The Sabermetric Revolution: Assessing the Growth of Analytics in Baseball (19 page)

Baseball’s supplemental revenue sharing was introduced in 1996 and then extended in the name of increasing competitive balance. The basic idea was that taking money away from rich teams like the Yankees (whose revenue sharing bill surpassed $100 million in 2010) and giving it to poor teams like the Marlins (whose receipts surpassed $40 million) would lower the top payrolls and raise the bottom payrolls. The resulting payroll compression would result in a more equal dispersion of team win percentages, engendering greater balance. Yet the RSD reported in
Table 7
suggests that the outcome didn’t match the expectations. What happened? Let us take a closer look.

Table 8
breaks down the changes in the RSD during different collective bargaining periods. Here it is seen more clearly that the increase in the ratio during the 1990s is coterminous with the introduction of the new supplemental revenue sharing system in the 1996–2002 CBA—a period during which the amount of revenue sharing grew from under $30 million to over $160 million. During the next CBA period, 2003–2006, the ratio creeps up, but not by a statistically significant margin. Then, during the 2007–2011 CBA, the ratio begins to modestly turn down, almost returning to its level in the early 1990s.

Since the correlation between team payroll and win percentage is far from perfect and since the presumed mechanism for promoting balance is via the narrowing of team payrolls, it makes sense to see how the increase in revenue sharing impacted the distribution of team payrolls. The coefficient of variation in team payrolls over the CBA periods is depicted in
Table 9
. (The coefficient of variation is the standard deviation divided by the mean; it allows for more meaningful intertemporal comparisons of distribution as the values in a data series grow.)

Table 8. Ratio of Standard Deviation to Idealized Standard Deviation (RSD) During CBAs

Table 9. Payroll Coefficient of Variation

The evidence here is that the leveling of the RSD during 2003–2006 was not a function of payroll leveling, but that the subsequent RSD leveling during the 2007–2011 CBA may well have resulted from the narrowing of payroll differentials.

Before turning to our explanation of this pattern, it is important to consider other indices of competitive balance, such as balance between seasons.
Table 10
looks at the degree of rotation among bottom dwellers in the American League (teams that finish last in their division) and
Table 11
considers the same in the National League. Obviously, it would be in the interests of each league not to have the same teams finishing last each year. The more rotation at the bottom, the greater the perceived balance in the league.
Table 10
shows that the percent of AL teams finishing last among all MLB teams fell steadily from 33 percent during the first half of the 1990s to 20 percent during the first half of the 2000s, but then increased modestly to 23 percent during the second half of the 2000s. Overall, this is not an encouraging record during this period of sharply increased revenue sharing, although it is consistent with the notion that the 2007–2011 CBA brought a change for the better.
Table 11
shows that the percent of NL teams finishing last has declined steadily throughout these four quinquennia, from 40.7 percent during the early 1990s to 26.7 percent during the last period.

On the top end, considering whether teams from large markets are more likely to make the playoffs than teams from small markets, and how this has changed over time, the evidence in
Table 12
is not encouraging either. Here the teams are put in quintiles, according to the population of their host city.
Table 12
shows that the teams in the top 20 percent of markets substantially increased their average number of playoff appearances per year between the 1996–2002 CBA and the 2003–2006 CBA, while the bottom 20 percent sharply decreased the number of their playoff berths up to the CBA of 2007–2011. During the latter CBA, the number at the top stabilizes while the number at the bottom increases.

Table 10. Rotation on the Bottom, American League

Thus, by all measures considered here, competitive balance in MLB appears to have deteriorated as the quantity of revenue sharing from rich to poor teams grew since the system was first introduced in 1996 through 2006. We are now ready to ask why this has occurred and why this trend may have begun to change with the 2007–2011 CBA.

Table 11. Rotation on the Bottom, National League

Table 12. Average Playoff Berths per Year by Population Quintile

As the size of the transfer in MLB’s revenue sharing has grown rapidly at almost 20 percent per year since its introduction in 1996, the method for calculating each team’s net payments and receipts has changed both during and between CBAs. The computation through 2006 depended on two basic systems: a straight pool plan and a split pool plan. The former taxes each team’s net defined local revenue at the same rate and then redistributes it in equal shares to all teams.
⁷
The marginal tax rate in the straight pool system, thus, is equal for all teams. The split pool system taxes only the top teams and redistributes only to the bottom teams, in each case on the basis of how far the team’s revenue deviates from the average team revenue. As a consequence of combining these two methods, the marginal tax rates between 1996 and 2006 were actually higher for the low revenue teams than for the high revenue teams. For instance, between 2003 and 2006, the marginal tax rate paid by the teams with above average revenue was approximately 39 percent, while that paid by teams with below average revenue was close to 48 percent.
⁸
The below average revenue teams “paid” a tax in the sense that when their revenue increased by $1, they received 48 cents less in transfers.

To illustrate, suppose the Dodgers and the Pirates were both considering the signing of a free agent pitcher and further suppose that each team estimated that the player would produce $10 million of additional revenue for the team. Given the differential marginal tax rates in the revenue sharing system that each team would face, the net (after sharing) incremental revenue for the Dodgers would be an estimated $6.1 million, while that for the Pirates would be $5.2 million. Thus, the bottom half of teams had a stronger disincentive to invest in improving team performance (such as by increasing payroll) than the top half.

This disincentive is compounded by the fact that teams experience different revenue elasticities with respect to increases in their win percentage. That is, depending on the size of the local market and the team’s win percentage, the impact of an additional win on team revenue will vary, and often vary significantly, among teams.
⁹
For instance, an extra win will bring more revenue to a team in New York than a team in Kansas City. New York has more
people with more income and more large corporations (to buy advertising, contract sponsorships, or purchase premium seating) than Kansas City, so the response to having a competitive team will be greater in New York than in Kansas City, other things being equal.

The other major factor that results in different revenue responses to wins (elasticities) across teams is a team’s position in its league standings. A team that sits in last place with a .400 win percentage is unlikely to excite its fan base by winning an extra game and raising its win percentage to .406. But a team with a win percentage of .512 and is one game away from making the playoffs may experience a significant fan response from an extra win. Thus, we would expect teams with low win percentages to have low elasticities and teams with high win percentages to have high elasticities—though this may level off or even become negative at very high win percentage levels. The relationship between revenue and win percentage is depicted by a win curve.

Estimating a win curve for MLB with data from 1992 through 2009, using
both a ninth degree polynomial and a piecewise (based on win percentage quintiles) regression with fixed team and year effects,
¹⁰
shows that the revenue is mildly responsive to improved team performance up to a win percentage of around .500. Between .500 and .570, the revenue response becomes very elastic; while above .570 the response begins to level off. This relationship is depicted in
Figure 11
.

Figure 11. Win Curves: Estimated Average Relationship Between WPCT and Team Revenue

If low revenue teams face both a flatter win curve and a higher marginal tax rate, it is unlikely in the extreme that transferring revenue to them will lead to payroll compression. This pattern is only reinforced when low win percentage teams are also the teams in the smaller markets. Thus, it should not be surprising that MLB team payrolls did not experience compression between 1996 and 2006.
¹¹

It is noteworthy, however, that MLB’s 2007–2011 CBA rectified the regressive tax rate. The primary distribution mechanism continued to be the straight pool system, which accounted for approximately 65 percent of the total transfer. The remaining transfer was based on team revenues in 2004–2005 and projected revenues for 2006–2007.
¹²
Hence, the secondary distribution was based on fixed revenues and was not affected by team actual revenue performance during the 2007–2011 period. The result is that each team faced close to identical marginal tax rates of around 30 percent, and the disincentive for bottom teams to lift payrolls that was built into earlier CBAs was eliminated during 2007–2011. This observation helps to explain why the distribution of payrolls became modestly more compressed since 2006 as well as why the RSD decreased.