Other entries in the series:

Competitive Balancing Act I—The King James Version: An Overview of the Literature, Scenes I, II, and III
Competitive Balancing Act II—This Is Pop: Redefining Large- and Small-Market by Population
Competitive Balancing Act III—C'mon Freddy, Everyone into the Poo-el: Reviewing the Available Player Pool
Competitive Balancing Act IV—Natural Resources: Attendance and Competitive Balance

Sisters is probably the most competitive relationship within the family, but once the sisters are grown, it becomes the strongest relationship.

— Margaret "Don't Call Me David" Mead

So far we have found little to refute the Rottenberg/Coase theory that free agency does not affect competitive balance. However, I found a couple of studies that were of interest because, if nothing else, they tried something different.

The first is a thesis from one Peter Fishman at Duke University ("Competitive Balance and Free Agency in Major League Baseball", May 2002). He also had professors Andrew Zimbalist and Rodney Ford help him out on the project. What makes his analysis different are two things: A) He takes into account the actual numbers of free agents in (or prior to) a given year whereas the others just use an on/off dummy switch for the presence of free agency. And B) his conclusion is that free agency has negatively impacted competitive balance.

Fishman's analysis takes into account the reverse-order draft, Andrew Zimbalist's talent compression (i.e., via a measure for percentage of American population playing major-league baseball), expansion (with a dummy variable for the first two years of an expansion team), number of games played, number of teams, and number of free agents. His findings are that "free agency does indeed have an effect on competitive balance" (p.10).

It sounds like a thorough study and therefore, a very credible answer, right? Well, I have a number of issues with it, the first being that the number of free agents tells you nothing about the quality of free agents. In the Seventies, you rarely saw average players on the open market, just superstars. That's how baseball is: look at the number of African-American role players before, say, the Seventies. Baseball integrated but just for the very good players. If you were a black backup catcher in the Fifties, you'd never see the light of day in the majors. Eventually, the conservative elements in the game came around or died out and things changed. It was the same in free agency. I'm sure if Joe McEwing had declared himself a free agent in the late Seventies, he would have effectively ended his career. But now the stigma has been lifted.

Fishman actually responds to this criticism in his "Extensions" section (#4 "log NFRAG", pp. 15-16):

There has been an increasing number of free agents since 1977. There was an average of 27 free agents per year during the late 1970’s compared to 122 annually during the 1990’s. The players who declared free agency during the 1970’s were generally of higher caliber than the average player (of the 122) who declared free agency in the 1990’s. Given that higher caliber players have a greater effect on winning, this might suggest that a linear model…would not be appropriate…My regression model counted the number of free agents, but it did not assess the overall quality of the free agent pool from year to year.

He reruns his regression again and concludes that the findings cannot disprove the Coase model (the results are still negative but are now not significant). He leaves the issue open for future investigation, but I think this one issue is enough to scuttle his original findings, and I have others.

Using the number of free agents is problematic at best. There are any of a number of potential free agents that re-sign with their original clubs for substantial increases. The fact that a large-market team can resign a good number of these players but small-market team cannot is supposedly the basis of competitive imbalance today. Besides telling nothing about the quality, the number of free agents tells you nothing about their point of origin.

Also, players often seem to switch teams in the year prior to their free agent year. Their new team will either use the players for their stretch run or will use their own resources to sign the player to a long-term contract without them ever testing the free agency waters. The flow seems to be from small- to large-market here as well, but this study ignores them.

Another problem is collusion, a practice used throughout baseball for three seasons (1985-87). However, it is not even mentioned in this study. Teams colluded to not sign players that were still desired by their previous teams in order to keep salaries low. The number of players who declared themselves free agents may not have changed, but the possibility of changing teams and following the Coase theorem sure did.

What about arbitration-eligible players? We have seen a great deal of them not being tendered contracts and being made (possibly unwilling) free agents. Those that do not get released have their salaries affected by the free agent signings and affect free agent signings.

Also, there have young players who have been locked up in long-term contracts in the mid-Nineties Indians mold. They may not have been eligible for free agency or even for arbitration as yet, but their contracts extend sometimes into the free agency period.

There are also those players that, in a given year, are under a multi-year contract that was signed when they were free agents. Potentially, their big-money contract would affect future signings by their teams. However, the players' free agent status is only recorded in the year they were free agents.

There are also other minor points: International players are not in the draft, so they are not included in these analyses. The nature of the draft has changed to the point where high-profile prospects are often passed over by small-market teams because they are afraid of the potential asking price. And yet, the amateur draft is merely represented in the study by an on/off switch. In one of Fishman's extensions (#2, "New York Yankees Effect", pp.14-15), he finds that removing the Yankees from the equation results in a negation of his original findings. Could one team have caused such an imbalance? Some think so today.

I have some problems in general with modeling, but I'll reserve them for after the final free agency study. One last problem is that the way that these studies all look at competitive balance within a season, not from season to season. Here's an example of what I mean. Compare the competitive balance between these two leagues:

Justice League, Year 1
Team A, 95-67
Team B, 90-72
Team C, 72-90
Team D, 67-95

Justice League, Year 2
Team A, 95-67
Team B, 90-72
Team C, 72-90
Team D, 67-95

The Little League, Year 1
Team W, 95-67
Team X, 90-72
Team Y, 72-90
Team Z, 67-95

The Little League, Year 2
Team Z, 95-67
Team Y, 90-72
Team X, 72-90
Team W, 67-95

One would think that the second league is far more competitive than the first given that the standings were reversed in the second year. However, as far as these studies are concerned both leagues are equally competitive in either year because their standings, by the win-loss numbers, are the same. But which team would you rather be, Team D, who finished 28 games back both years (in the Devil Rays mold), or Team Z, who finish way back in year one and the win the division the next (a la the Cubs in 2002-2003)?

The last free agency study, by E. Woodrow Eckard in 2001 ("Free Agency, Competitive Balance, and Diminishing Returns to Pennant Contention", Economic Inquiry, Vol. 39, No. 3, July 2001, pp. 430-443), takes a look at competitive balance from season to season instead of within one season only.

Less balance within a league means that teams with good, middling, or poor records tend to repeat them year after year. Over a given number of seasons it implies greater variation among teams in cumulative win percents and less variation in individual team win percents.

Eckard calculates "cumulative variance", i.e., the variance in winning percentage across all teams over a given period. He finds that "there are diminishing marginal returns to each additional year's 'production' of a championship-caliber team. Incentives are thereby reduced for successful clubs to bid continually for the services of the top players necessary to remain in contention." He then goes into how this affects of continual winning causing fan apathy, using Atlanta as an example, and thereby affecting attendance.

Frankly, this is where my eyes glaze over. I don’t buy these arguments necessarily. Fan apathy can result from continual winning but it sure as heck results from continual losing more often. Baseball is a form of entertainment and as long as there is some dramatic tension for the fans, they'll show up at the stadium. The Yankees seem to be able to sustain this dramatic tension for their fans.

However, there are a number of studies that delve into attendance being tied to fans' ennui based on Rottenberg's "uncertainty of outcome" hypothesis. Here are some examples: Young Hoon Lee ("Competitive Balance and Attendance in Japanese, Korean and U.S. Professional Baseball Leagues", July 2002), Brad Humphreys ("Alternative Measures of Competitive Balance in Sports Leagues", August 2001), and Leize Gaillard ("Attendance and Competitive Balance in Professional Sports", Davidson Economic Times & Review, Spring 2003).

My objection to these purely academic studies is that they do not properly model the game. There are plenty of wholes that can be punched in the basic premises of these studies. For example, the basic assumption that free agency either exists or it doesn't is specious at best. Fishman improved on this by adding in the count of free agents in a given year. However, he also assumes that the number of free agents correlates linearly to the degree of competitive balance in a league. That is, as the number of free agents increases it directly affects competitive balance. However, that assumption can be easily obliterated. Consider that if all players were made free agents every year, the competition for an individual player's talents would lessen. We have seen this in the last couple of seasons as scores of arbitration-eligible players are made into free agents when they are not tendered contracts. As a result the glut of talent has kept salaries from increasing.

Now if only a handful of players were eligible for free agency, the salaries of the best free agent players would be kept artificially high and therefore, would only be signed by the highest-revenue clubs causing competitive imbalance. Salaries in general would rise as more players were eligible for free agency since they would also create a case for a number of arbitration-eligible players, thereby apparently negatively impacting competitive balance. However, at some point there is a glut on the market and salaries can be kept low, positively affecting competitive balance presumably. Therefore, the relationship between the number of free agents and competitive balance is not nearly linear but rather an arc.

In the last section of the literature review, we'll look at a couple of the big guns, Bill James and Andrew Zimbalist. Then we'll try our hand at our own study.