitchers on a staff and have four pairs of pitchers, two closers, and two relief pitchers for use in extra
innings
ings and when paired pitchers can’t make it all four innings. It also seems logical to pair pitchers based on pitching
style. Much like a portfolio of stocks reduce
reduces idiosyncratic risk, each pair should be made so as to vary the pitching
styles as much as possible. So, a right handed pitcher would be paired with a southpaw to hedge the risk in the platoon
effect with overall style, pitch type selection, etc also taken into consideration.
Given all of the advantages of the Paired Pitching system
system,, it is important to remember that it is not a system for
every pitcher or every team. A team implementing this system would be making a commitment to filling their
t
pitching
staff with inexperienced young pitchers aand past-their-prime veterans – a considerably dissonant concept in today’s
tod
talent market. However, this commitment would ensure that a team without the means to compete for ace pitchers
would still prevent a significant number of runs allowed and they could focus their monetary attention on hitting. Also,
established major league starters would not be attracted to a team implementing this model, but that is the intention. A
Paired Pitching team would be ignored by the ace starters in the league and the team itself would ignore the desire to
enter into an arms race for the top dollar aces.
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MIT Sloan Sports Analytics Conference 2011
March 4-5,
5, 2011, Boston, MA, USA
9 Acknowledgments
I would like to thank
nk Jeffrey Simonoff and JC Bradbury for their assistance in vetting many of the statistical
methods used in this analysis.
10 References
[1] Euston, Jeff & USA Today. “2009 P
Payroll – Breakdown by Percentage.” http://mlbcontracts.blogspot.com
bcontracts.blogspot.com &
http://content.usatoday.com/sports/baseball/salaries/default.aspx
http://content.usatoday.com/sports/baseball/salaries/default.aspx. August 11, 2010.
[2] Prospectus Entertainment Ventures,, LLC. http://www.baseballprospectus.com. August 12, 20010.
[3] Smith, David W. “Do Batters Learnn During a Game?” June 7, 1996. http://www.retrosheet.ccom. September 8,
2010.
[4] MLB Advanced Media L.P. http:///mlb.mlb.com. September 9, 2010.
[5] Sports Reference LLC. “Inning Sum
mmary.” http://www.baseball-reference.com. May 20, 20110.
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MIT Sloan Sports Analytics Conference 2011
March 4-5,
5, 2011, Boston, MA, USA
Appendix A: 2009 Pitchers with 150+ IP as Starter
First Name
Last Name
IP
Tm
GS
Brett
Anderson
Bronson
Arroyo
Scott
Runs
BF
R / BF
175
OAK
220
CIN
30
94
735
0.13
33
101
923
0.11
Baker
200
MIN
33
99
828
0.12
Brian
Bannister
154
KCR
26
94
668
0.14
Josh
Beckett
212
BOS
32
99
883
0.11
Chad
Billingsley
196
LAD
32
94
823
0.11
Nick
Blackburn
205
MIN
33
103
882
0.12
Joe
Blanton
195
PHI
31
89
837
0.11
Mark
Buehrle
213
CHW
33
97
874
0.11
A.J.
Burnett
207
NYY
33
99
896
0.11
Trevor
Cahill
178
OAK
32
99
773
0.13
Matt
Cain
217
SFG
33
73
886
0.08
Chris
Carpenter
192
STL
28
49
750
0.07
Joba
Chamberlain
157
NYY
31
94
709
0.13
Aaron
Cook
158
COL
27
76
675
0.11
Kevin
Correia
198
SDP
33
92
830
0.11
Johnny
Cueto
171
CIN
30
90
740
0.12
John
Danks
200
CHW
32
89
839
0.11
Doug
Davis
203
ARI
34
101
889
0.11
Jorge
de la Rosa
185
COL
32
95
799
0.12
Ryan
Dempster
200
CHC
31
94
842
0.11
Zach
Duke
213
PIT
32
101
891
0.11
Scott
Feldman
189
TEX
31
87
791
0.11
Gavin
Floyd
193
93
CHW
30
93
797
0.12
Yovani
Gallardo
185
MIL
30
78
793
0.10
Jon
Garland
204
TOT
33
106
882
0.12
Matt
Garza
203
TBR
32
93
861
0.11
Zack
Greinke
229
KCR
33
64
915
0.07
Jeremy
Guthrie
200
BAL
33
120
874
0.14
Roy
Halladay
239
TOR
32
82
963
0.09
Cole
Hamels
193
PHI
32
95
814
0.12
Jason
Hammel
176
COL
30
94
771
0.12
Aaron
Harang
162
CIN
26
82
703
0.12
Dan
Haren
229
ARI
33
83
909
0.09
Felix
Hernandez
238
SEA
34
81
977
0.08
Livan
Hernandez
183
TOT
31
112
806
0.14
Edwin
Jackson
214
DET
33
93
890
0.10
Ubaldo
Jimenez
218
COL
33
87
914
0.10
Josh
Johnson
209
FLA
33
77
855
0.09
Jair
Jurrjens
215
ATL
34
71
884
0.08
Clayton
Kershaw
171
LAD
30
55
701
0.08
John
Lackey
176
LAA
27
84
748
0.11
John
Lannan
206
WSN
33
100
875
0.11
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First Name
Last Name
IP
Tm
GS
Runs
BF
R / BF
Cliff
Lee
231
TOT
34
88
969
0.09
Jon
Lester
203
BOS
32
80
843
0.09
Ted
Lilly
177
CHC
27
66
706
0.09
Tim
Lincecum
225
SFG
32
69
905
0.08
Braden
Looper
194
MIL
34
123
866
0.14
Derek
Lowe
194
ATL
34
109
855
0.13
Paul
Maholm
194
PIT
31
102
836
0.12
Jason
Marquis
216
COL
33
104
921
0.11
Kevin
Millwood
198
TEX
31
88
850
0.10
Brian
Moehler
154
HOU
29
101
694
0.15
Jamie
Moyer
162
PHI
25
91
699
0.13
Jeff
Niemann
180
TBR
30
84
769
0.11
Ricky
Nolasco
185
FLA
31
111
785
0.14
Ross
Ohlendorf
176
PIT
29
80
725
0.11
Roy
Oswalt
181
HOU
30
83
757
0.11
Carl
Pavano
199
TOT
33
119
854
0.14
Mike
Pelfrey
184
NYM
31
112
824
0.14
Brad
Penny
173
TOT
30
102
751
0.14
Andy
Pettitte
194
NYY
32
101
834
0.12
Joel
Pineiro
214
STL
32
94
865
0.11
Rick
Porcello
170
DET
31
81
720
0.11
Wandy
Rodriguez
205
HOU
33
77
849
0.09
Ricky
Romero
178
TOR
29
88
771
0.11
CC
Sabathia
230
NYY
34
96
938
0.10
Jonathan
Sanchez
163
SFG
29
82
710
0.12
Johan
Santana
166
NYM
25
67
701
0.10
Joe
Saunders
186
LAA
31
102
805
0.13
Max
Scherzer
170
ARI
30
94
741
0.13
James
Shields
219
TBR
33
113
930
0.12
Jeff
Suppan
161
MIL
30
106
748
0.14
Javier
Vazquez
219
ATL
32
75
874
0.09
Justin
Verlander
240
DET
35
99
982
0.10
Chris
Volstad
159
FLA
29
100
682
0.15
Adam
Wainwright
233
STL
34
75
970
0.08
Jarrod
Washburn
176
TOT
28
77
724
0.11
Jered
Weaver
211
LAA
33
91
882
0.10
Randy
Wells
165
CHC
27
67
694
0.10
Randy
Wolf
214
LAD
34
81
862
0.09
Carlos
Zambrano
169
CHC
28
78
733
0.11
Barry
Zito
192
SFG
33
89
818
0.11
9
MIT Sloan Sports Analytics Conference 2011
March 4-5,
5, 2011, Boston, MA, USA
Appendix B: ANCOVA Results
Factor
Time Faced
Type
fixed
Levels
4
Values
1, 2, 3, 4
Analysis of Variance for RA, using Adjusted SS for Tests
Source
BF
Time Faced
Error
Total
DF
1
3
327
331
S = 6.19916
Term
Constant
BF
Seq SS
31556.1
3401.2
12566.5
47523.8
Adj SS
672.6
3401.2
12566.5
R-Sq
Sq = 73.56%
Coef
ef
9.230
0.05681
SE Coef
2.799
0.01358
Adj MS
672.6
1133.7
38.4
F
17.50
29.50
P
0.000
0.000
R
R-Sq(adj) = 73.23%
T
3.30
4.18
P
0.001
0.000
Means for Covariates
Covariate
BF
Mean
204.6
StDev
106.9
Least Squares Means for RA
Time
Faced
1
2
3
4
Mean
19.87
24.77
25.50
13.27
SE Mean
1.3804
1.1621
0.7134
2.4537
NOTE:: One interesting output of the ANCOVA is the standardized residuals for each data point. The standardized
residuals represent potential outliers to the regression and since the data set is segmented by Times Faced it is possible to
see which pitchers over or under-index
index for each time faced factor. A standardized residual beyond ±2.5
± is most likely an
outlier. So, for example the standardized residual for the first time batters face Jeremy Guthrie is 3.03, suggesting that
Guthrie is significantly worse than his peers at facing batters for the first time. Alternatively, Dan Haren’s standardized
residual for the first time facing batters is -2.36, suggesting Haren is potentially much better than
han his peers when facing a
batter for the first time in a game. This might be a productive way of finding pitchers best suited for the Paired Pitching
system or even handling a pitching staff iin general.
10
MIT Sloan Sports Analytics Conference 2011
March 4-5,
5, 2011, Boston, MA, USA
Appendix C: Commentary and Additional Calculations
Fraction of an Inning: Most baseball datta warehouses record innings with the tenths spot representting the number of
outs. So if a pitcher lasted 4 innings andd 1 out in the fifth, his work for the game would be recorded
d as 4.1. In this
analysis innings are treated naturally, so tthe example of 4 innings plus one out would be noted as 4.333.
RA per BF for Paired Pitching: The dataa set used to calculate the RA savings over the course of thee season is per inning
data for the 83 pitchers listed in Appendiix A. Two assumptions are made. The first is that for a givven pair of pitchers
the pitcher starting the game and leavingg after the 4th inning will of course have the identical RA perr BF as his per inning
data suggests. The second and less obvioous assumption is that the pitcher responsible for innings 5 through 8 will also
produce RA per BF at the same rate as hhis 2009 data for innings 1 through 4. This assumption is baased on the fact that
entering the game in the 5th inning is the same as entering at the start of the game. This of course iss not controlling for
batting lineup and that omission is addreessed in the “Additional Research” section.
Average Innings per Season: The numbeer of innings pitched per season per team for each role in thee Paired Pitching
system is calculated based on the responssibility of each role. From Baseball-Reference.com it is kno
own that there were
143,440 IP in 2009, or on average 1,448 pper team. Of that average total, only 28 IP were extra innin
ngs and 124 were the
9th inning. Since the Paired Pitching systtem accounts for 2 pitchers for the 9th inning and 2 pitcherss for extra innings, it
can be assumed that on average the 8 paiired pitchers on a team would pitch 1,448 – 124 – 28 = 1,2996 innings.
Share of Innings: Share of Innings in Taable 3 is calculated using the number of innings pitched per role listed in Table 2.
1,296 is 89.5% of the total 1,448 IP per tteam. With 8 paired pitchers on a staff, each paired pitcher would be
responsible for about 11.2% of a team’s total IP. 124 IP by the closer equates to 8.6% of the total, or
o 4.3% per closer,
and the 28 extra innings, or 14 per relief pitcher, is about 1% per pitcher.
11