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The nonlinear behavior of competition: the impact of talent compression on competition


The competitiveness of a firm is intimately related to the productivity of its components. The distribution of profits should then be highly correlated with the distribution of productivity—the more equal distribution of productivity the more equal distribution of rents. To assess this argument, the present paper examines the time series behavior of competition within Major League Baseball. The above logic would suggest that the reason for the improvement in the competitive balance in MLB is a more equal distribution of playing talent. In the end, the improvement appears to be driven by increased player homogeneity rather than institutional changes.

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  1. The presumption, here, is not that these limits can’t be altered. They certainly may, through training, nutrition, self-selection, education... Rather the important assumption is that, while the pool is growing relatively quickly, the limits evolve slowly through time and thereby leads to the nonlinearity.

  2. I thank an anonymous referee for providing the Fortune 100 example.

  3. At a new conference (Friday, August 30, 2002) describing the recent (2002) Major league Baseball labor dispute agreement, Commissioner Bud Selig stated, “...the issue here was competitive balance and I feel this deal clearly deals with that.”

  4. In general, each league’s μ(wp) t is expected to equal 0.5, i.e., each game has a winner and a loser. However, with respect to Major League Baseball, two exceptions are possible. First, the introduction of inter-league play in 1997 allowed for each league’s μ(wp) t to differ from 0.5. Second, Major League Baseball has traditionally not played games between non-contenders toward the end of the season that inclement weather has caused to be postponed. In which case, the number of games played for each team will differ and each league’s μ(wp) t will not exactly equal 0.5. Given these possibilities, the actual mean winning percentage was utilized in the calculation of the idealized SD, rather than the assumed value of 0.5.

  5. The terminology here may be a bit misleading. Ideal in the present context is not meant to commutate preference; rather it represents a marker from which to gauge the level of competition. Intuitively, Quirk and Fort (1992) argue that the measure captures competitive balance as it compares, “... the actual performance of a league to the performance that would have occurred if the league had the maximum degree of competitive balance in the sense that all teams were equal in playing strengths. The less the deviation of actual league performance from that of the ideal league, the greater is the degree of competitive balance (p. 244).”

  6. A number of recent authors have found that attendance is maximized with p > 0.5.

  7. Empirically, the evidence on the impact of these changes has been rather mixed. Szymanski (2003) examines 20 empirical studies on the impact of the introduction of free agency on competitive balance and finds that nine estimate an improvement, four document a decline and seven found no impact.

  8. If, on the other hand, the individual team has win-maximization as its goal, then resources and institutional rules, such as roster limits, may allow some teams to stockpile the highest quality players. This may, in the end, decrease competitive balance. I thank a anonymous referee for raising the issue.

  9. The author would like to thank Sean Lahmen, author of the Baseball Archive——for the majority of the data on the number of foreign-born players in Major League Baseball. Authors’ calculations from individual team rosters for the period 1998–2005.

  10. The unit root and structural break tests were performed using the log of the three series.

  11. Indeed, given Commissioner Selig’s earlier comment, this would seem their intent.

  12. The average number of free agent filings in the late 1970s was roughly 25, while the average rate for the 1990s was roughly 130.

  13. The actual estimation removes a certain number (percentage) of observations from both ends of the data. The reason being that we cannot consider breakpoints too close to either ends of the sample because there are not enough observations around the break date too identify the sub sample coefficients. The solution, generally, is to trim the data. There is a trade off as less trimming increases the critical values and more decreases sample size. In the present context, we follow Andrews (1993) and trim 15% of each side of the data. Other trimming choices of 10% and 20% produced qualitatively similar results.

  14. The search for DUb and DTb is resolved by estimating the model for each feasible breakpoint and following one of several proposed rules to identify the optimal breakpoint.

  15. Perron and Vogelsang (1992) offer several other options, i.e., minimizing k or minimizing on the F-statistic. These all produced similar results.

  16. This approach was recently shown to have stronger sample properties. See Ng and Perron (1995).

  17. Perron (1994) provides the critical values.

  18. As our labor pool measure captures geographical diversity rather than racial diversity it is not entirely clear whether one would expect a break with racial integration. However, racial integration would allow Major League teams the opportunity to pursue players from other nations more easily than before.

  19. Each series was trimmed, as before, by 15%.

  20. The author gratefully acknowledges that the nonlinear unit root and co-trending tests were performed using Herman Bierens’ econometric package EasyReg. It is available at

  21. The interested reader is refered to Bierens (1997, 2001) for the more technical aspects of the tests.

  22. The analysis requires two choice variables, p and m. I incorporated p=4 and m=2. Other alternatives did not qualitatively alter the results.

  23. As before the tests were completed using the log of the two competitive balance series.

  24. Since the labor pool measure is bounded 0–100, the tests were conducted using log (100−% foreign-born/% foreign-born). I thank Herman Bierens for bringing this to my attention.

  25. MLB has expanded six times from the original 16 teams. In 1961, 1962, 1977, 1993 and 1998, MLB expanded by two teams, while four teams were added in 1969.


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Correspondence to Martin B. Schmidt.

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Schmidt, M.B. The nonlinear behavior of competition: the impact of talent compression on competition. J Popul Econ 22, 57–74 (2009).

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  • Competitive balance
  • Nonlinear
  • Co-trending

JEL Classification

  • C22
  • L83
  • O15