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Ownership of property-rights and the allocation oftalentsHaoming Liu a & Yohanes E. Riyanto aa Department of Economics , National University of Singapore , Singapore 117570Published online: 03 Jan 2008.

To cite this article: Haoming Liu & Yohanes E. Riyanto (2009) Ownership of property-rights and the allocation of talents,Applied Economics, 41:26, 3425-3436

To link to this article: http://dx.doi.org/10.1080/00036840701392869

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Applied Economics, 2009, 41, 3425–3436

Ownership of property-rights and

the allocation of talents

Haoming Liu and Yohanes E. Riyanto*

Department of Economics, National University of Singapore,

Singapore 117570

Under the reserve-clause system that assigns the property-rights on the

Major League Baseball players’ services to teams, player transfers are

negotiated between teams without the involvement of players. In contrast,

under the current free-agency system, players with free-agent status

negotiate directly with potential suitors. Thus, the system assigns the

property-rights to players. Using data extracted from the Baseball Archive

(http://baseball1.com), this article examines the effect of the change in

the property-rights assignment on the allocation of talents across teams.

We find that the change increased large-market teams’ shares of veteran

all-star players and the concentration of senior players.

I. Introduction

Three decades after the adoption of the free-agency

system in the American Major League Baseball

(MLB), people are still debating on whether it has

changed the allocation of talents across teams. On

one camp, backed up by the observation of sky-

rocketing player salaries, team owners argue that it

has weakened small-market teams’ ability to hold on

to their star players and reduced competitive balance.

On the other camp, many researchers (e.g.

Rottenberg, 1956; Fort and Quirk, 1995) believe

that the adoption of free-agency should not have

any effect on the allocation of talents across teams.The major change introduced by the adoption of

the free-agency system is that it gives senior players

the right to directly negotiate with teams that are

interested in their services. Before its adoption, once a

player was drafted by a team and signed a contract,

the rights to the player’s service was retained by the

team that drafted him even after his contract is

expired. This system is known as the reserve-clause

system. It effectively binds players to their teams until

they are released, retired or sold to other teams.

The ownership of property-rights on players’ services

is thus, assigned to teams. Under the current free-

agency system, which was adopted after 1976, a team

can only retain a drafted player for the first 6 years

unless it extends the initial contract with the player’s

agreement. Players become free-agents upon contract

expiry, which gives them the right to negotiate and

sign contracts with any teams. The free-agency

system, thus, assigns the ownership of property-

rights on players’ services to players.Clearly, under the reserve-clause system, team

owners can keep a star player as long as they want

without worrying that he might be lured by another

team. Under the free-agency system, if a team wants

to keep its star players who are free agents, it has to

pay them competitive salaries. Small-market teams

may find it difficult to compete with large-market

teams in hiring these players as the latter can always

outbid them by offering higher salaries. As a result,

many skeptics argue that large-market teams will hire

most of the talents at the expense of small-market

teams in the free-agency era.On the contrary, some researchers argue that even

under the reserve-clause system, small-market teams

*Corresponding author. E-mail: ecsrye@nus.edu.sg

Applied Economics ISSN 0003–6846 print/ISSN 1466–4283 online � 2009 Taylor & Francis 3425http://www.informaworld.com

DOI: 10.1080/00036840701392869

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do not have any economic incentives to keep all oftheir star players. They would sell their star players toteams, which value them most. Under the free-agencysystem, these players will be attracted to play forlarge-market teams. Thus, all in all, most star playerswould end up playing for large teams in both regimes.Consequently we should not expect any significantdifference in the allocation of talents between thereserve-clause and the free-agency period. Thisargument is motivated by the celebrated CoaseTheorem, which asserts that in the absence oftransaction costs and wealth effects, the allocationof property-rights should be irrelevant for theallocation of talents across teams.

The debate has attracted many empirical studiesanalysing the impact of free-agency on the allocationof talents across teams. Assuming that changes in theallocation of talents can only be achieved via players’mobility and these changes affect competitive bal-ance, most of these studies compared either thecompetitive balance or players’ mobility before andafter the change in the property-rights assignment.Competitive balance is usually measured by somesummary statistics of winning percentage (WP), suchas the SD of WP (e.g. Scully, 1989; Fort and Quirk,1995; Vrooman, 1995; Schmidt, 2004, 2006), the WPrank, the year-to-year changes of the WP rank (e.g.Scully, 1989; Fort and Quirk, 1995; Eckard, 2001),the difference between the actual SD and the ‘ideal’SD (e.g. Vrooman, 1995; Maxcy, 2002), and theconcentration level of team wins (e.g. Depken, 1999).These studies found that the introduction of free-agency either slightly improved competitive balanceor had no significant impact on it. Results fromstudies on player’s mobility are inconclusive as well.Hylan et al.(1996) found that free-agency reducedveteran pitchers mobility. Maxcy (2002) showed thatfree-agency raised player’s mobility, particularly forproductive players.

It should be noted that it is difficult to draw anycausal relationships from both types of studies. First,it is true that changes in the allocation of talents willaffect competitive balance when the pool of talents isfixed. However, allowing African Americans to playfor the MLB in 1947 and the globalization of baseballgame in the past decades undoubtedly enlarged thetalent pool. Second, while changes in the allocation oftalents can only be achieved by relocating playersacross teams, an increase in player’s mobility does notnecessarily changes the allocation of talents. This isbecause players’ relocation could be either due to thedifference in their productivity across teams or inpersonal preferences. For example, two equally

talented players might want to switch teams becausethey both want to play for the other player’s team.This type of move increases player’s mobility, butdoes not affect the allocation of talents. Therefore,even if we find that competitive balance or player’smobility in the free-agency era differs from that inthe reserve-clause era, we still cannot conclude thatthe allocation of talents has actually changed.

To circumvent the above limitations, this articleuses a novel approach that analyses the impact offree-agency on the allocation of talents directly. Wepropose to use two variables to measure a team’stalent level. The first one is the number of all-starplayers in a team. Arguably, teams with more all-starplayers possess more talents. If the adoption of free-agency changed talent allocation, it would alter theallocation of all-star players as well. An obviousshortcoming of this approach is that it treats teamswith the same number of all-star players equally.However, the talent level could differ considerablyacross these teams due to the variation in talent levelsamong all-star players and among nonall-starplayers. To complement this measure, we furtherconstruct an offensive talent measure by convertingvarious performance measures into efficiency playerunits based on the predicted run-producing ability.In this approach, the aggregate efficiency units ofeach team measures its stock of player’s talent.

II. Data

The data used in this article is mainly extracted fromthe Baseball Archive compiled by Sean Lahman,1

which contains the performance statistics of MLBplayers and teams and each team’s annual attendancebetween 1871 and 2001. We restrict our analysis tothe period of 1952–2001 that covers 25 years beforeand 25 years after the adoption of free-agency at theend of 1976.

Because annual attendance reflects both theintensity of fans’ preference and the number ofpotential fans in the market, which are closely relatedto a team’s revenue generating ability, we use it tomeasure market size. A team’s financial status isperhaps a better measure of market size than annualattendance. Unfortunately, team values are onlyavailable after 1989, which prevents us from examin-ing the impact of the introduction of the free-agency.We do use this information to analyse whetherattendance is a good proxy for teams’ financialstatus. Using the 1989–1998 data, we find that the

1 The dataset is downloadable from http://baseball1.com

3426 H. Liu and Y. E. Riyanto

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year-to-year variation in attendance can explain

about 54% of the year-to-year variation in a team’s

value and the between-team variation in attendance

can explain 64% of the variation in a team’s value.

This evidence suggests that attendance is a good

proxy.Table 1 reports annual attendance, ranked in

ascending order, in the starting and ending year of

the sample period. The ranking of the

attendance figure is surprisingly stable even after

6 out of 16 teams in 1952 had relocated to other

cities and 16 new teams were added during the

sample period. In terms of annual attendance, the

top four teams of the American League (AL) and

of the National League (NL) in 1952 were still in

the top half in 2001. In our later regression

analysis, we decide to use an unbalanced panel

data so that the information of the 16 new teams

can be included.2

Several researchers (e.g. Gould, 1986; Zimbalist,

1992 and Schmidt and Berri, 2003) have pointed

out that an increase in the size of talent pool

should increase competitive balance. This is because

an increase in the size of the pool makes it possible

for small-market teams to hire more talented

players, which will raise their winning probability.

To analyse the changes in the talent pool, we report

the distribution of both offensive and pitching

talents before and after 1976 in Table 2. We use

slugging percentage as a crude measure of offensive

talent and strike-out-walk ratio as a measure of

pitcher’s talent.3 We restrict our attention to

position players appeared at least 100 at-bats a

season and pitchers pitched at least 50 innings a

season. Our dataset contains 1299 position players

and 1002 pitchers before the end of 1976 and 1707

position players and 1484 pitchers after 1976. The

statistics show that both batting and pitching skills

increased over time although there are more players

in the free-agency era due to franchise expansions.

This suggests that the increase in the supply of

talents outweighs the increase in the demand.

Therefore, we cannot draw any causal relationship

between the adoption of free-agency system and

competitive balance even if we find that the

competitive balanced has changed.In the regression analysis, we use a player’s all-

star status to measure his talent level. Hence, a

team’s talent level is simply defined as its share of

all-star players.4 Although some all-star players

might not be the most talented players, the all-star

status does increase their popularity among fans

due to the extensive media coverage of all-star

games. Therefore, their marginal revenue products

tend to be higher than other players. If the transfer

of property-rights has any effect on the allocation

of talents, it will certainly affect the allocation of

all-star players.Our all-star dataset contains of 427 pitchers and

622 position players. The median experience of all-

star teams is 7.2, which is slightly higher than the

median experience of all MLB players 5.7. This

suggests that all-star teams are likely to be dominated

by senior players, who are directly affected by the

adoption of the free-agency system.Teams’ shares of all-stars before and after the

adoption of the free-agency system are reported in

Table 3. The first column of the table reports

teams’ rank of average attendance under the

reserve-clause and the free-agency era in ascending

order. T-S and S-S in the table, respectively,

indicates the share of total all-star players and

senior star players. Overall, it suggests that large-

market teams do have a larger share of all-stars

than small-market teams. However, the difference

between small and large market teams has declined

since the adoption of the free-agency system, which

can partly be attributed to an increase in the

number of teams in the past decades. Since, the

direct beneficiary of the free-agency regime is senior

players, we also report teams’ shares of senior all-

stars in columns S-S. From casual observation, it is

interesting to note that, under the free-agency

system, the large-market teams’ shares of senior

all-stars tend to be larger than their shares of

all-stars. For example, under the free-agency

regime, six out of the seven largest AL teams in

terms of attendance have a larger share of senior

2Our estimation results show that the estimates are not sensitive to whether we use a balanced or an unbalanced panel.However, due to the decline in sample size, some of the coefficients indeed become statistically insignificant even at the 10%level for the NL if the balanced sample is used.3 The slugging percentage is defined as (total bases)/(total number at-bats). Strike-out-walk ratio¼ (total number of strikeouts)/(total number of walk-on-balls).4 There are two leagues in the US MLB, the American League and the National League. In the middle of each baseball seasonsince 1933, an all-star team has been selected for each league. The teams were originally selected jointly by managers and fansfor the 1933 and 1934 season. In 1935–1946, the all-star teams were selected solely by managers. From 1947 to 1957, fanschose the the starting lineup and managers chose the remaining players. Between 1958 and 1969, managers, players andcoaches made the all-star team selections. In 1970, the vote again returned to fans for the selection of starters and remainsthere today. Normally, each team sends at least one player to the all-star teams.

Ownership of property-rights and the allocation of talents 3427

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all-stars. On the contrary, the small market teams’shares of senior all-stars tend to be smaller thantheir shares of all-stars.

In addition to a player’s all-star status (a binaryvariable), we also use a player’s predicted run-produ-cing ability to measure his offensive talent. To do so,we first evaluate the contribution of each offensivemeasure to team’s run production. Subsequently, wecalculate a player’s run-producing ability using theweighted sum of his various offensive measures,where the weight is defined as the correspondingoffensive measure’s contribution to team’s runproduction. The basic sample statistics at the teamlevel is given in Table 4.

III. Allocation of All-star Players

To test whether the change in the property-rights

assignment increased large-market teams’ shares of

all-star players, we run the following regression:

Sit ¼ �0 þ �1ait þ �2wit þ �3nit þ �4 ft þ �5ft � ait

þ �6 ft � wit þ �7tþ �8t2 þ "it ð1Þ

where Sit is team i’s share of all-star players, ait is the

log of annual attendance in a regular season, which is

our measure of teams’ market size, wit is the winning

percentage, nit is the number of teams in the league,

ft is a dummy variable (¼1 for the free agency era and

Table 1. Annual attendance and its rank at the beginning and the end of the sample period

1952 2001

Rank Attendance Team name Attendance Team name

American League1 518 796 St. Louis Brownsa 1 298 365 Tampa Bay Devil Rays2 627 100 Philadelphia Athleticsb 1 536 371 Kansas City Royals3 699 457 Washington Senatorsc 1 766 172 Chicago White Sox4 1 026 846 Detroit Tigers 1 782 929 Minnesota Twins5 1 115 750 Boston Red Sox 1 915 438 Toronto Blue Jays6 1 231 675 Chicago White Sox 1 921 305 Detroit Tigers7 1 444 607 Cleveland Indians 2 000 919 Anaheim Angels8 1 629 665 New York Yankees 2 133 277 Oakland Athletics9 – – 2 625 333 Boston Red Sox10 – – 2 831 021 Texas Rangers11 – – 3 094 841 Baltimore Orioles12 – – 3 175 523 Cleveland Indians13 – – 3 264 907 New York Yankees14 – – 3 507 326 Seattle Mariners

National League1 281 278 Boston Bravesd 642 745 Montreal Expos2 604 197 Cincinnati Reds 1 261 226 Florida Marlins3 686 673 Pittsburgh Pirates 1 782 054 Philadelphia Phillies4 755 417 Philadelphia Phillies 1 879 757 Cincinnati Reds5 913 113 St. Louis Cardinals 2 378 128 San Diego Padres6 984 940 New York Giantse 2 464 870 Pittsburgh Pirates7 1 024 826 Chicago Cubs 2 658 330 New York Mets8 1 088 704 Brooklyn Dodgersf 2 736 451 Arizona Diamondbacks9 – – 2 779 465 Chicago Cubs10 – – 2 811 041 Milwaukee Brewers11 – – 2 823 530 Atlanta Braves12 – – 2 904 277 Houston Astros13 – – 3 017 143 Los Angeles Dodgers14 – – 3 109 578 St. Louis Cardinals15 – – 3 166 821 Colorado Rockies16 – – 3 311 958 San Francisco Giants

aNow Baltimore Orioles.bNow Oakland Athletics.cNow Minnesota Twins.dNow Atlanta Braves.eNow San Francisco Giants.fNow Los Angeles Dodgers.

3428 H. Liu and Y. E. Riyanto

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0 otherwise), t is the time trend and t2 is its square and" is the disturbance term that can be decomposedinto,

"it ¼ �i þ �it,

where �i captures the team specific-effects and �it variesacross both teams and time. �i and �it have a mean ofzero and a variance of �2� and �

2� , respectively.

We include the wining percentage to capture fans’favouritism toward winning teams in their all-starvoting. The number of teams is included to controlfor the impact of league expansion on the allocationof all-stars. The dummy variable ft captures theimpact of switching from the reserve-clause regime tothe free-agency regime. A quadratic time trend isincluded to account for the smooth changes in theteams’ shares of all-star players over time.

An obvious problem of estimating Equation 1 isthat both attendance and winning percentage are notexogenous. On the one hand, winning teams andlarge-market teams have more financial resourcesthan other teams, they tend to hire more star players.On the other hand, teams with more star players canwin more games and attract more spectators. To dealwith the potential endogeneity problem, we instru-ment both attendance and winning percentage withtheir two-year lags. Clearly, a team’s current share ofall-star players does not affect its winning percentageand attendance 2 years ago.

Another challenge is how to interpret the coeffi-cient on the interaction term between free agency andthe attendance f� a. Because many things have

changed since the introduction of free agency, thechange in the relationship between market size andshare of all-stars might not be attributable to thetransfer of property-rights. One noticeable factor isthe fast and unbalanced growth of broadcastingrevenue across teams. For instance, the local broad-casting revenue of the New York Yankees increasedfrom $1.2 million in 1976 to $47 million in 1994 whileit only increased from $1 million to $4.5 million forthe Minnesota Twins.5 Since, a star player increasesboth his team’s gate revenue by attracting morespectators and his team’s broadcasting revenue byattracting more viewers, the inter-teams marginalrevenue product differential of all-stars has increasedsince 1977. Consequently, owners of large-marketteams now have a stronger incentive to buy starplayers than before. If the argument is correct, thenlarge-market teams’ shares of both senior and juniorstar players should have increased since 1977.However, if it is the transfer of property-rights thatis responsible for the change, then it will only bereflected in the increase of the large-market teams’shares of senior players.

To test the competing arguments, we run separateregressions using three types of share – the share ofall-stars (including both senior and junior), of seniorall-stars and of junior all-stars – as dependentvariables for the AL and the NL, respectively.Table 5 reports the estimation results. The coefficienton the attendance is positive for the NL but negativefor the AL. Since, none of the coefficients aresignificant even at the 10% level, our finding does

Table 2. Selected performance statistics for position players and pitchers

Slugging ratio Strike-out-walk ratio

1952–1976 1977–2001 1952–1976 1977–2001

1% 0.216 0.231 0.563 0.6985% 0.258 0.275 0.800 0.92310% 0.282 0.300 0.941 1.05025% 0.324 0.342 1.204 1.32450% 0.375 0.393 1.587 1.72275% 0.431 0.449 2.077 2.22290% 0.484 0.504 2.658 2.87195% 0.520 0.539 3.088 3.41299% 0.596 0.608 4.111 5.111Mean 0.380 0.398 1.718 1.891Variance 0.006 0.007 0.556 0.815Number of observations 6624 9642 4545 6705Number of players 1299 1707 1002 1484

Notes: The sample of position players consists of those who have batted at least 100 times in a year.The sample of pitchersconsists of players who have pitched at least 50 innings in a year. The Slugging ratio¼ (number of total bases)/(number ofat-bat). The Strike-out-walk ratio¼ (number of strike-out)/(number of walk).

5Data source: various issues of Broadcasting & Cable, compiled by Rodney Fort.

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Table 3. Team share of all–stars before and after the adoption of free–agency system

Before After

Rank T-S S-S Team name T-S S-S Team name

American League1 0.042 0.024 Texas Rangers 0.053 0.045 Minnesota Twins2 0.082 0.063 Oakland Athletics 0.066 0.055 Oakland Athletics3 0.101 0.094 Cleveland Indians 0.068 0.046 Seattle Mariners4 0.095 0.113 Minnesota Twins 0.050 0.030 Chicago White Sox5 0.106 0.118 Baltimore Orioles 0.039 0.047 Tampa Bay Devil Rays6 0.068 0.045 Anaheim Angels 0.065 0.070 Detroit Tigers7 0.116 0.135 Chicago White Sox 0.082 0.077 Cleveland Indians8 0.085 0.073 Kansas City Royals 0.061 0.062 Kansas City Royals9 0.108 0.104 Boston Red Sox 0.061 0.067 Texas Rangers10 0.103 0.114 Detroit Tigers 0.095 0.090 Boston Red Sox11 0.173 0.178 New York Yankees 0.073 0.077 Anaheim Angels12 – – – 0.119 0.152 New York Yankees13 – – – 0.074 0.077 Toronto Blue Jays14 – – – 0.078 0.090 Baltimore Orioles

National League1 0.035 0.021 San Diego Padres 0.058 0.050 Pittsburgh Pirates2 0.053 0.045 Milwaukee Brewers 0.078 0.068 Montreal Expos3 0.087 0.080 Chicago Cubs 0.056 0.062 Milwaukee Brewers4 0.095 0.104 Pittsburgh Pirates 0.069 0.062 San Francisco Giants5 0.117 0.119 San Francisco Giants 0.076 0.083 San Diego Padres6 0.080 0.069 Philadelphia Phillies 0.067 0.062 Houston Astros7 0.035 0.035 Montreal Expos 0.054 0.042 Florida Marlins8 0.137 0.115 Cincinnati Reds 0.070 0.066 New York Mets9 0.057 0.058 Houston Astros 0.099 0.099 Cincinnati Reds10 0.124 0.144 Atlanta Braves 0.089 0.083 Atlanta Braves11 0.128 0.141 St. Louis Cardinals 0.071 0.072 Chicago Cubs12 0.067 0.040 New York Mets 0.084 0.101 Philadelphia Phillies13 0.135 0.152 Los Angeles Dodgers 0.084 0.098 St. Louis Cardinals14 – – – 0.094 0.091 Los Angeles Dodgers15 – – – 0.078 0.107 Arizona Diamondbacks16 – – – 0.067 0.076 Colorado Rockies

Notes: Teams are ranked based on their average attendance over the respected period. T-S is the share of total all-starsand S-S means the share of senior all–stars.

Table 4. Basic sample statistics

American League National League

Share of all-star players 0.083 0.087Log of annual attendance 14.162 14.244Log of annual attendance�F 8.717 8.517winning percentage 0.498 0.498Winning percentage�F 0.301 0.293Number of teams per league 12.549 11.985Runs scored (per season) 701.34 674.78Total number of singles (per season) 984.98 980.79Total number of doubles (per season) 238.00 233.94Total number of triples (per season) 34.211 38.012Total number of home runs (per season) 140.28 129.71Total number of walks (per season) 535.16 512.48Total number of strik outs (per season) 850.70 900.12Total number of outs (per season) 3134.8 3096.3Number of observations 598 572

Note: F¼ 1 for free-agency period and 0 otherwise.

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Table

5.Theim

pact

oftransferringownership

oftheproperty-rightto

players’services

onteam’sshare

ofall-starplayers

AmericanLeague

NationalLeague

Total

Senior

Junior

Total

Senior

Junior

(1)

(2)

(3)

(4)

(5)

(6)

Logofannualattendance

�0.0166

(0.0288)

�0.0149

(0.0449)�0.0039

(0.0493)

0.0189

(0.0147)

0.0003

(0.0229)

0.0284

(0.029)

Logofannualattendance�F

0.0518

(0.0318)

0.1012

(0.050)**�0.0552

(0.0549)

0.0081

(0.0253)

0.068

(0.0377)*

�0.0869

(0.0492)*

Winningpercentage

0.7405

(0.1121)***

1.0814

(0.177)***

0.2079

(0.1946)

0.5616

(0.0941)***

1.0598

(0.1462)***�0.1772

(0.1853)

Winningpercentage�F

�0.2297

(0.1914)

�0.5173

(0.3025)*

0.1401

(0.3326)

0.0375

(0.250)

�0.3983

(0.3773)

0.6294

(0.4871)

F�0.6048

(0.377)

�01.1626

(0.5921)**

0.7234

(0.6506)�0.1318

(0.272)

�0.7614

(0.4199)*

0.9175

(0.5333)*

Tim

etrend

0.0003

(0.002)

�0.0005

(0.0031)

0.001

(0.0035)�0.0016

(0.0009)*

�0.0007

(0.0016)

�0.0027

(0.0018)

(Tim

etrend)2

�1.00e-05(0.00003)

�0.00002(0.00004)

4.00e-06(0.00004)

0.00002(1.00e-05)�

3.00e-06(0.00002)

0.00005(0.00003)**

Number

ofteamsper

league�0.0096

(0.0053)*

�0.0064

(0.0084)�0.0143

(0.0093)�0.0069

(0.0025)***�0.0074

(0.0042)*

�0.0064

(0.005)

Constant

0.0597

(0.3653)

�0.1533

(0.5683)

0.1816

(0.6237)�0.3528

(0.1836)*

�0.3449

(0.2846)

�0.1136

(0.3613)

Obs

568

568

568

542

542

542

Notes:Numbersin

parenthesisare

SE.F¼1forthe1977–2001periodand0forthe1952–1976period.

***meanssignificantatthe1%

,**meanssignificantatthe5%

level

and*meanssignificantatthe10%

.

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not support the claim that large-market teams hired

more all-star players before 1977. Also, the coefficient

on the interaction term f� a is not statistically

significant when the share of all-stars (including

both senior and junior) is used as the dependent

variable. However, the coefficient on f� a is positive

and significant for both the AL and the NL when the

share of senior all-stars is used as the dependent

variable. A one log-point increase in annual atten-

dance raises a team’s share of senior all-star players

by 10 percentage points for the AL and by 6.8

percentage points for the NL. This implies that

large-market teams hired more senior all-stars in the

period of 1977–2001 than in 1952–1976.When the share of junior all-stars is used as the

dependent variable, the coefficient on f� a is negative

and statistically significant for the NL. Moreover, the

hypothesis that the coefficient on f� a in column (2)

is the same as in column (3) can be rejected at the 5%

level and the hypothesis that they are the same

between columns (5) and (6) can be rejected at the 2%

level. This indicates that shares of junior all-stars

respond to the adoption of free-agency differently

from shares of senior all-stars. We argue that this is

because small-market teams become reluctant to

trade out their junior star players as a response to

losing their senior star players. As a result, large-

market teams’ shares of junior star players fell after

the introduction of free agency, but their shares of

senior star players moved in the opposite direction.The coefficient on winning percentage is always

positive no matter which share is used as the

dependent variable. This suggests that winning

teams hire more star players, both senior and

junior. However, the coefficient on f�w is positive

when the share of senior all-stars is used as dependent

variable while it is negative when the share of junior

all-stars is used as the dependent variable. Because

large-market teams generally win more games than

small-market teams, the actual changes in the

allocation of all-stars are not as strong as have been

suggested by the coefficient on f� a. However, since

the impact of f� a dominates that of f�w, large-

market teams’ shares of senior all-stars are still larger

in the free-agency era.To sum up, our findings show that the change in

the assignment of property-rights on senior players’

services has strengthened both the positive effect of

market size on teams’ shares of senior all-star players

and the negative impact of market size on teams’

shares of junior all-star players.

However, before we draw a causal relationship

between changes in property-rights and in the

allocation of talents, several cautionary notes are in

place. First, the starting lineup of the all-star team

consists of players from the fans’ voting. Because

large-market teams have more fans, their players tend

to be over represented. This is further enhanced by

the advance of TV coverage. Second, since many

senior all-star players have been selected into all-star

teams several times in their carrier, they are likely to

be able to attract more fans than junior all-stars. As a

result, the commercial value of the service of senior

all-stars might be larger than that of junior all-stars.

Moreover, the differences in their commercial value

could have been increased with the further commer-

cialization of the MLB games.If the rise in the extent of media coverage raises the

relative value of senior to junior all-stars, particularly

among large-market teams, then teams with more

lucrative TV contracts will hire more senior all-stars.

However, when we include the log of TV revenue into

the random-effects estimation, its coefficient is not

significant even at the 10% level, suggesting that

a team’s share of all-star players does not depend on

its TV revenue. We also conjecture that the weak

correlation between a team’s TV revenue and its

share of senior all-stars might be due to the positive

correlation between TV revenue and the number of

spectators attracted to the stadium. However, if we

replace ait and f� ait with the log of TV revenue and

its interaction with the free-agency dummy f, the

coefficients on the log of TV revenue and on the

interaction term are not significant even at the 10%

level. The evidence suggests that the increase in the

concentration level of senior all-stars is not driven by

the increase in the relative value of senior to junior

all-stars.Finally, because managers of all-star teams (or the

league) might want each team to have at least one all-

star player, these players from winning teams may be

more talented than players from losing teams.6 Using

the 1990s’ data, we find that all-stars from the

nonlosing teams ðWP � 0:5Þ batted 10 more runs

than their counterparts from losing teams

(WP<0.5). The evidence supports our conjecture.

Since, large-market teams tend to be winning teams

rather than losing teams, shares of all-stars under-

estimate large-market teams’ shares of talents.

Adjusting the share of all-stars by performance will

strengthen the correlation between market size and

the share of senior star players.

6 Since the start of the all-star games, only three teams failed to send at least one player to the all-star team, they arePhiladelphia Phillies in 1934 and 1945, Brooklyn Dodgers (now, Los Angeles Dodgers) in 1935, Cincinnati Reds in 1934.

3432 H. Liu and Y. E. Riyanto

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In summary, our analysis suggests that the changein the assignment of property-rights on seniorplayers’ services brought about by the free-agencysystem has altered the allocation of all-star players.

However, since only less than 10% of the MLBplayers can be selected into all-star teams, theallocation of all-stars might not be able to depicta complete picture of the allocation of talents. Inthe next section, we use another talent measureto examine the change in the relationship betweenthe level of talent and market size.

IV. Allocation of the Run-producingAbility

To win a baseball game, a team has to score enoughruns. Hence, the most valuable talent of a positionplayer is his run-producing ability. The number ofruns scored and the number of runs batted-in are thetwo most widely used run-producing measures.Unfortunately, these two measures depend on bothplaying talent and batting order. For example, a leadoff-hitter might be able to score more runs thanplayers behind him, but he is less likely to bat-in moreruns. Therefore, neither of the two statistics is a goodmeasure of a player’s run-producing ability. To maketalent comparable across players, we convert variousoffensive performance statistics into potentialnumber of runs produced. To this end, we use atwo-step procedure that resembles the one used byBlass (1992).

In the first step, we estimate the value of differentoffensive inputs to a team’s run-producing ability, r.

rit ¼ �0 þ �1sit þ �2dit þ �3trit þ �4hit þ �5bit

þ �6soit þ �7oit þ eit, ð2Þ

where �0s is a vector of parameters, sit is thenumber of singles of team i batted in year t, d isthe number of doubles, tr is the number of triples, h isthe number of home runs, b is the number ofwalk-on-balls, so is the number of strike outs, o isthe number of outs excluding strike outs and e is theerror term. The equation is estimated for the AL andthe NL separately.

Table 6 reports the estimation results. The coeffi-cient can be interpreted as the contribution of thecorresponding offensive input to a team’s runproduction. For example, to generate two runs, ateam need to bat either four singles or three doubles.A player’s run-producing ability is then defined as thesum of his offensive inputs multiplied by the run-producing value of its corresponding input. By doingso, we convert an array of heterogenous offensiveperformance measures into an additive run-produ-cing ability. The sum of the potential run-producingability of each team would be a good measure of itsoffensive ability.

In the second step, we regress teams’ shares ofoffensive talents on the log of annual attendance andother control variables. To control for the potentialendogeneity of the attendance and the winningpercentage in year t, the two-year lag of theattendance and the winning percentage are used asinstrumental variables. The control variables are thesame as in Equation 1.

Table 7 reports the estimation results. Thenumber of attendance has no impact on a team’sshare of offensive talent in the AL, but has anegative effect in the NL before the transfer of theownership of property-rights on players’ servicesfrom teams to players in 1976. We cannot detectany significant correlation between a team’s shareof run-producing ability and its market size in boththe AL and the NL even after 1976. However, if weuse a team’s share of senior player’s run-producing

Table 6. The estimated value of various offensive measure to a team’s run-producing ability

American League National League

Single 0.5024 (0.0194)** 0.5268 (0.0186)**Double 0.7717 (0.0462)** 0.7411 (0.041)**Triple 1.362 (0.1151)** 1.041 (0.1033)**Home runs 1.417 (0.0342)** 1.442 (0.034)**Walk 0.3735 (0.0147)** 0.342 (0.0145)**Strike outs �0.0915 (0.0091)** �0.089 (0.009)**Out �0.111 (0.0062)** �0.1089 (0.006)**Time 0.2151 (0.3493) 0.1003 (0.3772)(Time)2 �0.0018 (0.0062) 4.2e-05 (0.0064)F � 2.823 (4.256) � 4.768 (4.142)Number of observation 598 572

Notes: Numbers in parenthesis are standard errors. F¼ 1 for the 1977–2001 period and 0 for the 1952–1976 period.** means significant at the 5% level.

Ownership of property-rights and the allocation of talents 3433

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Table

7.Theim

pact

oftransferringownership

oftheproperty-rightto

players’services

onteam’sshare

ofrun-producingability

AmericanLeague

NationalLeague

Total

Senior

Junior

Total

Senior

Junior

Logofannualattendance

�0.001

(0.004)

�0.0108

(0.0255)

0.006

(0.0191)

�0.0079

(0.002***)

�0.008

(0.0126)

�0.0129

(0.0078)*

Logofannualattendance�

F0.0036

(0.0043)

0.0692

(0.0285)**�0.0565

(0.021)***

0.0091

(0.0034)***

0.0586

(0.0208)***�0.0182

(0.0129)

Winningpercentage

0.0886

(0.0148)***

0.5191

(0.1013)***�0.1735

(0.0738)**

0.110

(0.0127)***

0.6037

(0.0806)***�0.1748

(0.0501)***

Winningpercentage�F

�0.0237

(0.0252)

�0.1842

(0.1724)

0.0588

(0.1259)

�0.0635

(0.0338)*

�0.5669

(0.2081)***

0.1599

(0.1294)

F�0.03

(0.0506)

�0.8744

(0.338)***

0.7765

(0.2485)***�0.0949

(0.0367)***

�0.5448**

(0.2316)**

0.1797

(0.144)

Tim

e�0.0002

(0.0003)

�0.0005

(0.0018)

0.0002

(0.0013)

�0.0013

(0.0001)***

�0.0008

(0.0009)

�0.0014

(0.0005)***

(Tim

e)�2

2.00e-06

(3.00e-06)�

1.00e-05

(0.00002)

1.00e-05

(0.00002)

0.00002

(2.00e-06)***

2.00e-06

(1.00e-05)

0.00003

(8.00e-06)***

Number

ofteams

�0.0095

(0.0007)***�0.0077

(0.0049)

�0.0118

(0.0035)***�0.0071

(0.0003)***

�0.0068

(0.0023)***�0.0073

(0.0014)***

Constant

0.1701

(0.0505)***

0.0799

(0.322)

0.2176

(0.2418)

0.2419

(0.0248)***

�0.0068

(0.157)

0.4572

(0.0976)***

Observations

568

567

568

542

542

542

Notes:Numbersin

parenthesisare

SE.F¼1forthe1977–2001periodand0forthe1952–1976period.

***meanssignificantatthe1%

,**meanssignificantatthe5%

level

and*meanssignificantatthe10%

.

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ability as the dependent variable, the impact ofmarket size becomes much more significant after1976 although the coefficient on annual attendancehardly changes. For instance, a one-log pointincrease in annual attendance decreases a team’sshare of senior run-producing ability by 1.08percentage points in the AL before 1977 butraises it by 4.84 percentage points after 1976.Similarly, for the NL, the corresponding numbersare �0.8 and 5.78 percentage points. If we use ateam’s share of junior player’s run-producing abilityas the dependent variable, the correlation betweenmarket size and share of junior player’s run-producing ability become even more negative after1976. This finding is consistent with what havebeen found in the previous section.

Overall, the empirical evidence documented inthis section suggests the following results. First, theadoption of free-agency has changed the allocationof senior star players. Secondly, large-market teamstend to acquire more senior talented offensiveplayers in the free-agency era than they were usedto be in the reserve-clause era. Thirdly, the increasein the concentration of senior star players has littleimpact on the allocation of total offensive talents(the sum of senior and junior star players). Thethird result explains why previous studies cannotreach a conclusion on whether the introduction ofthe free-agency has changed competitive balanceof the MLB games.

V. Conclusion

In this article, we investigate whether the transfer ofthe ownership of property-rights on senior players’services from teams to players in the MLB due tothe adoption of the free-agency system affected theallocation of playing talents. Using a team’s shareof all-star players as a measure of its talent level,we find that the transfer of ownership increasedlarge-market teams’ shares of all-star players,especially senior star players whose property-rightsare affected by the adoption of free-agency.Because all-stars only account for a small propor-tion of MLB players, a team’s share of all-starscannot fully reflect its talent level. To this end, wecomplement this measure by another variable –a team’s share of run-producing ability that isconstructed by aggregating the predicted runproducing ability of all regular players.This measure should provide a more completepicture of the allocation of talents. Results fromthis measure also suggests that the concentration

level of senior star players increased in favour oflarge-market teams while the concentration level ofjunior star players raised in favour of small-marketteams.

One might argue that the change in the alloca-tion of senior players is attributable to the impactof the increase in TV revenues. Because themarginal revenue-product of senior players islikely to be higher in large-market teams thathave a wider TV coverage, those teams havestronger incentives to hire senior players. To testthe robustness of our results to this argument, weinclude TV revenues as a control variable in ouranalysis. The coefficient on TV revenues is insig-nificant even at 10% level, which suggests that theincrease in TV revenues has no significant effect onthe allocation of senior players.

Our findings can be explained as follows. Small–market teams are less likely to trade their juniorstars in the free-agency era as it became harder forthem to keep their senior star players. Thus,keeping junior star players are the next best thingfor these small-market teams. This different impactof free-agency on the allocation of senior andjunior star players can partially explain whychanges in the allocation of senior players havelittle impact on the competitive balance of theMLB.

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