A Proposal for Incentive-Compatible Revenue Sharing in Major League Baseball

Transcription

1 Journal of Sport Management, 2012, 26, Human Kinetics, Inc. Official Journal of NASSM ARTICLE A Proposal for Incentive-Compatible Revenue Sharing in Major League Baseball Michael G. Wenz Northeastern Illinois University This paper proposes a payroll tax and revenue sharing model for Major League Baseball that better aligns the incentives of individual team owners with league-wide goals of competitive balance and cartel profit maximization. The author demonstrates why the current system is poorly suited for improving competitive balance, then argue for a system of transfer payments based on a more aggressive payroll tax combined with a subsidy distributed based on on-field performance rather than market size or financial performance. High-payroll teams would contribute disproportionately to the revenue-sharing pool, while successful teams would receive disproportionately large subsidies. By increasing the marginal value of a win through the performance-based subsidies, small-market teams will see increased incentives to invest in playing talent. The author presents some limited financial data and suggest how to calibrate the model to yield the optimal level of competitive balance and optimal revenue split between players and owners. Professional sports leagues in general, and Major League Baseball in particular, are interesting in that the teams act in collusion to set up a cooperative system of rules designed to maximize league-wide profits, but within this system, they ask their member firms to compete vigorously on the field with each other. Profit maximization for the league depends on the ability of member clubs to stage a contest with an uncertain outcome, and the demand for the league s product depends on the amount of uncertainty the level of competitive balance that exists. The highest level of competitive balance that can exist occurs when all teams are equal, and each team has the same probability of winning each contest and of winning league championships. This ideal, however, is not likely to be consistent with either leaguewide or individual club profit maximization. With perfect competitive balance, wins by a popular team in a large geographic market are in higher demand and will generate more in revenues than wins by a less popular team in a smaller market. Market forces will, through the market for playing talent, tend to push the odds of winning games and championships toward the large market teams, but at a cost of decreasing competitive balance. There have been a number of approaches, including player drafts, salary caps, and restrictions on player mobility that have been tried in various sports leagues to restore competitive balance, with varying degrees of success. This paper presents a novel approach to addressing the inherent difficulty in aligning the differences in individual team goals for profit maximization with Wenz is with the Dept. of Economics, Northeastern Illinois University, Chicago, IL. the league-wide goal of achieving the level of competitive balance necessary for maximizing the total profits earned by the cartel. Under the current labor agreement, some teams who receive revenue-sharing funds appear to be simply pocketing the funds and not using them to increase their stock of playing talent. This runs counter to the stated goals of the revenue sharing agreement, but is completely predictable based on existing rules and economic theory. The approach considered here is based on a competitive balance payroll tax similar to the one in existence now, but supplemented by a revenue sharing plan that distributes revenue sharing monies based on performance on the field rather than lump sum transfers to select teams as is currently done. The regime suggested here relies on three policy levers that can be used to balance the interests of three competing interest groups. The interest groups are the individual teams, the collective organization of teams acting as a cartel, and the players, represented by a union. The first two policy levers include a tax on payroll and a gate-sharing component for local team revenues, both of which are part of the current agreement. The third lever is a transfer payment to clubs based on on-field performance, which is not part of the current agreement but would replace the current revenue-sharing transfer payment program that is based on economic need. Basing the revenue transfers on performance increases the incentive of all clubs to acquire talent, but the effect is relatively larger on small market clubs, and when combined with the payroll tax will lead toward improvements in competitive balance. This paper proceeds as follows. First, the case for actively managing competitive balance is presented. 479

2 480 From the Editor Second, the current institutional features used to promote competitive balance are analyzed and their shortcomings noted. Next, an outline of this three-lever policy regimen is presented, supplemented by some rough guidelines for calibration. The secretive and private nature of MLB revenue data prevents a fully parameterized model, but the outline presented here would be useful to players and owners who have access to the relevant data to guide future rounds of labor discussions. The final section concludes and notes some additional effects of this approach as well as some suggestions for further study. The Case for Improving Competitive Balance Critical to the appeal of sports to its fans is the uncertainty of the outcome of the game. Fans prefer to see their favorite team win, and certainly team attendance and revenues vary positively with increased winning probability, though as winning approaches certainty, the contest no longer provides any appeal. Intuitively, while Yankees fans like to see the Yankees win, they ll still pay more to see them play a playoff contender than an also-ran. From a purely competitive standpoint, the ideal level of competitive balance is one of equal playing strengths for all teams. However, with profit-maximizing owners facing different demand curves, the equilibrium conditions for firm profit maximization should not be expected to predict an even distribution of playing talent. Market size, certainly, and also the relative loyalty and fickleness of a team s fans both influence the height and the slope of the demand curve facing the team and thus their derived demand curve for talent. There are other candidates for the ideal level of competitive balance, such as the level that maximizes consumer surplus or total surplus, but in this context, the target level of competitive balance is the one that maximizes payments to the cartel formed by the three groups noted above players, individual club owners, and the league. These three groups are responsible for establishing the rules of the cartel, and as will be shown below, the three policy levers of the payroll tax, the gatesharing rate, and the performance-based transfer payments can be used to manage the distribution of revenue across the interest groups. Fan interests enter the model since they affect the demand for playing talent and thus team revenues. Revenues are modeled to depend on a combination of fan utility in home and national markets and on the relative ability to extract revenues from fans in home and national markets. Home fan utility is derived from seeing the local team win, while national utility is derived from the quality of the contest, which is a function of competitive balance. Individual clubs are driven into the market for talent primarily by local fans, and fail to internalize all of the effects that their participation in the market for talent has on competitive balance. This externality provides an opportunity for policy intervention. While fans influence demand at the local and national level, they have no seat at the rule-making table. Policies affecting the optimal level of competitive balance will be determined through collective bargaining between players and owners and should be viewed through that lens.the most basic model developed in the literature for understanding competitive balance is presented by Quirk and Fort (1993) and is illustrated in Figure 1. In this approach, a two-team league is considered, where the two teams are profit-maximizers who face heterogeneous demand functions and bid for talent in a competitive labor market. The horizontal axis measures Team A s winning percentage, w a, and Team B s winning percentage, w b, is (1-w a ). The marginal revenue product of an additional win is higher for Team A at all levels in the case illustrated in Figure 1. This may result from being located in a larger market or having less fan loyalty. In the case illustrated Figure 1 Competitive balance with heterogeneous demand.

3 From the Editor 481 below, the equilibrium winning percentage is.600 for Team A and.400 for Team B. Szymanski (2001) develops a model that considers the sources of fan utility as stemming from the desire of fans to see their favorite team win, but also the desire of fans to see a good competition. In an individual contest between teams a and b, fan utility is given by U = µ a w(t a ) + µ b w(t b ) +θw(t a )w(t b ) (1) where μ i is the utility derived by fanbase i from winning and q is the fraction of utility derived from the quality of the contest. Here, each team s expected winning percentage w is expressed as a function of the talent share of team i, and μ i represents the increase in utility among fanbase i following a victory. The parameter μ may capture things like market size and fan intensity, with μ increasing in large markets and with more fickle fans. The last term in equation (1) can be thought of as representing the interest of the national fans who simply wish to see a good game. Szymanski refers to these fans as couch potatoes. For league-wide utility maximization, a particular team s optimal winning percentage is shown to increase with increases in the marginal utility of a victory but also increase with the degree of competitive balance which is captured by the product of w(t a )and w(t b )1. Szymanski then assumes that team owners are able to expropriate some fraction φ of fan utility as revenues through ticket sales, merchandise, or media viewership. The parameter φ will capture things like the local market income or local policies that affect revenues2. Each firm s profit function is given by π i = ϕ i µ i w i (t i ) ct i (2) where c is the market price of talent and t i is the amount of talent purchased by team i. Profit maximization by each team leads to the condition that the ratio of talent between clubs should be equal to the ratio of their marginal utilities of winning. The model implies that profit-maximizing clubs would produce the socially optimal level of competitive balance only by chance (Szymanski 2001, p.73) and that teams with the strongest fan response to winning are likely to be overly strong from a social welfare standpoint. That is, profit-maximizing clubs are unlikely to achieve the league-wide optimal level of competitive balance. Current Policy for Competitive Balance Major League Baseball rules governing the market for playing talent are outlined in a document called the Basic Agreement (Major League Baseball; Major League Baseball Players Association 2007), which outlines several mechanisms for improving competitive balance. These mechanisms include a player draft, restrictions and conditions on player movement, and revenue sharing of broadcast and road gate receipts. They also include a payroll tax on high payroll teams and an additional revenue-sharing agreement for clubs that are less financially successful than others. The economics associated with various mechanisms used to achieve competitive balance for league health has been covered at length in the literature (e.g., Quirk and Fort 1993, Leeds and von Allmen 2008), but the payroll tax and current revenue sharing components are of particular interest and will receive further discussion below. American players enter the available talent pool primarily through the Rule 4 player draft, and foreign players enter professional baseball as free agents. The Rule 4 player draft has two important components that are designed to enhance competitive balance. The first is that teams are assigned draft positions based on the reverse order of the standings the weaker teams get first crack at the top talent. Second, teams which lose veteran players to another club through free agency are awarded an additional pick in the next free agent draft. Whether the players are signed or drafted into an organization, the drafting club nearly always signs the player to a minor league contract and retains control over the player for some period of time, with the period depending on when the player is assigned to a major league roster. When the player is assigned to a major league roster, the club has six seasons of control over the player, though the player is eligible to file for binding-offer salary arbitration after the third (and in some cases the second) season in the majors. After six years, the player is eligible for free agency, though some players sign multiyear contracts that extend beyond this period with their original club. With some restrictions, players can be traded between clubs. Under this regime, players who are not yet eligible for free agency or arbitration earn substantially less than players who are eligible for free agency, while players who are arbitration-eligible fall somewhere in between (Krautmann 1999). The result has been for the small market, low revenue clubs to develop rosters of young, pre-free agency players and for the large market, high revenue clubs to be the big spenders in free agency. While the player draft provides some balance to this, the link between a player s draft rank and actual performance is weak and subject to a great deal of luck, and while the link between market size and rank in the standings is correlated, it is not perfectly so3. Taken together, small market teams may have a small advantage in acquiring players in the prefree agency period. For the post-free agency group of players, the group that generally contains the best players and biggest stars, the market incentives discussed above still lead to a distribution of talent that favors those with high marginal revenue product functions. To level the playing field between the large market clubs and the small market clubs, Major League Baseball has instituted a competitive balance tax on teams with high payrolls. Teams with payrolls over a certain threshold ($170 Million in 2010, $178 Million in 2011 and 2012) are subject to the competitive balance tax on payrolls above the tax threshold, with tax rates equal to 22.5%, 30%, or 40%. The exact rate depends on whether

4 482 From the Editor the club maintains payrolls above the threshold for multiple years, with the rate increasing for serial high-salary clubs. In 2010, the only two teams to exceed the threshold were the New York Yankees and Boston Red Sox. Since the luxury tax was instituted in 2003, the Yankees have been subject to the tax each year, the Red Sox have paid tax in five of eight years, and the Los Angeles Angels and Detroit Tigers have paid tax once. The economics of the payroll tax are relatively straightforward. If we assume that all clubs have the same production function and face the same supply curve for playing talent 4, then this translates into an increase in the marginal cost for teams which choose to operate at the spot on their winproduction function beyond the level of wins where this threshold begins. Figure 2 illustrates how this affects competitive balance in the case where the threshold is set at a level corresponding with the level of talent required to play.500 baseball and the level of talent required to play.700 baseball. If we reduce the marginal revenue product of players signed beyond the threshold level by the amount of the tax, we can see how this affects the resulting equilibrium distribution of playing talent. Figure 2 shows that a tax set at a threshold below the equilibrium level of competitive balance will in fact improve competitive balance, while a tax set at a higher level will not lead to a change in the equilibrium. Proceeds from the competitive balance tax are distributed primarily to a general fund to pay player benefits and to a fund used to support industry growth. They are not returned directly to the clubs. In addition to the payroll tax, Major League Baseball has a revenue sharing program that has been constructed seemingly to ensure the financial survival of the small market clubs. There are two primary components of revenue sharing. The first is a straight 31% distribution of the total of local club revenues through the Revenue Sharing Fund, and the second is a distribution of the Central Fund, which consists of revenue generated by the central league office, primarily but not only for national television contracts. The Basic Agreement presents a number for each team called Net Defined Local Revenues which is used to calculate a Performance Factor that forms the basis for distribution of revenues from the central fund. This table is reproduced as Table 1. The method for determining these numbers is not precisely defined in the Basic Agreement, but it can be inferred that they depend roughly on each club s local revenues less their nonpayroll operating expenses, with some allowances and modifications for clubs with new stadiums. A positive Performance Factor translates into a net contributor into the revenue sharing plan, while a negative Performance Factor indicates that the club is a net recipient of revenue sharing, compared with what would exist under a straight redistribution of local and central fund revenues. Large market teams are net contributors, with the New York Yankees topping the list. Small market clubs are the net recipients, with the Tampa Bay Rays at the bottom of the rankings. It is important to note that the amount of revenue sharing depends only indirectly on the team s performance on the field, and to the degree that it does, it perverts incentives for small market teams to increase their competitiveness. A team that increases its revenues by improving its on-field performance to attract fans may actually reduce its Performance Factor and revenue sharing amounts in future labor agreements. While this effect is small in magnitude, it is important to note that it works in the wrong direction from the standpoint of improving competitive balance. Team financial records are difficult to come by, so understanding exactly the amount of revenue sharing that occurs is difficult. However, recently the website deadspin.com obtained leaked consolidated financial statements for the Pittsburgh Pirates for , the Tampa Bay Rays for , the Florida Marlins for , the Los Angeles Angels of Anaheim for Figure 2 Competitive balance with payroll tax.

5 From the Editor 483 Table 1 Performance Factors for Revenue Sharing Team Net Defined Local Revenue Performance Factor New York Yankees 309, % Boston 252, % New York Mets 200, % Chicago Cubs 187, % Los Angeles Dodgers 177, % Seattle 145, % Chicago White Sox 141, % Los Angeles Angels 138, % St. Louis Cardinals 134, % San Francisco 132, % Houston 126, % Atlanta 116, % Texas 113, % Philadelphia 106, % Washington 103, % Cleveland 102, % Baltimore 100, % San Diego 95, % Cincinnati 80, % Arizona 78, % Colorado 69, % Detroit 67, % Oakland 67, % Minnesota 64, % Milwaukee 60, % Pittsburgh 55, % Toronto 49, % Kansas City 48, % Florida 45, % Tampa Bay 40, % Source: MLB Basic Agreement (Major League Baseball; Major League Baseball Players Association 2007) , the Seattle Mariners for , and the Texas Rangers for , though there is some possibility the Texas Rangers data are unofficial (Craggs 2010). Deadspin calls these perhaps some of the most closely guarded information in sports. Unfortunately, the teams use different labels and groupings for their revenue data, so it is difficult to parse out for some of the teams exactly which revenues are collected under which part of the revenue sharing plan for each of the clubs, but the Rays, Marlins and Angels financial statements provide enough detail for meaningful comparisons. Selected information from these statements is provided in Table 2. In 2008, the Marlins were net recipients of $48.0 million in local Revenue Sharing Fund transfers and $31.3 million from the Central fund with $139.7 million in revenues and a $29.4 million Net Income. The Angels in 2008 received a net of $27.2 million from the Central Fund and were net contributors of $14.7 million to the local Revenue Sharing Fund. They earned $237.8 million in revenues and $7.1 million in Net Income. The Marlins, then, received $4.1 million more from the Central Fund and netted $64.4 million more through the local Revenue Sharing Fund for a total of $68.5 million in competitive balance adjustments when compared with the Angels. The Marlins spent just $29.8 million on player salaries in This is strong evidence that revenue sharing monies are not being used to improve on-field performance. There are three noteworthy effects of the revenue sharing plan from an economic standpoint. First, the local revenue sharing agreement is essentially a gate-sharing

6 484 From the Editor Table 2 Selected Financial Statement Information for Selected Teams, Revenues (millions) Angels 2008 Marlins 2008 Rays 2008 Local Revenues $ $ 46.8 $ 76.4 Local Revenue Sharing Central Fund Other Total Revenue Expenses Player Payroll Local Revenue Sharing 14.7 Central Fund 11.6 Other Total Expenses Net Income* Source: (Craggs 2010), except ( + ). Player payrolls are taken from (Cot s Baseball Contracts 2010) to ensure a consistent methodology for calculating payrolls. The methodology is complicated and not transparent in the individual club financial statements. *Net income includes depreciation, interest, amortization, and taxes; Revenues and Expenses do not, so totals do not add exactly. plan, the economic effect of which is to depress demand for players and reduce player salary, but with no effect on competitive balance (Quirk and Fort 1993). Essentially, the marginal revenue product curves are pushed downward by the fraction of revenue that is shared. Secondly, the redistribution is a lump sum amount that depends on the financial performance of the club, not the on-field performance. This does not provide clubs with any economic incentive whatsoever to improve the performance of their team on the field. The basic agreement attempts to address this: [E]ach club shall use its revenue sharing receipts in an effort to improve its performance on the field. Each payee club, no later than April 1, shall report on the performance-related uses to which it put its revenue sharing receipts in the preceding Revenue Sharing Year. Consistent with this authority under the Major League Constitution, the Commissioner may impose penalties on any Club that violates this obligation (Major League Baseball; Major League Baseball Players Association 2007, p. 112) It is unclear what evidence the league would require to conclude that a team has not spent the proceeds of revenue sharing on improving on-field performance, or whether any enforcement activities would contain sufficient teeth. It is worth at least a mention here that despite this provision in the collective bargaining agreement, the league may not in fact want to improve competitive balance, preferring to keep the bottom teams weak to boost the winning percentages of the large-market teams with larger fan bases. Third, revenue sharing may be necessary to ensure the financial health of the small market franchises. The fixed costs of running a major league baseball team are high, especially given the high cost of supporting a minor league system. The Rays, for instance, spent over $20 million in 2008 and 2009 on scouting, player development, and operations of farm clubs, compared with $35 million in player salaries (Craggs 2010). It may be the case that revenue sharing is necessary to ensure club survival, though it has been noted that clubs often have incentives to hide their true financial health (Zimbalist 1992). Finally, it should be noted that even teams with very low payrolls can be somewhat competitive given the nature of the industry. At any one time, there are 750 players on major league active rosters and approximately another 450 on a major league roster, though these players are actually assigned to a minor league club. The largest number of players that any one team can control at one time is 40; the Rule 5 draft allows clubs to draft players, with some restrictions, from other organizations who are not on the original club s 40-man roster, placing a strong restraint on a team s ability to significantly hoard major league-ready talent in the minor leagues. In addition, as noted above, restrictions on player movement give clubs an opportunity to hold on to good young players before they are able to negotiate a market-value contract or file for binding salary arbitration. Thus, even clubs with very low payrolls will still be able to win some fraction of games. Sabermetricians have developed a number

7 From the Editor 485 of ways to examine the value of a team full of replacement level players that is, the expected performance of a team filled with the marginal entrant into the major leagues, or, more accurately, the marginal entrant into a starting lineup. Baseball-Reference, a leading publisher of baseball statistical analysis, estimates that a team full of replacement-level players would play at approximately a.320 expected winning percentage (Forman 2010). This provides a lower bound on the competitive balance scale. Teams with good players who have not yet reached arbitration or free agency should be expected to improve on this expectation at very low or no additional cost. On the other end, the highest winning percentage for a team in a single season since the league expanded to 30 teams belongs to the 2001 Seattle Mariners, who went for a.716 winning percentage, though they exceeded their win expectation based on performance. In summary, the payroll tax may work to improve competitive balance at least in theory, though in practice, it is set at such a high payroll level that it affects few teams. Gate sharing drives down player salaries, but does not affect the incentives for competitive balance. Revenue sharing in general may help teams survive, but does not affect team incentives to improve competitive balance, though there is a weak threat in the basic agreement that may provide some incentive to use revenue sharing funds for improving on-field performance. In addition, institutional features that keep players from signing for their marginal revenue product in their early career and keep high-spending teams from hoarding talent ensure some level of competitive balance. An Incentive-Compatible Path to Competitive Balance Relative to the baseline case of pure market-based competitive balance as presented in Figure 1, Major League Baseball has not moved particularly far. Gate sharing drives down the cost of playing talent but with no effect on competitive balance, and payroll taxes have affected a very small number of teams, maybe as small as one. As noted above, if baseball has stumbled on the profitmaximizing level of competitive balance, relying on the payroll tax and gate sharing by lump sum would bring about this result only by chance. There are three overlapping interests that must be accounted for to achieve the optimal level of competitive balance. The first is to maximize league-wide extraction of utility of fans that is, to produce a product that provides a high utility value by providing a level of competitive balance that balances the desires for fans to see their favorite team win with the desire for fans to see good contests. The second is to acknowledge that teams operate as profit-maximizers and as such will work to equate marginal revenue product with the prevailing wage, and that threats of punishment as noted above are not likely to be persuasive. Finally, owners and players collectively bargain over the distribution of economic rents, and the collective bargaining agreement will reflect this reality. The basic model used here follows Szymanski (2001) in spirit, with some minor modifications. First, the decision variable for teams is the talent level, t i, chosen from the pool of league-wide talent T. The probability of winning is an increasing function of talent, w(t), with w (t)<0.5 Second, fan utility from a sporting contest consists of three components. The first is the utility each local fan base gets from winning, and the second is the utility derived by the quality of the contest, which accrues to the national fan base. The national fan base may be thought of as the couch potatoes in Szymanski s model. Local fan utility depends on a team s on-field performance, along with a measure of market potential, m i, and is translated into revenue through an extraction parameter, j i, that is analogous to that of Szymanski and may differ across locations. National fan utility for a given contest depends on the relative and overall strength of the two teams in the contest, and is assumed here to be a linear function of the product w(t i )*w(t j ). At a contest level, national interest is increasing in t i and t j, and at a league-wide level, national interest is decreasing in the variance of t. Then total utility is given by U = n i = 1 µ w(t ) +θ n i i i 1 n j = 1 w(t )w(t ) i j (3) where Θ represents the intensity of national interest to competitive balance. Note that the second term is primarily an externality there are (n 2 -n)/2 pairs of contests, and team i only can influence their half of n of them. Note also that the second term is maximized when playing strengths are equal across teams. The first term in (3) is translated into revenues through the extraction parameters φ i, which can vary across teams. The second term is translated into revenues through Θ.6 Then league-wide revenues are given by R = n i = 1 ϕ µ w(t ) +θ n i i i i = 1 n j = 1 w(t )w(t ) (4) 1 j To this model, we add two components. The first is a gate sharing parameter, α, that represents the fraction of local revenues that is kept by the host club. (1- α), then, is the amount of local revenue that is shared with the rest of the league. The second is a Central Fund, which earns revenues by extracting some fraction of the utility of national fans. In practice, the primary source of Central Fund revenues is national broadcast media contracts, the value of which is presumably linked to league health and competitive balance. If gate sharing and central fund revenues are evenly distributed, then the profit function of teams is given by π i = αϕ i µ i w(t i ) + θ n + A n ct i where Θ is the league total amount of the Central fund and A is the league total amount of the Local Fund, or (1 α ) n 1 ϕ µ w(t ). Club profit maximization means i i i (5)

8 486 From the Editor that in equilibrium, the marginal revenue product is equalized across clubs at the wage rate in the market for talent. αϕ i µ i w (t i ) + 1 α n n k = 1 ϕ ϕ w (t k k i ) = αϕ j ϕ j w (t j ) + 1 α n n k = 1 ϕ µ w (t k k j ) The first term represents the impact of a team s talent level on its local revenues, scaled by the revenue sharing parameter. The second term represents the share of team i from the local fund, and depends on the talent share of each team in the league. Teams have some incentive to be concerned with the effects of their investments in talent on their competitors, but as n becomes larger, this incentive becomes weaker. Determining the optimal level of competitive balance does not appear to be straightforward, and would make for interesting further research. However, if we choose a target for the level of competitive balance, it is possible to design a system that is incentive-compatible with all three issues. Suppose that the unfettered market would produce a.600/.400 talent split as we had in Figure 1. The first step is to choose the level of competitive balance that maximizes league-wide utility of fans. The second step is to choose a regime of taxes and subsidies that would produce this level of competitive balance, and the third step is to use gate sharing to calibrate the price of talent to the level that provides the negotiated distribution between owners and players. Figure 3 captures the intuition behind the process. Arrows 1 reflect the increase in firm marginal revenue product associated with the performance-based revenue sharing component. Arrows 2 reflect the recalibration of the gate sharing parameter to produce a wage (6) consistent with the collectively bargained distribution between players and owners. The second step requires further explanation. As it stands, the current approaches to achieving competitive balance fall short on two dimensions. First, the payroll tax is too high to restrain spending. And second, the recipients of revenue sharing have no market incentive to spend their receipts on improving their performance. What we are left with is effectively a lump sum transfer of revenues from large market to small market teams that provides little or no improvement in competitive balance. What is necessary is to discourage spending by the large market teams and encourage spending on talent by the small market teams. A prime reason that the payroll tax is set too high to affect most teams comes about because the players union, for obvious reasons, is not willing to accept a high tax on payrolls. However, if the payroll tax were combined with a subsidy, this would presumably be tolerable. The trick, however, is to design the subsidy in a way that promotes small market team spending on improving their performance. The method proposed here is to distribute revenue sharing funds based on on-field performance rather than on financial health. Teams would be rewarded for on-field performance rather than financial health. The distribution would assign shares of a revenue-sharing pool based on winning percentage. A simple formula like share = win% * poolsize n / 2 would suffice. The teams that win will receive disproportionately large shares, so at first glance, this would seem to simply make the rich teams richer. The offset comes from the way the subsidies are funded the rich teams (7) Figure 3 Calibrating the model.

9 From the Editor 487 will pay a disproportionately large share of money into the revenue sharing fund. In this framework, team profits are given by π i = αϕ i µ i w i + w i 30 (1 α )ϕ jµ j w j + (8) j = 1 n / 2 CF(σ w ) / n ct i where α is the fraction of revenue sharing and CF represents Central Fund Revenues, which are a function of league-wide competitive balance, σ w. Note that team revenues have changed from the model presented in equation (2). Profit maximization requires now that the ratio of talent between team i and j must be equal to the ratio of local marginal utilities plus the revenue-sharing value of a win, and the revenue-sharing value of a win is equal across all teams. Adding the revenue sharing component the ratio of marginal revenue products must be getting closer to 1, and thus the equilibrium ratio of talent must be getting closer to 1 as well. Competitive balance therefore must be increasing, and is an increasing function of the gate sharing parameter, (1-α). In 2008, according to Table 2, the Marlins netted $48 million in local revenue sharing and the Angels were net contributors of $14 million. Currently, 31% of local revenue is shared. If Net Defined Local Revenue (NDLR) as presented in Table 1 is a reasonable approximation of the revenue sharing base, then approximately $35 million per team is going into the local revenue sharing pool. This looks to be about consistent with the information contained in the leaked financial statements as well. It appears that an additional $30 million or so per team is shared through the Central Fund, though it is not apparent that either the Central Fund or NDLR figures are publicly available. Precision, though, is not critical the objective here is simply to think about broad parameters for improving competitive balance. Taken together, the local and central fund components provide about $2 billion league-wide for potential use in revenue sharing. Table 3 begins with the figures in Table 1 and combines them with assumptions that 31% of NDLR is contributed to the revenue sharing pool, Central Fund revenue is divided evenly between the teams and is not part of the revenue sharing pool, and teams perform on the field (regular-season only) at their average winning percentage from 2000 to Payroll taxes, for now, are ignored. Revenue sharing net transfers are presented as well. Under this proposal and assuming teams did not change their behavior toward signing players, the Yankees would have contributed $53.8 million in revenue sharing $96.0 million paid in, and $42.1 million taken out due to their.597 winning percentage. The Angels, noted above, would contribute $3.7 million net $42.9 million paid in and $39.2 million taken out due to their.556 winning percentage. The Marlins would receive a $21.7 million net receipt $14.2 million paid in and $35.4 million taken out due to their.501 winning percentage. The worst team in baseball over this period was the Kansas City Royals. Their net distribution would have been $14.3 million on $14.9 million paid in and $29.3 million paid out. It is useful to examine the magnitudes that such a program would have on competitive balance. An examination of the data presented in Table 1 shows that the highest performing team, the Yankees, won an average of 97 games and would have a claim of $42.1 million against revenues in the revenue sharing pool, while the Royals averaged 67 wins and had a claim of $29.3 million against the revenue sharing pool. The marginal value of the revenue sharing component of a victory works out to about $435,000 per win. An improvement from 67 wins to 81 wins (.500) would bring about an increase of approximately $6 million in revenues. The marginal cost of a win has been estimated to be approximately $4.5 million per win in 2008 (Cameron 2008).7 These estimates are based on the contracts of players purchased in the free agent market and do not necessarily represent the cost of a win for all teams, but it provides a ballpark benchmark. Adding the revenue sharing component to this suggests an increase in the marginal revenue product of playing talent of about 10%. Importantly, this additional amount directly influences the demand curve for talent for small market teams and provides an incentive for them to use revenue sharing to improve the product on the field. Some important issues remain. The increase in marginal revenue product that comes with linking revenue sharing to winning percentage will put upward pressure on salaries. There are a couple of ways to offset this. First, as noted above (Quirk and Fort 1993), increasing the fraction of gate sharing revenue will reduce the demand for talent, but with no effect on competitive balance. Second, an expansion of the payroll tax could be used, and presumably the union would be tolerant of this in exchange for the subsidies in collective bargaining. Note that complete reliance on the payroll tax is insufficient as a solution to the competitive balance issue in part because it does not provide low-payroll teams an incentive to spend on talent and in part because it is unlikely to survive collective bargaining. In addition, it is not at all obvious that 31% is the right level for revenue sharing, but the league can either adjust this percentage or use the money in the Central Fund to calibrate the level of competitive balance to the one that maximizes league wide profitability. The last column of Table 3 presents the change in revenue sharing payments based on a 50% revenue sharing split and an additional $300 million contribution from the Central Fund. That would result in an increase in the marginal revenue product of a win of about $825,000, approximately a 20% premium on the price of talent. The last issue of concern is ensuring the survival of franchises. The weakest franchise, according to the NDLR figures in the collective bargaining agreement, was the Tampa Bay Rays. Under the 31% revenue sharing plan, the Rays would net $17.7 million at their average win level, much less than the $35.3 million they netted in In addition, under the new plan, they would, in equilibrium, have higher player costs as they began to compete for revenue sharing dollars. However, they will partially offset this with an increase in their optimal win percentage at the new equilibrium level of competitive

10 488 From the Editor Table 3 Estimated Net Transfers Under Proposed Revenue Sharing Regimes Team Net Defined Local Revenue (millions) 31% Contribution to Pool (millions) Win %, Share of 31% Pool (millions) Net transfer at 31% local revenue sharing (millions) Net transfer at 50% local revenue sharing + $300 million Central Fund contribution (millions) New York Yankees Boston New York Mets Chicago Cubs Los Angeles Dodgers Seattle Chicago White Sox Los Angeles Angels St. Louis Cardinals San Francisco Houston Atlanta Texas Philadelphia Washington Cleveland Baltimore San Diego Cincinnati Arizona Colorado Detroit Oakland Minnesota Milwaukee Pittsburgh Toronto Kansas City Florida Tampa Bay balance, and an increase in the health of the league will provide an increase in revenue as well. The magnitude of these effects is unknown. Switching to the 50% plus $300 million from the Central Fund plan would generate $37.1 million in revenue sharing but reduce the Central Fund payout by $10 million. This brings things closer to the status quo, and by tinkering with the revenue sharing rate and, if necessary, the formula for allocating Central Fund revenues, there is a path to ensuring franchise survival. Conclusions and Implications This paper outlines an incentive-compatible path to enhancing competitive balance and league-wide profitability. There are three policy levers that can be manipulated to align the incentives of different agents. First, identify the level of competitive balance that maximizes league-wide profits, then create a subsidy fund that subsidizes on-field performance as a way to increase the level of competitive balance accompanied by a payroll tax on high payrolls. The second step is to negotiate a revenue-sharing rate that divides the spoils in an acceptable way between the players and the owners. Suppose that the free-market distribution provides a.600/.400 split, while the optimal level is at.550/.450. Adding a performance-based revenue sharing component will reduce the optimal talent disparity between the two teams, but will drive up marginal revenue product and salaries. This is indicated by Arrows 1 in Figure 3. Adjusting the revenue sharing rate will allow the league to calibrate the demand for players to the desired level. This is indicated by Arrows 2 in the diagram. Player cost C* is recaptured by adjusting the revenue sharing rate.

11 From the Editor 489 This framework increases the current level of competitive balance by providing small-market teams with an incentive to improve their level of playing talent. Under the current regime, there is real concern that the very low payroll teams simply take the lump sum transfer they receive now and add it to their bottom line. While the lump sum transfer may be necessary to ensure the financial survival of the franchise, it does not lead to any adjustment in competitive balance. Rewarding competitive improvements would do that. The desired level of competitive balance from a revenue-maximizing league cartel is not equal playing strengths across teams, and it is possible that the league would prefer to decrease the level of competitive balance. It is also possible that the national fans prefer dynasties to parity, so that the assumption that national interest increases with increases in competitive balance is false, and that these dynasties have not just short but also long run implications for national fan interest. Without much more data on revenues than the deadspin.com data, however, it is difficult to test these assumptions. What this model does is to take the owners and the collective bargaining agreement at its word that the cartel desires to enhance competitive balance and provide a mechanism for doing so. Adding some precision to the revenue functions in the model will make for interesting future research, though limited access to MLB financial records make this task difficult. Conceptually, however, the model can provide a useful guide to insiders during labor negotiations. Including a performance-based revenue sharing component alongside appropriately administered payroll taxes and gate sharing arrangements will provide an incentive for small-market teams to spend, rather than pocket, their revenue sharing component and improve the level of competitive balance across the league. Notes 1. The win probabilities in equation (1) are expected winning percentages for the team over a whole season, not for an individual contest. In other words, the utility generated from national fans will be higher when two.600 teams play than when two.400 teams play. However, note also that the average product of win probabilities in an n-team league is maximized when all of the talent shares are equal and all of the win probabilities are.500. That is, for example in a 4-team league with two.600 teams and two.400 teams, the average product of w a * w b, our measure of contest quality, accounting for both absolute and relative talent, is.24667<.25, which is the contest quality in a league when all teams are evenly matched. 2. Differences in stadiums and stadium agreements will influence the parameter φ, as well as local rules such as the Chicago Cubs limitation on night games or local ticket taxes. 3. The most recently negotiated collective bargaining agreement places tighter restrictions on the signing of draft picks and foreign players that may level the playing field somewhat, though the uncertainty associated with draftee performance remains. 4. Vrooman (Vrooman 1995) discusses the case where these assumptions are not valid. For example, if players want to play in warm weather, or if a team s home ballpark characteristics differ in meaningful ways, the cost of acquiring playing talent or the production function itself may differ. 5. Presumably, it is harder to increase your winning percentage from.700 to.701 than it is to increase your winning percentage from.400 to The parameter Θ can be thought of as the product of both national fan interest and the national extraction parameter, a scalar. This monotonic transformation preserves the ordinal properties of the utility function, and a util is thus defined as the amount of additional enjoyment needed to extract an extra dollar out of the national fan. 7. Much of the work on estimating the marginal cost of a win has been done by Sabermetricians rather than economists. Economists are generally uncomfortable with the assumption of linearity in the production function for wins, which leads to the unrealistic conclusion that the same player must always be worth more in a high marginal product location. Economics predicts that the price of a unit of talent should be constant across teams if the market is sufficiently competitive, but that talent may translate into a different number of wins in different team contexts. See (Fort and Tango 2010) for an interesting discussion. References Cameron, D. Win Values Explained: Part Six. December 29, (accessed October 7, 2010). Cot s Baseball Contracts. Los Angeles Angels of Anaheim (accessed 10 4, 2010). Craggs, T. MLB Confidential: The Financial Documents Baseball Doesn t Want You to See com/ / (accessed October 1, 2010). Forman, S. WAR Replacement Levels. 9 13, baseball-reference.com/blog/archives/8225 (accessed 10 4, 2010). Fort, R., & Tango, T. Replacement Level Discussion. April 14, (accessed October 7, 2010). Krautmann, A. (1999). What s wrong with Scully s estimates of a player s marginal revenue product. Economic Inquiry, 37(2), doi: /j tb01435.x Leeds, M.A., & von Allmen, P. (2008). The Economics of Sports (3rd ed.). Boston, MA: Addison-Wesley. Major League Baseball and Major League Baseball Players Association. MLB Basic Agreement. Major League Baseball pdf (accessed October 1, 2010). Quirk, J., & Fort, R.D. (1993). Pay Dirt: The Business of Professional Team Sports. Princeton, NJ: Princeton University Press. Szymanski, S. (2001). Income inequality, competitive balance, and the attractiveness of team sports: Some evidence and a natural experiment from English soccer. The Economic Journal, 111(February), F69 F84. doi: / Szymanski, S., & Kesenne, S. (2004). Competitive Balance and Gate Revenue Sharing in Team Sports. The Journal of Industrial Economics, 52(1), doi: / j x Vrooman, J. (1995). A General Theory of Professional Sports Leagues. Southern Economic Journal, 4(April), doi: / Zimbalist, A. (1992). Baseball and Billions. New York: Basic Books.