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. 1 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 2 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 3 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]. 4 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: 5 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. 6 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. 7 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 8 MIT Sloan Sports Analytics Conference 2011 March 4-5, 5, 2011, Boston, MA, USA 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

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