The distribution of wins

1
Competitive Balance

• The distribution of wins
• in professional team sports most consistent with
• the maximization of
• league profits.

2
Neal, Walter. The Peculiar Economics of
Professional Sports Quarterly Journal of
Economics 78 (February, 1964) 1-14.

• Louis-Schmelling paradox
• The inverted joint product or the product joint
• Joint product - two products technologically
  resulting from a single process.
• Product joint - An indivisible product from the
  separate processes of two or more firms.
• Professional baseball produces several
  interrelated streams of utility
• In-person viewing of the game
• Broadcasts of games
• League standing effect
• Fourth Estate Benefit
• Conclusion The several joint products which are
  products joint of legally separate business firms
  are really the complex joint products of one
  firm, and this firm is necessarily an
  all-embracing firm or natural monopoly.

3
Neale (1964), cont.

• Four possible cases of interleague competition
• Major League Baseball solution the joining of
  two leagues into one monopoly.
• The professional football solution of the 1940s
  The bankruptcy of one league.
• Survival of two or more leagues that are not
  economically competitive due to geographic
  distances or the institutions of sport and
  culture.
• Survival of two or more leagues that are
  economically competitive and which could be
  sportingly competitive.
• The second case is the most common solution.
  Geographic distances and culture institutions
  seem to be overcome overtime (exception CFL and
  Japanese baseball).
• In general, additional leagues bid up costs and
  reduce revenues, hence reducing the profitability
  of each league.

4
Uncertainty of Outcome

• Why is balance important? Uncertainty of
  outcome is crucial to the demand for sporting
  events. The works of Knowles, Sherony and
  Haupert (1992), and Rascher (1999) found that
  Major League Baseball attendance was maximized
  when the probability of the home team winning was
  approximately 0.6. These studies suggest that
  consumers prefer to see the home team win, but do
  not wish to be completely certain this will occur
  prior to the game being played.
• Knowles, Glenn, Keith Sherony, and Mike Haupert.
  1992. The Demand for Major League Baseball A
  Test of the Uncertainty of Outcome Hypothesis.
  The American Economist, 36, n2, Fall 72-80.
• Rascher, Daniel. 1999. A Test of the Optimal
  Positive Production Network Externality in Major
  League Baseball. Sports Economics Current
  Research, Edited by John Fizel, Elizabeth
  Gustafson and Lawrence Hadley. Praeger 27-45.

5
Perfect Competitive Balance

• But do fans want perfect competitive balance?
• Teams in larger markets generate greater revenue
  from an additional win than teams in smaller
  markets. If marginal cost is the same for all
  teams, then teams in larger markets would
  maximize profits at a higher winning percentage
  than teams in smaller markets.
• This leads to four questions
• how do we measure competitive balance?
• what determines competitive balance?
• how much competitive balance does a league need?
• and do fans really care?

6
Measuring Competitive Balance

• Standard deviation S(PCT actual - PCT
  mean)2/number of teams0.5
• Idealized standard deviation (if every team was
  equal) (.500)/ N0.5
• Where N number of games each team plays in a
  season
•  With a normal bell shaped distribution
• 2/3 of league will be within one standard
  deviation
• 95 will be within two standard deviations
• 99 will be within three standard deviations

7
The Noll-Scully Measure

• CBit s(wp)itactual/ s(wp)itideal
• with s(wp)itideal µ(wp)it / vN
• Where
• s(wp)it is the standard deviation of winning
  percentages within league (i) in period (t)
• µ(wp) it is league (i)s mean
• N is the number of teams

8
What determines competitive balance in
professional sports?

• Schmidt, Martin B. and David J. Berri. (2003)
  On the Evolution of Competitive Balance The
  Impact of an Increasing Global Search. Economic
  Inquiry, 41(4) 692-704.

9
Competitive Balance in the AL

• Figure 1 - Noll-Scully Competitive Balance (CBt)
  Measures
• American League (AL)

10
Competitive Balance in the NL

• Figure 1 (cont.) - Noll-Scully Competitive
  Balance (CBt) Measures
• American League (NL)

11
A Simple Empirical Model

• Table I - OLS Trend Estimates for (CBt)
• Dependent Variable (Sample - 1911 2000)
• CBt AL Constant Time
• 2.742 -0.012 (0.109) (0.002)
• CBt NL Constant Time
• 2.439 -0.008 (0.108) (0.002)
• Standard errors are beneath each coefficient.
• The results indicate that competitive balance
  improved throughout the 20th century.

12
What explains the pattern?

• Institutional factors
• The Reserve Clause
• Reverse-order draft
• Free agency
• Revenue sharing
• Payroll and Salary Caps
• Expanding Populations or Talent Compression

13
The Belief in Institutions

• Consider Commissioner Bud Seligs comment on the
  recent (2002) Major League Baseball labor
  agreement
• . . . the issue here was competitive balance and
  I feel this deal clearly deals with that.
• From the news conference announcing the
  agreement, Friday, August 30th, 2002.

14
Major League BaseballsBlue Ribbon Panel

• Convened to examine
• The Economic Stability of MLB
• Competitive Balance in MLB
• Four members
• Yale president Richard C. Levin
• Former Federal Reserve chairman Paul Volcker
• Former Senator George Mitchell
• Columnist George Will

15
The Blue Ribbon PanelThe Conclusions

• a significant disparity exists in the resources
  member teams
• For example, for the 2000 season the salary of
  the highest paid player in MLB exceeded the
  entire payroll of the Minnesota Twins (BRP 2000
  p. 9).
• such differences in market size has allowed a
  collection of teams to consistently field
  playoff-contending teams.
• teams located in smaller-markets are incapable of
  fielding teams that can challenge for post-season
  success. Consequently, for the smaller-market
  teams the outcome of the season is known before
  the season is started.

16
The Blue Ribbon PanelRecommendations

• The Blue Ribbon Panel recommended a number of
  changes
• recommended that foreign players be subject to
  the draft
• teams maintain the rights of draftees beyond the
  one-year period they currently hold.
• an annual "competitive balance draft," under
  which the eight clubs with the worst records
  could draft players not on the 40-man roster of
  the eight playoff teams.
• Most of these seem to limit player movement or to
  convey greater rights to Major League Baseball
  teams

17
The Coase-Rottenberg Theorem

• When there are no transaction costs the
  assignment of legal rights have no effect upon
  the allocation of resources among economic
  enterprises. Stigler (1988)
• When there are no impediments to the buying and
  selling of playing talent, the assignment of the
  rights to this talent will have no effect upon
  the allocation of players among Major League
  Baseball teams. Rottenberg (1956)

18
On an empirical level

• the impact of the reverse-order draft in 1965
• El-Hodiri and Quirk (1971), Demsetz (1972), and
  Quirk and Fort (1992) all found no tangible
  impact
• Daly and Moore (1981) and Daly (1992) both found
  an improvement
• the impact of the free agency in 1976
• Szymanski (2003) examines (20) empirical studies
  on the impact of the introduction of free-agency
  in 1976 on competitive balance and finds that (9)
  estimate an improvement, (4) document a decline
  and (7) found no impact

19
If not institutional factors, what?

• Evolutionary Biologist Stephen Jay Gould
• the distribution of athletic talent in a
  population should be normally distributed.
• At the right-tail of the distribution would lay
  those with the greatest level of athletic ability
  and assuming that there is a bio-mechanical limit
  to potential ability or talent, the athletes in
  the far right-tail tend to be relatively equal.

20
Goulds Hypothesis (Part 1)

• At the beginning of the 20th century, people
  playing Major League Baseball were only white
  Northeastern American males.
• The population baseball could draw upon was
  relatively small and correspondingly, there
  existed a large degree of heterogeneity between
  players.
• As the probability of winning is closely aligned
  with playing talent, such diversity may lead to
  low levels of competitive balance.

21
Goulds Hypothesis (Part 2)

• As the population of players Major League
  Baseball has to choose from rises, new players
  are added to the population in much the same way,
  i.e., normally.
• The absolute number of players close to the limit
  would rise and, given player demand, as would the
  average players talent level or ability.
• The Gould hypothesis, therefore, argues that as
  the talent pool rises greater player homogeneity
  should be observed.

22
Goulds Hypothesis (Part 3)

• In which case, one should see a corresponding
  rise in the probability of a poor team beating a
  stronger team
• as the poor team is now stocked with players
  closer in talent to those of the stronger team.
• Following the theme, increased player demand
  through, for example, expansion should decrease
  competitive balance.
• Such increased homogeneity in talent reduces
  individual player differences between competing
  teams and therefore would increase the likelihood
  of a less talented team beating a more
  talented team.
• This suggests that, for example, racial
  integration would increase competitive balance
  because teams were able to choose from a larger
  talent pool.

23
No .400 Hitter since 1941
Player Year Average
Nap Lajoie 1901 0.4265
Joe Jackson 1911 0.4081
Ty Cobb 1911 0.4196
Ty Cobb 1912 0.4087
George Sisler 1920 0.4073
Ty Cobb 1922 0.4011
Rogers Hornsby 1922 0.4013
George Sisler 1922 0.4198
Harry Heilmann 1923 0.4027
Rogers Hornsby 1924 0.4235
Rogers Hornsby 1925 0.4028
Bill Terry 1930 0.4013
Ted Williams 1941 0.4057
24
Cursory Evidence
25
Competitive Balance Across Sports
Sport League Years Avg. Level of CB
Basketball NBA 1967-68 to 1975-76 2.59
ABA 1967-68 to 1975-76 2.60

Baseball AL 1901-2000 2.12
NL 1901-2000 2.08

Hockey NHL 1972-73 to 1978-79 2.59
WHA 1972-73 to 1978-79 1.89

Football NFL 1960-1969 1.57
AFL 1960-1969 1.58

Soccer Bundesliga 1964-95 1.32
NASL, MLS 1967-84, 1996-2000 1.34
26
Baseballs Labor Pool

• Globalization of baseball is now evident on the
  playing fields in the United States.
• Players still hail from the traditional areas of
  recruitment, such as the United States, Dominican
  Republic, Puerto Rico, Venezuela, and Cuba
• Many players from Mexico, Australia, Japan, and
  Korea also play in the Major Leagues. Even such
  countries as Spain, Belgium, the Philippines,
  Singapore, Vietnam, Great Britain, Brazil,
  Nicaragua, and the Virgin Islands have produced
  professional baseball players.
• In 2000, the number of foreign-born players on
  Major League Baseball rosters was 312,
  constituting 26 percent of all players (Levine et
  al, 2000).

27
Schmidt Berri (2003)

• Competitive Balance and Major League Baseballs
  Labor Pool are cointegrated
• MLBs Labor Pool is weakly exogenous
• Other factors, captured through various dummy
  variables, appear not to be relevant.

28
Back to Perfect Competitive Balance The work of
Stefan Szymanski (from the Western Economic
Association meetings in 2005)Tilting the Playing
Field (less)
29
Empirical specification for model designed to
explain attendance in MLB

• Data- club attendance, wins, new ballparks,
  strikes, 1978-2003
• Not capacity constrained
• Panel regression
• ? (Attendance)it ? ?i ?t ?i ?
  (winpercentage)it ?Xit ?
• issues price, alternative functional forms, lags

30
Estimated increase in attendance due a unit
increase in win percentage (e.g. from 50 to
51) American League
31
Estimated increase in attendance due a unit
increase in win percentage (e.g. from 50 to
51) National League
32
Redistributing wins would have big effects
33
Attendance maximising distribution of wins in the
2003 National League
34
Empirical issues

• Linear model fits best but is not plausible at
  the extremes
• Almost all observed win percentages lie between
  0.33 and 0.66
• Capacity constraints may bind at very high win
  percentages
• Alternative is to fit a quadratic model to the
  linear estimates
• This approach favours the conventional
  competitive balance justification for restraints

35
Fitting a quadratic model from the linear
estimates
36
American League 2003
37
National League 2003
38
Optimal distribution of wins, American League
2003, quadratic model
39
Impact of optimal win distribution 2001-2003
40
Szymanski Conclusions

• The impact of wins on attendance varies across
  the league.
• In other words, fans ask more (or less) of their
  teams in different markets.
• If Major League Baseball wished to maximize
  league attendance, it would not want perfect
  competitive balance.
• Attendance would increase with less competitive
  balance (relative to what we see)

41
How does competitive balance impact league
demand? According to Schmidt-Berri (2001)

• Competitive balance has a larger impact (i.e.
  more competition leads to more demand) the longer
  the time period one considers.
• In other words, balance across three years has a
  smaller impact than balance over five years.
• from the article.These results suggest that
  fans may not prefer competitive balance in a
  given season, but over time, the slogan wait
  till next year must remain valid for the teams
  located toward the bottom of the standings

42
more Schmidt and Berri (2001)

• from The Wages of Wins
• The largest impact was seen when we looked at
  improvements in our five-year measure. A movement
  from the least competitive five-year measure to
  the highest level of balance would result in
  about 3,500 additional fans per game for each
  team. This works out to a 14 increase in
  attendance. Again, this was the largest impact we
  found. So a very large change in competitive
  balance across the longest time period we
  considered, and 14 is all the oomph we uncover.

43
How does competitive balance impact league
demand? According to Humphreys (2002)

• from The Wages of Wins
• Humphreys looked at three measures of competitive
  balance, the Noll-Scully, the Herfindahl-Hirschman
  Index, and Humphreys Competitive Balance Ratio
  (CBR).
• Humphreys (2002) defines the CBR as follows The
  CBR scales the average time variation in won-loss
  percentage for teams in the league by the average
  variation in won-loss percentages across seasons
  it indicates the relative magnitude of each type
  of variation across a number of seasons (p.
  137).
• In a model designed to explain league attendance
  Humphreys found that only the CBR was
  statistically significant.
• Although Humphreys does not address this issue,
  his results suggest that a movement from the
  lowest observed level of balance to the highest
  would increase a teams attendance by 4,000 fans
  per game. Again, that is quite similar to what we
  found with the Gini Coefficient.

44
Competitive Balance Lessons from The Wages of
Wins

• The measurement of competitive balance should
  focus on outcome in the regular season, not the
  post-season.
• Relative to its history, baseball is more
  balanced today.
• Relative to sports like football and soccer,
  baseball is not as balanced. Compared to
  basketball, though, baseball does not have a
  competitive balance problem.
• Competitive balance appears to be dictated
  primarily by the underlying population of talent,
  not league policy.
• Although we can find a statistical relationship
  between competitive balance and attendance, the
  estimated economic significance seems quite
  small. Consequently, it is not clear whether the
  fans truly care about the level of balance in a
  league.
• The relationship between team revenue and wins
  suggests that perfect competitive balance would
  actually lower league revenues.