An Army of Super Relievers: Building the Optimal Pitching Staff

An Army of Super Relievers: Building the Optimal Pitching Staff Hamilton Marx Candidate for MBA, Class of 2015 Duke University, The Fuqua School of Business Durham, NC 27707 Email: hamilton.marx@duke.edu Abstract When compared to starters, relievers in Major League Baseball throw with greater velocity, strike out more opposing hitters, and concede a lower batting average, on-base percentage, and slugging percentage. By abandoning the traditional starting pitcher role and allowing each pitcher to throw more often but in shorter stints, teams can take advantage of this improved performance. First, I analyze pitcher velocity data and find that the pitchers who move from a starter role to a reliever role see a significant increase in fastball velocity. Next, I examine the pitch usage patterns of the two roles, and find that relievers are able to maintain a higher performance level with fewer pitch types. Further, while it is clear that a pitcher loses effectiveness each time he faces a hitter in a game, I identify contributing factors by analyzing pitch usage data and hitters success rates off of different pitch types. Ultimately, I develop an optimization model and apply it to each 2013 MLB team to quantify the performance benefits of radically changing current pitcher usage roles. The model shows that the advantage in preventing runs is significant, and could be the difference in making or missing the playoffs for certain teams. 1 Introduction Many of the most difficult decisions that confront a baseball manager involve determining when to remove a starting pitcher from a game, and determining who to bring in once the starter is removed. Complicating the decision of when to remove a starter is the existence of the times through the order penalty ( TTOP ). Pitchers seem to have an advantage at the start of a game, but the advantage shifts to the hitter with each at bat, and with each pitch of an at bat as well. The concept is intuitive as hitters become more familiar with the timing and movement of a pitch, the pitcher s release point, etc., the batter should have more success. The actual quantifiable impact of the TTOP is astounding, and as starting pitchers get deep into games, their managers are often faced with a decision that will determine if the game is won or lost. I am proposing a pitching model where traditional starter and closer roles are eliminated, current starters are asked to throw more often but in shorter stints, and current relievers are asked to throw more innings. This model will accomplish three important goals: (1) minimize the TTOP, (2) distribute total innings in closer proportion to talent, and (3) use top pitchers in the highest leverage situations. In this paper, I will evaluate different metrics to quantify the performance effects of changing a pitcher s role, develop a model to optimize a pitching staff, and ultimately place a run value and win value on implementing the Super Reliever Model for every 2013 Major League Baseball team. 2 Starters vs. Relievers It is no secret that relief pitchers, when compared to starters, are more effective on a rate (or per batter) basis, despite the general perception of not having starter ability or stuff. Relievers hold the advantage in just about every metric imaginable. Perhaps most telling is the significant advantage relievers hold in weighted on-base average ( woba ), which is a metric developed by Tom Tango that uses linear weights to assign values to each potential offensive outcome of a plate appearance (excluding intentional walks and bunts) [1]. Every mention of woba herein refers to a pitcher s woba against, or the woba of all the batters a pitcher faces. The actual starter vs. reliever metrics for 2013 can be seen in Appendix 1. The approach of relief pitchers can be different than that of starters, since they only face a handful of batters per outing. The number of pitchers who enter a game for only one hitter has also risen dramatically, and as a result of avoiding unfavorable matchups it is logical that these pitchers would fare better. Further, by entering in the middle

of a game relievers face a slightly weaker pool of hitters (avoiding the top of the lineup more often). Despite these advantages, I found that the majority of the benefit relief pitchers have is due to the fact that they are rarely susceptible to the TTOP. While the TTOP is a fairly well-known phenomenon, managers willingly allow their starters to succumb to the penalty in order to use more specialized relievers late in games when leverage is perceived to be higher. In order to manage the bullpen in this manner, starters have to get deep into games. The average team in 2013 had 241 innings where a starter was facing a hitter for the third time, where the penalty is especially significant. Using aggregate totals from 2008 to 2013 and excluding pitchers batting and pinch hitters from the sample, the penalty is as follows: Table 2.1: Times Through the Order Penalty, 2008-2013 TTO TBF AVG OBP SLG woba K% K-UIBB% 1 252,326.258.321.407.320 17.5% 9.9% 2 246,289.269.332.430.333 15.5% 8.2% 3 189,386.276.338.445.341 14.4% 7.4% 4+ 20,949.271.333.417.327 13.4% 6.6% The TTOP is clear, and gets progressively worse with the exception of the fourth time through. There is a survivor bias of sorts here, as the pitchers left in to face a lineup for a fourth time are generally your elite starters and almost by definition had been pitching exceptionally well that particular day. Weather and the lop-sided game effect are likely contributing factors as well. We can further examine the TTOP by evaluating the batted ball trends over each time through the order. The percentage changes are slight, but with the run value of a line drive at 1.26 runs per out, even a small change makes a significant difference. As outlined in Appendix 2, the line drive rate steadily increases the second and third time through the order, while fly balls (.13 runs per out) increase and ground balls (.05 runs per out) [2] decrease significantly the third time through, driving the increase in slugging and woba each time through. 3 Pitch Usage In order to evaluate potential ways to mitigate the TTOP, I looked at pitch selection by time though the order to pinpoint any trends. After analyzing Pitch FX data [3] for every pitcher season since 2008 where the starter had faced a minimum of 100 batters in the third time through bucket (giving us a sample of almost 2 million total pitches), we see the pitch usage breakout as follows: Table 3.1: Pitch Selection by Time Through the Order FB/SI SL/CU/CH TTO FF FT FC SI Total SL CH CU Total 1 43.5% 10.2% 4.8% 6.7% 65.3% 11.8% 10.5% 8.4% 30.7% 2 37.0% 9.0% 5.0% 6.0% 56.9% 14.4% 13.4% 11.2% 39.0% 3 35.8% 8.9% 5.1% 5.9% 55.6% 14.7% 14.0% 11.6% 40.2% 4 35.3% 9.2% 5.5% 6.1% 56.1% 13.9% 13.3% 11.6% 38.8% I only included pitches that were used over 5% of the time: four-seam fastballs ( FF ), two-seam fastballs ( FT ), cutters ( FC ), sinkers ( SI ), sliders ( SL ), change-ups ( CH ) and curveballs ( CU ). We see that starters throw significantly more fastballs the first time around, in line with the traditional notion of establishing the fastball early to set up breaking pitches later on. We can also evaluate the effectiveness of each pitch by time through the order, calculating the woba of each pitch: 2

Table 3.2: woba by Pitch Type and Time Through the Order TTO FF FT FC SI SL CH CU 1.351.352.315.353.273.289.266 2.358.358.327.360.296.311.300 3.363.361.331.371.309.325.302 4.357.349.338.340.297.304.290 I also looked at SwSt% (swinging strikes per pitch) and whiff rate (swinging strikes per swing) as further measures of pitch effectiveness. The chart of SwSt% is located in Appendix 3. Regardless of which metric you choose, every pitch is susceptible to the TTOP. So while the secondary pitches are more effective overall, they lose effectiveness each time through the order, as pitchers throw fewer fastballs and more breaking pitches. While certain pitchers can overcome the TTOP for starts at a time or even a whole season, a pitcher s rate of avoiding or succumbing to the penalty has shown to have no predictive value, and every pitcher is susceptible to it. In building our staff, however, some pitchers will inevitably have to face a lineup more than one time through. To plan accordingly, it is important to evaluate which pitchers (if any) can avoid the burden best. To do so, I grouped pitchers from the previous sample based on how many pitch types they threw, with 10% usage as the threshold to qualify as a pitch. The results are seen in Appendix 4. I lumped the handful of one-pitch pitchers with the two-pitch pitchers, and the handful of six-pitch pitchers with the five-pitch pitchers. As we would expect, pitchers that can mix five or six pitches with frequency see smaller drop-offs in production the second and third times through the order than those with fewer pitches. This is particularly noticeable the third time around. Those with only one or two pitches (generally heavy fastball pitchers) actually start out better than their counterparts, but get hit harder quickly as batters become familiar with them. Unless we have a pitcher with five or six legitimate pitches, we should avoid the third time through the order whenever possible. Excluding the five-pitch bucket, we find that even the least effective group during the second time around is better than the most effective group the third time around. 4 Performance Advantage In addition to avoiding the TTOP, there is a clear velocity advantage when pitchers throw fewer innings at a time. The average fastball velocity per time through the order stays relatively high (91.4 to 91.2 to 91.1 the first three times through), but this is likely because starters know they need to throw upwards of 100 pitches and are unable to throw with max effort for an entire game. As a result, starters get hit harder even the first time through the lineup than relief pitchers do overall. By being able to air it out more, relievers had a 1.1 mph fastball velocity advantage compared to starters in 2013 (92.5 vs. 91.4). We get a similar answer when evaluating pitchers who have switched from starter to reliever in successive years. Using data from 2002 to 2013 and thresholds of 110 start innings and 40 relief innings, these pitchers gained an average increase of 1.3 mph in fastball velocity as relievers. Since the Super Reliever Model will take advantage of the shorter stint approach, I wanted to make sure the aging trends with respect to velocity were not dramatically different between starters and relievers. As we can see in Appendix 5, the aging curves are similar, with relief pitchers maintaining the slight edge throughout. To measure the impact velocity has on run prevention, I performed a series of regressions. Using velocity as the independent variable and fielding independent pitching ( FIP a metric that takes defense out of the equation) as the dependent variable yielded a slope coefficient of -0.1. FIP is measured as runs per 9 innings, so it is a small but not insignificant result. It is important to note that the r-squared values of each of these regressions was weak (<0.3), but we can still learn from the slope coefficients. The r-squared simply quantifies how much of the variance is explained by velocity. When I looked at the components of FIP individually, I found that the biggest impact is with strikeouts. The regression results are located in Appendix 6, and show a positive 0.009 slope coefficient for K%. Average K% is around 18.5% and it is generally clustered around 15-22%, so a 0.9% gain is significant. The other FIP components I used (BB% and HR/9) both yielded small negative slopes (0.002 for BB% and.04 for HR/9). While small, these results extrapolated over an entire season would amount to about 18 runs (this is assuming every starting pitcher gains 1 mph in velocity and relief pitchers stay constant). While clearly not the only factor, an increase in fastball velocity has a positive impact on run prevention. The best way to quantify the benefit of pitching in relief may be by looking at pitchers who have been used as starters and relievers in the same year. Since 2008, there have been 678 seasons where a pitcher has appeared as a starter and as a reliever. We can weigh each pitcher s woba by role by the harmonic mean of each player s plate 3

appearances against ( PA ) (minimum number of PA against). For example, in 2008 Justin Masterson had 194 PA as a starter and 121 PA as a reliever. His woba for each role is weighted by the 121 PA, rather than using 121 for the reliever bucket and 194 for the starter bucket. All total, the sample yields a.352 woba as starters, and a.324 woba as relievers. We can thus make the assumption that the pure talent differential between a starter and reliever is about 28 points in woba. Plugging this difference into our weighted runs above average wraa formula [(woba league average woba)/scale * PA] [4], we find that since starters average about 25 batters faced each game, moving them all to relief roles would translate into about.57 runs per game (92 runs over 162 games). We estimated the impact of the velocity increase to be 18 runs over a season, which seems to confirm that the majority of the relief pitcher advantage is in simply avoiding the TTOP. As we have established, almost 30% of a starter s workload comes against that dreaded third time through the order whereas relief pitchers almost never face a lineup more than once at a time. We also know that relief pitchers perform with fewer overall pitch types in their repertoire. The average relief pitcher throws 2.6 pitches, whereas the average starter throws 3.4 pitches (10% usage rate to qualify as a pitch ). If a starter no longer had to face an opponent for a second or third time in a game, he could conceivably eliminate a pitch from his arsenal. To further examine this point, I evaluated all starting pitchers whose repertoire decreased by 1 pitch (requiring that pitch to dip below 5% to qualify as eliminated). The year after eliminating a pitch, pitchers saw an increase in K% (17.4 to 19.2) and a decrease in BB% (6.9 to 6.6), HR/9 (1.08 to 1.05), and RA/9 (4.55 to 4.21). The sample is extremely small so we can t assume this will always be the case, but it gives thought that there may be a benefit to simplifying a pitcher s repertoire, which clearly could be achieved in the Super Reliever Model. 5 Leverage Another important tool to evaluate the best way to deploy a pitching staff is the game leverage index ( LI ), which measures the possible change in win probability of each situation. A tie game will have higher LI than a 10-run game, and a bases loaded two out situation will have a higher LI than a bases empty situation. Simply put, it behooves managers to go to their best pitchers in high leverage situations. For this reason, teams employ LOOGYs (left-handed one-out guys) and other bullpen specialists that are often asked to face just one hitter in a big situation before hitting the showers. When a starting staff can get deep into games managers can use the bullpen more aggressively. What I have found is that we can actually implement the Super Reliever Model without completely sacrificing these specialists. To evaluate when to turn to certain pitchers, we can look at when the high leverage situations occur. Dave Studeman did exactly this in a recent post on The Hardball Times, measuring the average LI of each inning of 2013 [5]. In equal base-out situations, LI obviously increases as the game goes on (tie game, no one out, no one on in the first inning has a lower LI than the same situation in the ninth inning), but the average LI by inning actually stays somewhat constant. The first inning is actually on average more important than the sixth or seventh. The LI by half inning is as follows: Table 5.1: Leverage Index by Half Inning Inning 1 2 3 4 5 6 7 8 9 Top 0.96 0.96 0.94 0.95 0.95 0.95 0.97 0.98 0.92 Bottom 0.97 0.94 0.94 0.96 0.93 0.95 0.95 0.96 1.74 Aside from the bottom of the ninth, where the LI is inherently high because the game is coming to an end, the average LI by inning is similar, proving there are plenty of high leverage situations early in games. Teams should not be hesitant to go to a top relief pitcher in the fourth or fifth inning if the LI is high else risk letting the game get out of hand with your top pitchers unused. We see this all the time with closers, as managers prefer to wait to the ninth inning to use them rather than in a high LI situation earlier in the game. Having the flexibility to use a LOOGY against a tough lefty in a bases loaded situation in the fourth inning without taking innings away from a top starter would be a tremendous advantage. In saving top relievers for the eighth and ninth innings, we also severely restrict the total number of innings of some of our best pitchers. Shifting innings from a back-end starter to a dominant reliever has obvious benefits, especially if those starter innings occur during the third time through the lineup. 4

6 Pitcher Optimization Model We can now use what we ve learned about pitcher roles and the TTOP to build our optimization model. The first decision relates to workload constraints. A healthy pitcher throwing every three games would be going on two days rest 38 times, and three days rest 16 times. Is this plausible, and if so, how many innings could he throw? We have to go back to the 1970 s and 1980 s to find pitchers who threw in two to four inning stints with regularity. With this sample, we can estimate how many pitches they threw per outing and evaluate whether the workload had any effect on productivity or longevity of career. While we don t have pitch information prior to 2002, we can estimate the pitches per outing based on the overall generational trends in strikeouts and walks. Estimating 4.82 pitches per strikeout, 5.42 pitches per walk, and 3.38 pitches for everything else, pitchers in the 1970 s and 1980 s threw 26-28 pitches per game on average, and upwards of 40 with regularity. These pitchers could maintain this model (throwing frequently on fewer than two days rest) without adverse effects, giving us confidence that a few innings every third day is in fact plausible (knowing the average pitches per inning in 2013 was a little more than 16). Based on this knowledge, we can set a conservative percentage increase cap in workload for relievers at 30%, based on the average relief innings of the top pitchers now versus then. Assuming there is no difference in the durability of pitchers between eras, today s relievers should be able to handle longer outings without suffering much in performance. With respect to starters, we can compare the average pitcher under each scenario: if a starter takes his turn every 5th game for a 162 game season and averages six innings each time, he will end up with 198 IP (33 starts * 6 IP). Throwing three innings on average every third game will end up with 162 IP (54 games * 3 IP). Thus, a transition to throwing every third day would result in an 18% workload reduction, or 82% of their typical starter workload. Capping every full time starter s innings at 82% of 2013 totals will take into account the fact that more efficient pitchers will throw more innings, as opposed to simply assigning every starter 162 IP or some other baseline. In some cases, a pitcher had around 100 IP as a starter not because he was injured, but because he was not in the rotation the entire season. In these cases we need not set the 82% constraint since these pitchers could theoretically throw that many innings or more in our model. Pitchers that were injured, however, still have their innings multiplied by the factor. I am assuming the injury would have occurred on the same date and they will have missed the same amount of time, thus will still have fewer innings. The same injury principle is applied to relievers, still increasing their workload by as much as 30% since they will be throwing more often/more innings at a time when they are healthy. Also of note is the way I treated young pitchers, taking the position that they would not have arrived any sooner to the big leagues had their team been implementing this model (though that may be a reasonable assumption to make). If a player was called up early in the season and sent back down because the rotation spot was no longer there, I allowed for a slight innings increase. For example, Tony Cingrani of the Reds threw just 104.2 IP because the Reds didn t need him in the rotation for a large portion of the year, whereas in my model he would have thrown 123.1 IP (still less than what he threw between AAA and Cincinnati), staying with the big league club all year. Now that we have our workload constraints, we need to set the performance rate changes of switching roles for our optimization model. Since the TTOP is not predictive and can vary over an individual season, I didn t want to simply take what a starter s performance would look like if they avoided the third time through the order. Instead, we can take the total season woba for each pitcher and adjust it up or down based on the woba difference we calculated in part 4 for starters and relievers. According to that analysis, the difference in moving from a starter to a reliever is 28 points of woba. To adjust a starter s woba by this full amount would be misleading since these pitchers are still throwing significant innings and will be asked to throw more pitches per outing than current relievers are. Similarly, relief pitchers should not get as steep of a penalty since they are increasing their workloads relatively modestly, and are still avoiding the TTOP for the most part. We can take a conservative estimate and use 14 woba points both directions. If you take the position that the benefit for starters in higher or that the penalty for relievers is less, then I may be understating the benefits of the Super Reliever Model. I also added an additional 4 point penalty for specialty relievers, or those with high platoon splits, if we increase their workload. Ideally these pitchers can maintain their one or two batter per appearance role. Now that we have our optimization model constraints, we can solve for each team s optimal workload breakout, requiring the new total innings to equal the actual 2013 total innings. We can then simulate what the Super Reliever Model would have meant for each team in 2013 (in terms of runs allowed) based on the adjusted woba and innings count of each pitcher. After running the model we have a mean estimate for each team of the run differential between the 5-man rotation model and the Super Reliever Model. The results can be found in Appendix 7. Every team but one (the Tigers) is projected to have benefited from the Super Reliever Model, with the impact on wins ranging as high as five. 5

7 Conclusion Five wins will not take a last place team to the playoffs, and teams may be hesitant to implement such a drastic change for an uncertain payout, but for a fringe playoff team it could be the difference in winning a division. Based on the Super Reliever Model, the Texas Rangers should have won the AL West instead of having their season end in a wild-card tiebreak game. There are a number of other considerations to be mindful of, such as in-game strategy consequences (pinch hitting, platoon impacts, baserunning, etc.), roster construction implications, changes in injury risk, and barriers to implementation. The platoon advantage is especially interesting, as opposing teams would theoretically be forced to either pinch hit early in a game or accept a bad matchup, if in the Super Reliever Model we could alternate lefties and righties. The biggest barrier to implementation is in getting buy-in from the players, and in being able to attract free agent pitchers who aren t accustomed to the model. For that reason, implementation would be easiest on a team of young pitchers (it would also help a team with an innings cap on a young pitcher like Stephen Strasberg and Matt Harvey, as we ve seen recently). Further, it is important to keep in mind that the model can be tailored to different teams who have 1 or 2 top veteran starters, leaving those pitchers alone to throw 7+ innings every fifth day but implementing the model for the remaining schedule. While managers have used the Super Reliever Model for games at a time (Joe Maddon did it in the Rays final playoff game of 2013), I think eventually a team will use it over the course of a season, gaining a significant edge in the process. 6

8 Acknowledgements I would like to acknowledge the plethora of writers on websites like Fangraphs.com, Baseball Prospectus, BeyondtheBoxScore.com, The Hardball Times, and others that inspired much of this research, especially those dealing with Pitch FX, without which most of this research could not be done. 9 References [1] www.fangraphs.com. Accessed January 6, 2014. <http://www.fangraphs.com/library/offense/woba/> [2] www.fangraphs.com. Accessed January 6, 2014. <http://www.fangraphs.com/library/pitching/batted-ball> [3] MLB Advanced Media LP. www.mlb.com Accessed January 6, 2014. [4] www.fangraphs.com. Accessed January 6, 2014. <http://www.fangraphs.com/library/offense/wraa> [5] www.thehardballtimes.com. Accessed January 6, 2014. <http://www.hardballtimes.com/main/blog_article/leverage-index-by-inning/> 10 Appendices Appendix 1: Starter vs. Reliever 2013 Metrics 2013 TBF AVG OBP SLG woba K% K-BB% HR/9 SwSt% Starters 121,434.259.319.408.325 18.9% 11.5% 1.01 8.7% Relievers 63,438.243.316.374.292 21.7% 12.8% 0.87 10.4% Appendix 2: Percent Change in Batted Ball Types by Time Through the Order 0.80% 0.60% 0.40% 0.20% 0.00% -0.20% -0.40% -0.60% -0.80% 1 2 3 Line Drive Ground Ball Fly Ball Pop Up 7

Average Velocity (mph) Appendix 3: Swinging Strike % by Time Through the Order TTO FF FT FC SI SL CH CU 1 4.2% 4.5% 9.1% 4.4% 13.1% 13.9% 8.4% 2 4.2% 4.5% 9.0% 4.4% 12.1% 12.7% 8.0% 3 4.1% 4.5% 8.9% 4.3% 11.5% 12.0% 8.0% 4 3.8% 4.3% 7.7% 3.8% 11.1% 10.9% 7.6% Appendix 4: TTOP by Number of Pitchers in the Arsenal 1 or 2 5 or 6 TTO pitches 3 pitches 4 pitches pitches 1.309.311.315.313 2.325.323.328.320 3.338.337.333.318 4.334.326.321.312 Appendix 5: Fastball Velocity Aging Curve, Starters vs. Relievers 96 95 94 93 92 91 90 89 88 87 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Age SP RP Appendix 6: Regression Results of Fastball Velocity Impact on K% Correlation Matrix Variable K Perc FBv K Perc 1.000 FBv 0.467 1.000 Regression Statistics R Square Adj.RSqr Std.Err.Reg. # Cases # Missing t(2.5%,4408) 0.218 0.218 0.049 4410 0 1.961 8

Summary Table Variable Coeff Std.Err. t-stat. P-value Lower95% Upper95% Intercept -0.634 0.023-27.198 0.000-0.680-0.589 FBv 0.009 0.000 35.066 0.000 0.009 0.010 Appendix 7: Benefit of Super Reliever Model ( SRM ) in Runs Allowed and Wins 1 Team Runs Scored: 2013 Runs Allowed: 2013 Runs Allowed: SRM RA Diff Pythag Wins 1 : 2013 Pythag Wins 1 : SRM Additional Wins Mets 619 684 639 45 73.6 78.6 5.0 Yankees 650 671 629 42 78.6 83.4 4.8 Rangers 730 636 596 40 91.2 95.8 4.7 Twins 614 788 741 47 62.8 67.2 4.3 Royals 648 601 571 30 86.6 90.3 3.7 Braves 688 548 521 27 97.6 101.2 3.5 Blue Jays 712 754 720 34 76.8 80.1 3.4 Brewers 640 687 660 27 75.8 78.7 3.0 Marlins 513 646 620 26 64.2 67.1 3.0 Cardinals 783 596 572 24 100.8 103.6 2.8 Pirates 634 577 556 21 88.0 90.7 2.7 Mariners 624 756 731 25 66.9 69.4 2.4 Astros 610 848 818 30 57.3 59.7 2.4 Padres 618 700 677 23 71.8 74.2 2.4 Orioles 745 709 687 22 84.7 87.0 2.3 Reds 698 589 571 18 93.5 95.7 2.2 Rays 700 646 627 19 86.9 89.2 2.2 Giants 629 691 671 20 74.0 76.3 2.2 Nationals 656 626 608 18 84.5 86.6 2.2 A's 767 625 606 19 96.0 98.2 2.2 White Sox 598 723 702 21 67.1 69.2 2.1 Red Sox 853 656 638 18 100.1 102.1 2.0 Angels 733 737 719 18 80.6 82.4 1.8 Rockies 706 760 743 17 75.5 77.2 1.7 Dbacks 685 695 680 15 79.9 81.6 1.7 Cubs 602 689 676 13 71.0 72.4 1.4 Dodgers 649 582 571 11 89.0 90.4 1.3 Phillies 610 749 736 13 66.0 67.2 1.2 Indians 745 662 653 9 89.7 90.7 1.0 Tigers 796 624 625-1 98.8 98.7-0.1 1 Pythagorean win formula per BaseballReference.com = (Runs Scored^1.83) / (Runs Scored^1.83 + Runs Allowed^1.83). 9