A unified theory of capital and labor markets in major league baseball.

• Author: Vrooman, John

There is nothing more limited than a limited partner in the Yankees.

- John McMullen, 1979, former New York Yankees minority owner and former Houston Astros majority owner.

The economics of professional sports has been relegated to the realm of labor theory by the assumption that owners of sports franchises are simply maximizers of profit in vacuo. Theory developed within this vacuum [11; 12; 15; 16; 18; 19] has been preoccupied with Rottenburg's invariance proposition [13] that the distribution of talent within Major League Baseball (MLB) is independent of the legal ownership of that talent. According to this Coasian argument, the institution of free agency in MLB would not affect the real decisions of teams, but it would result in the transfer of wealth from owners to players in the form of higher player salaries, reduced exploitation, diminished profits and lower franchise values. As predicted, the player-cost share of league revenues rose from 20 percent to 58 percent over the first two decades of free agency in MLB. Unfortunately, the explosion in MLB players' salaries has been attributed by association to the institution of free agency, itself.(1) Symptom-treating policies such as payroll caps and luxury taxes, which have been conceived from this myopic view, have been ineffective [12] and potentially deleterious [18]. During the same two-decades, however, over 40 MLB franchise ownerships were coincidentally transferred amid a revolutionary transition of MLB ownership structure from sole sportsman to leveraged syndicate.(2) This paper explores the possibility that the salary escalation during the free agency period was partially the result of the capital market game of leveraged syndication being actively played on a labor market field of free agency. The major problem in developing a theory to unify capital and labor market behavior stems from Modigliani and Miller's irrelevance proposition [10] that the financial and real decisions of a firm (MLB club) are necessarily independent. The weakness of the irrelevance proposition, however, is that the separation of capital and labor markets logically rests on the conventional assumption of profit maximization. If owners are more generally viewed as sportsmen, who prefer winning games beyond the profit maximum, then it can be shown that the capital market decisions of MLB owners become inseparably linked to the real operational decisions of the baseball players' labor market.

1. A Unified Capital and Labor Theory

   The Irrelevance Proposition

   A unified theory of capital and labor markets has been deemed difficult, if not impossible, following the seminal statement by Modigliani and Miller (MM) [10] of their famous separation theorem, in two parts. The first separation principle holds that "the market value of any firm is independent of its capital structure . . . i.e., the average cost of capital to any firm is completely independent of its capital structure and is equal to the capitalization rate of a pure equity stream of its class (emphasis original) [10, 268-69]." Whereas the second separation principle forcefully suggests that "it follows that optimal operating decisions of the firm do not depend on its financing decisions; that is, operating and financing decisions are separable (emphasis added) [3, 152-53]." Subsequent discussions of the MM theorem have involved the realism of its limiting assumptions [9; 17], but the irrelevance of financial decisions for the real decisions of the firm has remained logically unassailable.(3) The unified theory proposed here seeks to relax the underlying assumption of the second principle of separation: that the MLB franchise is acting in the best interest of equity and debt holders [10, 288]. The argument follows a path blazed by Scitovszky [14] and later redeveloped through the agency theory of Jensen and Meckling [7].

   The implications of the first separation principle can be shown through a simple model of the ownership (syndication) and financial (leverage) structures of MLB franchises of the risk class [Epsilon]. Generally the value of the MLB franchise can be represented as the sum of outstanding debt D and equity X, divided into the general partner's [Alpha] share and the limited partners' (1 - [Alpha]) ownership share:

   V = D + [Alpha]X + (1 - [Alpha])X (1)

   where X is cash flow after interest [Pi] - [r.sup.*]D capitalized at a rate [Rho] reflecting the financial risk of leverage:

   V = D + [Alpha]([Pi] - [r.sup.*]D)/[Rho] + (1 - [Alpha])([Pi] - [r.sup.*]D)/[Rho] (2)

   where D = [Lambda]V and [Rho] = [r.sup.*] + [Epsilon]/(1 - [Lambda]) is a risk-free rate [r.sup.*] adjusted for MLB business risk [Epsilon] concentrated on the unlevered portion (1 - [Lambda]) of the franchise V. If the franchise is unlevered ([Lambda] = 0), then (2) reduces to the sum of the equity partnership shares discounted at an interest rate r reflecting only the MLB business risk [Epsilon]:

   V = [Alpha][Pi]/r + (1 - [Alpha])[Pi]/r (3)

   where r = [r.sup.*] + [Epsilon]. If the franchise is partially levered ([Lambda] [greater than] 0) but solely owned ([Alpha] = 1) then (2) reduces to:

   V = D + ([Pi] - [r.sup.*]D)/[Rho] (4)

   where D = [Lambda]V and [Rho] = [r.sup.*] + [Epsilon]/(1 - [Lambda]). In the case of nonsyndicated, unlevered ownership ([Alpha] = 1; [Lambda] = 0), the value of the MLB franchise becomes the expected value of "the pure equity stream of its class:"

   V = X = [Pi]/r. (5)

   According to the first separation principle of the MM theorem, leverage is irrelevant to the valuation of the franchise, because any increase in the value of the club due to the use of cheaper risk-free debt [r.sup.*] in either (2) or (4) is exactly offset (according to the law of conservation of risk) by an increase in the cost of equity [Rho]. If each MLB franchise is subject to the same business risk [Epsilon], then all combinations of leverage and syndication for a franchise are equivalent to the capitalization of "a pure equity stream of its (risk) class;" that is, equations (1) (2) (3) and (4) are each equivalent to (5). According to the second separation principle, the operation of a MLB team is then independent of its financial or ownership structure. This is true, however, only if each owner is assumed to maximize the value of his franchise with respect to winning. If an owner is a pure profit maximizer, then the maximization of his equity share [Alpha](1 - [Lambda])V requires real decisions that remain consistent with the overall franchise value maximum [Delta]V/[Delta]w = 0. In contrast, if owners are generally perceived as sportsmen, who jointly maximize franchise values and the satisfaction derived from winning, then the second separation principle does not necessarily follow from the first. The irrelevance proposition, therefore, obtains only in the exceptional case of the pure profit maximizer. In the optimization of the multiple objectives of a sportsman owner, the capital and labor choices of MLB owners become linked in a manner that influences the on-field performance of their teams.

   The Sportsman Effect

   The optimization problem facing the sole ([Alpha] = 1), unlevered ([Lambda] = 0) sportsman owner concerns the joint maximization of franchise value (V) and the satisfaction (S) derived from winning (w) such that the differential: dS = ([Delta]S/[Delta]V)dV + ([Delta]S/[Delta]w)dw = 0, where: dV/dw = [Delta]([Pi]/r)/[Delta]w = 1/r([Delta][Pi]/[Delta]w) = -([Delta]S/[Delta]w)/([Delta]S/[Delta]V) for [Rho] = r. The sportsman reaches an optimum where the marginal value of the franchise with respect to winning is equal to the negative of the rate of substitution (RS) between winning and franchise value: MV = (MR - MC)/r = -RS. Compare the general sportsman optimum at B in Figure 1 with the customary, but unnecessarily limiting case of profit maximization ([Delta]S/[Delta]w = -RS = 0) at A. This leads to a defining proposition for the sole sportsman owner.

   PROPOSITION 1. The sportsman owner sacrifices franchise value for winning and expands the talent of his club beyond its value maximum. The resulting undervaluation of the franchise is the sportsman effect.

   In a classic argument, Scitovszky [14] noted that the sportsman optimum at B would also maximize the residual of franchise value above a minimum value necessary to keep the owner in MLB. Following Scitovszky's reasoning, the indifference curve [S.sub.0] in Figure 1 represents the minimum satisfaction that will keep the sportsman in the game. The vertical distance beneath [S.sub.0] is the franchise value necessary to compensate the owner for the on field performance of the team, and the difference between franchise value [V.sub.0] and minimum satisfaction [S.sub.0] (the envelope [Omega]-[Omega][prime]) is the residual value that is to be maximized by the sportsman at B-C.(4) For winning percentages above [Omega], winning no longer compensates the owner for the loss in franchise value, and for winning percentages below [Omega][prime], the franchise value no longer compensates the sportsman for losing. If the owner's satisfaction were to fall below [S.sub.0], the sportsman would sell the MLB franchise.

   The constraints of league competition create an obvious complication for the optimization solution [w.sub.1] when a sportsman encounters an opponent who seeks a winning percentage [w.sub.2], such that [summation of] [w.sub.i] [not equal to] 1.000. The equilibrating mechanism for the simultaneous solution of a league of sportsmen is the cost per unit of talent for all teams in the league. If [summation of] [w.sub.i] [greater than] 1.000, then the excess demand for talent and winning within the league will force the cost per unit of talent to increase, and the aggregate demand for talent and winning will decrease for all clubs in the league. Conversely, if [summation of] [w.sub.i] [less than] 1.000, then the negative excess demand for talent will depress player costs and increase cash flows...