Here's a sample:

...III. Literature review

A number of previous studies have examined the marginal revenue product of professional baseball players. The pioneering econometric study on pay versus performance of Major League Baseball was provided by Scully (1974). While Scully's approach has undergone much scrutiny, it remains one of the primary methods of estimating a player's MRP. A number of studies have modified Scully's basic model, used more recent data, and improved estimation procedures. Scully (1974) estimates MRP in a two equation model. The first is a team revenue function which relates team revenues to the team win-loss record and the principal market characteristics of the area in which the team plays. Then he estimates a production function, relating team output and win-loss percentage to a number of team inputs. Scully's results show that players were paid only 10-20% of their marginal revenue product in data for the 1968-69 seasons. Scully found that the economic loss of professional baseball players under the reserve clause is of considerable magnitude (Scully 1974).

Krautman (1999) revisits the Scully technique for estimating the MRP of professional baseball players. Using a sample of available free agents from 1990-1993, he attempts to show that the Scully technique is sensitive to the manner in which marginal product is measured. The approach estimates the market return on performance from a regression of free agent wages on performance. These market returns are then applied to the performance of reserve-clause players, giving estimates their market values. Krautman's results indicate that the average apprentice (less than three years of Major League experience) receives about 25% of his MRP and the typical journeyman (more than three, but less than six, year of Major League experience) receives a salary that is essentially commensurate with his value (Krautman 1999).

MacDonald and Reynolds (1994) examine if the new contractual system of free agency and final-offer arbitration brought salaries into line with marginal revenue products. Using public data for the 1986-87 seasons, they include all players, both hitters and pitchers, who were on a major league roster as of August 31, 1986 and August 31, 1987. First, they analyze whether any economic evidence of owner collusion exist during the 1986-87 period. Secondly, they use a systematic analysis of final-offer arbitration in baseball - established three years before free agency - and find it has a stronger independent effect on salaries than the much publicized free agency. Last, they test the `superstars' model of Rosen (1981) and find the salaries of the very highest paid players in Major League baseball disproportionately exceed their relative productivity advantage, as the `superstars' model predicts. They find that major league salaries do generally coincide with the estimated marginal revenue products. Experienced players are paid in accord with their productivity; however, young players are paid less than their marginal revenue product, on average (MacDonald and Reynolds 1994).

Thus, the previous literature seems to agree that, on average, more experienced players are paid a wage approximately equal to their marginal product while younger players appear to be paid a wage significantly less than their marginal product. These previous studies have used data from a few seasons and from the early 90's or earlier. To my knowledge, no previous studies have utilized data over multiple seasons or as recent as the mid to late 90's.

IV. Team Model and Marginal Revenue Product

Employing one more unit of labor generates additional income for the firm because of the added output that is produced and sold. Thus, the marginal income generated with a unit of input is the multiplication of two quantities: the change in physical output produced (marginal product) and the marginal revenue generated per unit of physical output. Thus, the additional income created from hiring an additional worker is termed the marginal revenue product (MRP). In theory, a firm would be willing to pay a worker a wage up to his MRP. In a competitive labor market we would expect workers to be paid a wage equal to their MRP.

The players' marginal revenue product in baseball is the ability or performance that he contributes to the team and the effect of that performance on team revenue (Scully 1974). This effect can be direct or indirect. Ability contributes to team performance and victories raise gate receipts and broadcast revenues. Therefore a players' market worth can be defined as the amount of team revenue produced by his contribution to attracting paying fans to see and hear the team compete (Scully 1974).

Ignoring special appeal for `superstars', a player's MRP essentially is based on each player's contribution to significant team performance variables, the effect of these performance variables on winning percentage, and, in turn, the effect of winning percentage on team revenue. I also assume that the team production function is linear and is written as:

[formula's symbols will not transfer]

where WINPCT = percentage of games won by a team
RC = Total team runs created for the season
ERA = teams earned run average per 9-inning game
NATLG = 1 if team is in the National League, 0 otherwise
CONT = 1 if team finished within 5 games of first place in the division, 0 otherwise
OUT = 1 if team finished 20 or more games out of first place in the division, 0 otherwise

As described below, runs created is a useful measure of offensive production because it not only gives weight to hitting and slugging averages, but also to offensive production like walks, stolen bases, sacrifices, and similar efforts. ERA is the best overall defensive measure because it reflects a pitcher's ability to prevent runs from scoring.

ERA is also a good defensive measure for team pitching, although it does not account for errors. However, more than just team hitting and pitching performance can determine winning. One or two runs win many games during the season. In this instance, pitching and hitting performance will make less difference in the outcome. The two dummy variables CONT and OUT, introduced by Scully (1974), adjust for these factors. The variable CONT captures team morale (hustle, quality of managerial and on the field decision making) which will substantially determine which team wins a higher share of these close games. The variable OUT captures the disheartenment of loosing and bringing up players from the minor leagues. The variable NATLG is specified to compensate for quality of play. The American League has a designated hitter to bat in place of the pitcher. This substitution, not allowed in the National League, should increase runs created in the American League...