New Approaches to Player Valuation: Analyzing How Wins Generate Revenue for Major League Baseball Teams

1. New Approaches to Player Valuation: Analyzing How Wins Generate Revenue for Major League Baseball Teams Graham Tyler Brown University ’12 Honors Thesis in Economics

2. Unique Nature of Baseball • Everything that baseball players do on the field is recorded • Easier than in almost all other professions to quantify performance • Defining product as wins, we can determine a players product for any given period of time • If we know how wins generate revenue, we can determine a players marginal revenue product—the amount of revenue he was responsible for generating—for a period of time

3. Motivation • If we can estimate a player’s marginal revenue product we can use this information to analyze various economic phenomena and test economic theories across a wide range of topics • Monopsonistic exploitation (Raimondo, 1983) and owner collusion (Bruggink and Rose, 1990) • Presence of a winner’s curse in auctions (Cassing and Douglas, 1980) and (Burger and Walters, 2006) • Human capital theory of labor markets (Blass, 1992) • Status of MLB owners as rational, profit maximizing, and having essentially perfect information

4. Previous Methods for MRP Estimation • Anthony Krautmann’s method based on the economic theory of markets • Commercial approach utilized by analysts such as Vince Gennaro (Diamond Dollars) and Nate Silver (Baseball Between the Numbers)

5. Scully Model (Gerald Scully, 1974) • Estimate player’s added wins • New sabermetric methods have given us Wins Above Replacement (WAR) • Estimate the added revenue from a win through regression of revenue on team wins • MRP=WAR*wins

6. Adding Complexity to the Revenue-Wins Model • Nonlinearity • Wins increasing probability of making playoffs more valuable than additional wins at lower win totals • Team Specificity • Wins probably more valuable for some teams

7. Market Size, Pay, and PerformanceJohn D. Burger and Stephen K. Walters(2003) • Linear spline function at a threshold number of wins to capture nonlinearity • Interaction between market size and wins to capture increased marginal revenue from wins for teams in larger markets • Implies team variation in returns to winning is entirely due to variation in market size

8. Regression Model • Used data released from 2000 Blue Ribbon Panel hired by MLB to assess growing disparity in local revenues between teams and the effect on competitiveness • Regression Model: • TRit = α1 + α2t+ β0Mit + β1Mit • Wit + β2Mit • W2it + β3Stadiumit + β4Ageit + εit • TR = real local team revenue in millions of 1999 dollars; • t = time trend • M = market size, measured as metropolitan area population in millions • W = regular season wins • W2 = wins above the contention threshold of 84 • Stadium = a binary dummy variable that takes a value of one if the team has a new or significantly renovated stadium • Age = number of years since the opening of a new or renovated stadium

9. Hypotheses and Assumptions of My Research • Assumptions • Revenue-win relationship is nonlinear and varies by team • Hypothesis 1: Price is an omitted variable when not included in the revenue-win model • If price is set in anticipation of team performance it is correlated with revenue and with actual wins • Hypothesis 2: Team variation cannot fully be explained by market demographic factors • Hypothesis 3: Teams can be grouped by similar returns to winning and there will be variation in the revenue-win relationship by group among the three different CBAs of the last 15 years

10. Hypothesis Testing Strategy • H1 and degree of team variation tested through Model 1: • Revenueit=0Teami + 1 Teami *WinPctit + 2Teami*WinPct2it1/2 + 3Priceit + 4Stadiumit-1 + 5Stadiumit-2 + 6Newit-1 + 7Newit-2 +8Playoffsit-1 + 9t + it • F-test of team win coefficients tests team variation in returns to winning • F-test of team win coefficients in unrestricted version vs. version restricting price=0 tests H1

11. Hypothesis Testing Strategy Continued • H3 Tested through a categorical version of Model 1: • Revenueit=0Categoryj*CBAt+ 1Categoryj *WinPctit*CBAt + 2Categoryj*WinPct2it1/2*CBAt + 3Priceit + 4Stadiumit-1 + 5Stadiumit-2 + B6Newit-1 + B7Newit-2 + 8Playoffsit-1 + 9t + it • If we can group similar teams this clustering should produce clearer estimates that will vary within group across the three time periods if the CBAs had a significant effect on the return to winning

12. Replication of Burger and Walters Results

13. Pooled Teams Version of Model 1

14. Results of Full Specification of Model 1 • Validation of H1 (significant difference between win coefficients in restricted vs. unrestricted models) • Significant team variation • Many insignificant win coefficients (large SE’s) • Some teams look as expected • Some teams have significant negative linear coefficient OR significant negative threshold coefficient • For ARI this negative win coefficient persists in specification 4 (when threshold variable is omitted) • For some teams nonlinear specification appears to make sense and threshold coefficient is significant, for others this may not be the case

15. Robustness Check: Categorized Version of Model 1 • Teams categorized through two methods • 1) 5 groups based on teams with similar estimates for returns to winning • 2) 5 groups determined theoretically based on knowledge of teams’ fan bases and historical performance • Both groupings result in very few significant win coefficient estimates • Indicates it is very difficult to group teams based on returns to winning • No definitive evidence CBAs had significantly different effect on returns to winning

16. Variation Across Teams in Returns to Winning

17. Testing H2 • Model 2 tests how much of the team variation in the returns to winning can be explained by a team’s market characteristics: • Coefficienti=0 + 1Marketi + 2Incomei + 3Divisioni + 4Distancei + 5Sportsi + i,

18. Results of Model 2 Estimation: Linear Combination of Win Coefficients

19. Implications of Model 2 Results • Market size explains almost none of the variation • Picks up effects of “pro sports” variable and “distance” variable when these are individually left out • About 40% of team variation cannot be explained

20. What DO We Know? • Price Matters (sometimes) • ARI is the least affluent U.S. market in the sample • Expected winning  perceived higher demand  higher prices  reduced attendance/revenue due to high consumer price elasticity of demand  high price, high wins (if wins correlated with predicted wins), low revenue • Model estimates average effect of price across teams with significant positive coefficient • Wins coefficient for ARI is then its deviation from the average price effect across all teams, not actually the returns to winning

21. What DO We Know? • Perpetual winning or losing reduces the returns to winning

22. What DO We Know? • There appears to be a capacity constraint due to limited number of seats in the stadium

23. What DO We Know? • Market size is not the determining factor • Anecdotally: LAA vs. LAD, CHC vs. CWS, SF vs. OAK (very different estimates, baseline revenues, and returns to winning for teams within the same market) • Seems that in larger markets with two teams there is an established team with a large fan base and baseline revenue vs. a team trying to expand fan base with more variation in revenue (and thus in some cases higher returns to winning)

24. Caveats • Small sample size and specification of the model

25. Caveats Continued • Potential unobserved factors • Television deals • Lagged effect of winning (CWS) • Historical relationship with fans • Can this be created over time?

26. Future Research • Relationship between winning and valuation of franchise as a whole • Teams typically sell for 2-2.5x revenue