Testing Causality Between Team Performance and Payroll The Cases of Major League Baseball and English Soccer

Abstract

The link between team payroll and competitive balance plays a central role in the theory of team sports but is seldom investigated empirically. This paper uses data on team payrolls in Major League Baseball between 1980 and 2000 to examine the link and implements Granger causality tests to establish whether the relationship runs from payroll to performance or vice versa. While there is no evidence that causality runs from payroll to performance over the entire sample period, the data shows that the cross section correlation between payroll and performance increased significantly in the 1990s. As a comparison, the paper examines the relationship between pay and performance in English soccer, and it is shown that Granger causality from higher payrolls to better performance cannot be rejected. We argue that this difference may be a consequence of the open market for player talent that obtains in soccer compared to the significant restrictions on trade that exist in Major League Baseball.

Full text

JOURNALOFSPORTSECONOMICS / May 2002Halletal. / TEAM PERFORMANCE AND PAYROLL
Testing Causality Between Team
Performance and Payroll
The Cases of Major League Baseball
and English Soccer
STEPHEN HALL
STEFAN SZYMANSKI
Imperial College
ANDREW S. ZIMBALIST
Smith College
The link between team payroll and competitive balance plays a central role in the theory
of team sports but is seldom investigated empirically. This paper uses data on team pay-
rolls in Major League Baseball between 1980 and 2000 to examine the link and imple-
ments Granger causality tests to establish whether the relationship runs from payroll to
performance or vice versa. While there is no evidence that causality runs from payroll to
performance over the entire sample period, the data shows that the cross section correla-
tion between payroll and performance increased significantly in the 1990s. As a compar-
ison, the paper examines the relationship between pay and performance in English soc-
cer, and it is shown that Granger causality from higher payrolls to better performance
cannot be rejected. We argue that this difference may be a consequence of the open mar-
ket for player talent that obtains in soccer compared to the significant restrictions on trade
that exist in Major League Baseball.
The Commissioner’s Blue Ribbon Panel on baseball economics was established
“to consider whether revenue disparities among clubs are seriously damaging com-
petitive balance, and, if so, to recommend structural reforms to ameliorate the prob-
lem” (Levin, Mitchell, Volcker & Will, 2000). The Panel’s report published in July
2000 concluded, inter alia, that “large and growing disparities exist” and that reve-
nue sharing and the payroll tax “have produced neither the intended moderating of
payroll disparities nor improved competitive balance” (p. 1). In this article, we
examine player payrolls and their effect on outcomes, notably the winning records
149
AUTHORS’NOTE: We wish to thank Roger Noll, Shreya Jain, and Bhavani Harimohan for their com-
ments and research assistance.
JOURNAL OF SPORTS ECONOMICS, Vol. 3 No. 2, May 2002 149–168
© 2002 Sage Publications

of the teams. There are two aspects to our approach. First, we explore whether there
is in fact a large variation in payrolls among the teams that is correlated with win-
ning. Clearly, a (positive) correlation between payrolls and playing success is a sine
qua non for establishing that revenue disparities play any role in determining com-
petitive balance. Moreover, this correlation should be strong if it is to bear the
weight of a causal link from revenue inequality to competitive imbalance. Second,
we test directly whether any such causal link exists, in a statistical sense. In addition
to performing the relevant tests for Major League Baseball (MLB), to sharpen our
results we carry out similar tests for English soccer.
We find that the correlation between team performance and payroll is relatively
weak in MLB from 1980 to the mid-1990s and robust thereafter. The correlation for
English soccer is strong throughout the tested period, 1974-1999. Granger causal-
ity tests affirm that in English soccer the causality runs from payroll to performance
and that in MLB the causality runs from performance to payroll during 1980-1994.
The results for MLB during 1995-2000 are consistent with causality running in
both directions.
We conclude by considering the institutional features of MLB and English pro-
fessional soccer that may account for these statistical results. We argue that the
restrictions on trading in player markets that are a recognized feature of baseball
limit the scope for turning income into success and also enhance the opportunities
for players to turn success into income. Nevertheless, the sharply growing revenue
disparities in MLB since 1990 have reopened the opportunity to differentiate team
performance through payroll. The presence of long-term contracts and restrictive
labor market rules, however, seem to prevent the identification of unambiguous
one-way causality.
By contrast, the well-established and accepted player markets of soccer leagues
(not just in England but worldwide) ensure that players are paid a market rate for
what they do. Not only are soccer clubs free to buy a better team in the market but
the market worldwide is large enough to ensure that such a team can be assembled
relatively quickly, and consequently spending determines success.
THE CORRELATION BETWEEN PLAYER SPENDING AND WINNING
Baseball
Playing talent is the principal input used by clubs to generate success on the
field. In a perfectly competitive industry, we would expect that each player would
receive his expected marginal revenue product in wages. Scully’s (1974) seminal
article suggested a direct test of the competitiveness of the market by comparing an
individual player’s wages with his estimated marginal revenue product based on the
relationship between (a) playing success and team revenue and (b) player perfor-
mance statistics and success. He found that marginal revenue products were sub-
150 JOURNAL OF SPORTS ECONOMICS / May 2002

stantially above player salaries, a finding accounted for by the operation of the
reserve clause that granted team owners monopsony power.1The introduction of
free agency from 1976 onward substantially undermined, if not eliminated, the
monopsony power of the owners. Zimbalist (1992) employed a modified Scully
method for baseball and found that salaries were on balance much closer to mar-
ginal revenue products, although there were substantial differences among differ-
ent categories of players. In general, free agents appeared to earn in excess of their
marginal revenue products (MRPs), whereas rookies continued to earn substan-
tially less. This finding in itself can be taken as evidence that the market for playing
talent does not function efficiently. In an efficient market with free agency, players
offered less than their expected MRP would receive better offers from rival teams
and move, whereas players whose salaries exceeded MRP would face either layoff
or a pay cut. However, this conclusion is necessarily tentative, given the difficulties
inherent in measuring MRP.
Quirk and Fort (1999) suggest another approach. They argue that under free
agency, “A player will end up playing for the team for which he adds most reve-
nue . . . and he will earn something between what he is worth to that team and what
he would be worth to the team that places the second highest value on his services”
(p. 81), and from this they conclude that “teams presumably pretty much get what
they pay for” (p. 83). To test this proposition they then look at the correlation
between the rank of regular-season winning percentages (i.e., highest, second high-
est, third highest, etc.) and the rank of player payroll cost by team averaged over the
7 seasons during 1990-1996. They find that for the American League the correla-
tion coefficient is 0.509, whereas for the National League it is 0.135. Neither of
these correlations is statistically significant. They conclude that payrolls “were
essentially worthless in explaining the won-lost records in baseball (p. 86).” A
related exercise conducted by Zimbalist (1992) reports a low correlation coefficient
for baseball and concludes that “average team salary has been related only tenu-
ously to team performance” (p. 96).2
This conclusion is striking because it challenges the idea that teams with larger
revenue bases can successfully corner the best players in a free agency market by
offering the highest salaries. There might be other mechanisms that enable wealthy
teams to attract the best players. First, it might be that benefits in kind and other per-
quisites that do not appear in the accounting data underlying player salaries are the
means by which the wealthy attract the talented, but this seems unlikely in an era of
such remarkable salary and payroll inflation. Second, it might be that the quality of
the coaching staff and player training facilities gives the wealthier teams the ability
to extract more from players of a given talent. This also seems unlikely to explain all
of the variation in performance, given that payroll itself constitutes such a large
fraction of total costs (53% for the average club in 1999 according to the Blue Rib-
bon Panel, and even more for the median club). Third, it may be that players are
attracted to the largest revenue markets because of the greater opportunities to earn
Hall et al. / TEAM PERFORMANCE AND PAYROLL 151

endorsement and promotional income outside the club. This could imply that sala-
ries need be no higher than (and may be slightly below) the alternative to attract a
player to a large revenue market. Indeed, if this were the case, we might expect to
find a negative correlation between success and club payrolls.
In this study, we first look at the relationship between payroll and performance,
using pooled data for Major League Baseball (MLB) during the period 1980-2000.
In particular, we focus on winning percentages in the regular season and payroll
spending by each team relative to the average payroll spending of all teams for the
season. If wealthy teams can buy success, we conjecture, then the most precise
measure of their spending is the ratio rather than the rank. For example, given that
luck still plays a part, then the team that spends the most is more likely to achieve
the highest ranking if it spends 10 times the average rather than 5 times the average.
Moreover, winning percentages are a more accurate measure of success than rank
of winning percentages because a team with the season’s highest winning percent-
age will generally be deemed more successful if it achieved this with a 0.65 rather
than a 0.60 record.
Figure 1 is a scatter diagram for all clubs during all years in the data. The solid
line is a linear regression line, and the figure indicates that the R2for this regression
is about 0.24; in other words, spending relative to the average accounts for about
24% of the variation in yearly winning percentages—only a modest correlation.
However, given that there are numerous factors that may influence a team’s perfor-
mance in a particular season, many of them purely random, a more reliable test of
the effect of spending might be to consider those teams that overspend during the
long term to see if they outperform the rest. To look at this, we averaged winning
percentages for each team during the 21 years and averaged their annual spending
relative to the average. Although this process of averaging may obscure a great deal
of within-group variation, it gives a clear idea of the relationship between long-term
spending and long-term success. The long-term average relationship is depicted in
Figure 2.
Each dot on the graph represents a particular team (the New York Yankees,
Florida Marlins, and Montreal Expos are labeled), and as before the regression line
shows the linear relationship between the variables and the R2gives an indication of
the degree of correlation.3What is striking about this chart is that the degree of cor-
relation is much greater than in Figure 1, suggesting that during the longer term
consistently high spending is associated with a high level of success.
A Comparison With English Soccer
The league structure of English soccer is somewhat different from that of MLB.
The top division in England (called the Premier League) currently consists of only
20 teams, but at the end of each season the 3 worst performing teams are relegated
or demoted to the immediately junior division (called the Football League First
Division) and replaced by the 3 best performing teams in that division. An analo-
152 JOURNAL OF SPORTS ECONOMICS / May 2002

gous relationship exists between the Football League’s First and Second Divisions
and its Second and Third Divisions. This system of promotion and relegation per-
mits a significant degree of mobility among the 92 teams that participate in the four
divisions, both in theory and in practice. Since 1987, there has also been a small
amount of mobility at the bottom, as the worst performing team in the Third Divi-
Hall et al. / TEAM PERFORMANCE AND PAYROLL 153
R
2
= 0.2364
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0 0.5 1 1.5 2 2.5
Team payroll spending relative to average team in a season
Regular season winning percentage
Figure 1: Annual Payroll and Winning in Baseball: 1980-2000
R
2
= 0.7067
0.4
0.42
0.44
0.46
0.48
0.5
0.52
0.54
0.56
0.58
0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Average of team payroll spending relative to annual average
Average regular season winning percentage
Yankees
Florida
Montreal
Figure 2: Average Payroll and Average Winning Percentage: 1980-2000

sion has been relegated to junior competition and replaced by the most successful
lower league team. Thus, between 1987 and 1999 there were 99 teams appearing in
the four divisions, of which only 5 were never either promoted or relegated. Of the
teams, 32% played in only two different divisions, whereas 43% played in three and
12% managed to play in all four during the 12-year period.4
Given this degree of mobility, it is misleading to analyze the top division in isola-
tion. Instead, we have used a balanced panel of 39 teams that were present in the
leagues during the 26 seasons 1973-1974 to 1998-1999. These clubs provide a rep-
resentative sample of all the divisions during the period. The promotion and relega-
tion structure of league soccer renders the interdivisional comparison of winning
percentages meaningless; therefore, some other measure of success needs to be
adopted. Here we use league ranks measuring from the top of the Premier League
(1) to the bottom of the Football League Third Division (92). Payroll costs5are
taken from published company accounts and are again expressed relative to the
average payroll of all teams for a season.6Figure 3 illustrates the relationship
between league rank (transformed into the log odds of league rank) and spending
relative to the average.
Although there are clearly a number of outliers at the top and bottom ends of the
performance distribution, the overall correlation between performance and player
spending seems much stronger for English soccer than for baseball, as indicated by
the R2of 0.74. When we look at the relationship between payroll and success during
26 years for each of the clubs on average (see Figure 4), we similarly find a much
closer correlation than we do in baseball.7
Before concluding from this that there is a genuinely closer correlation between
payrolls and performance in soccer than in baseball, it is necessary to consider the
relevant ranges of the data. There is both more variation in success and more varia-
tion in payroll spending in soccer than in baseball. Thus, the standard deviation in
player payrolls (relative to the season’s average) for the baseball data during the
period 1980-2000 is 0.33, less than half that of the soccer data 0.76 (covering 1974-
1999). The differences in performance are also much greater in soccer, given the
much larger number of teams involved.
One way to compare like with like is to look at the winning percentages and sal-
ary variation of teams in the Premier League only. The standard deviation of pay-
rolls for teams appearing in the Premier League is only 0.34, almost exactly the
same as the standard deviation for MLB. The standard deviation of winning per-
centages is much larger for the Premier League (0.11) than for baseball (0.07). This
is all the more striking because the much longer season in baseball (around 160
games compared to around 40 for the Premier League) would imply that the effect
of variation due to chance would be much smaller in the former;8therefore, if pay-
rolls did influence success systematically the effect should be more, not less
apparent.
154 JOURNAL OF SPORTS ECONOMICS / May 2002

Figures 5 and 6 are the analogous charts for Figures 3 and 4, considering only top
division soccer teams. In fact, by inspection, these charts now resemble Figures 1
and 2, respectively, rather closely.
Hall et al. / TEAM PERFORMANCE AND PAYROLL 155
R
2
= 0.9439
-3
-2
-1
0
1
2
3
4
5
-1.5 -1 -0.5 0 0.5 1 1.5
Average of log team spending relative to season average
average of - log [league rank/(93 - league rank)]
Liverpool
Scunthorpe United
Figure 4: Team Average Spending and Average League Position: 1974-1999
2
R = 0.7355
-5
-4
-3
-2
-1
0
1
2
3
4
5
-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2
Log of team payroll relative to the season average
- log [league rank/(93- league rank)]
Figure 3: Payroll and Winning in English Soccer: 1974-1999

We can directly compare the implied relationship between winning percentage
and relative payroll spending for MLB and the Premier League by looking at the
simple regression equation for Figures 1 and 5:
Win % in MLB = 0.404 + 0.097 payroll/(average payroll)
156 JOURNAL OF SPORTS ECONOMICS / May 2002
R
2
= 0.3386
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 0.5 1 1.5 2 2.5
payroll relative to season average
winning percentage
Figure 5: Winning Percentage and Payroll for Top Division Soccer Teams: 1974-1999
R
2
= 0.7883
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Average payroll spend relative to the season average
average winning percentage
Figure 6: Team Average Spending in the English Top Division: 1974-1999

Win % in Premier League = 0.327 + 0.191 payroll/(average payroll).
In MLB, a team spending 50% of the average could expect a 0.453 winning per-
centage, whereas a team in the Premier League with similar underspending would
only achieve a record of 0.423. Similarly, a team spending 50% more than the aver-
age in baseball could only expect a winning percentage of 0.550, whereas in the
Premier League the team could expect a winning percentage of 0.614. Alterna-
tively, a team spending two standard deviations above the mean would have a win
percentage of .564 in MLB and .649 in the Premier League. Performance at the top
level of English soccer seems much more sensitive to spending than performance at
the top level of baseball.
The regression estimates above are highly significant at conventional levels—
for both equations, the t-statistic on relative payrolls is more than 13. However, nei-
ther regression directly establishes causality from player spending to team
performance.
SPENDING, PERFORMANCE, AND CAUSALITY
Background
The commonsense view is that you get what you pay for. Teams compete in the
market for playing talent, bidding up salaries to the point where wages equal mar-
ginal revenue products, and therefore total payroll is a perfect predictor of perfor-
mance. Moreover, in sports markets where players perform on a regular basis in
front of large audiences, the usual hidden information and hidden action accounts
of market failure are not plausible.
So, how might it come about that a causal relationship from pay to performance
is not visible statistically? It might be that the mechanism works but only imper-
fectly, due to factors such as player complementarities, managerial talent, injuries,
luck, poor judgement, and so forth. Too much noise might obscure the true underly-
ing causal relationship. If the trading market is itself very thin, as it has become in
baseball in the free agency era, then trades may fail to occur at efficient prices.
Prior to free agency, player trading was frequent—for example, Daly and Moore
(1981) quote an average figure of nine trades per team per season between 1955 and
1964 and eight trades per team per season between 1965 and 1973. Eckard (2001)
states that this amounted to 7.8% of all players in the period 1973-1975. Since then,
however, player trading has much diminished, and the phenomenon of cash sales
has more or less disappeared (Daly, 1992; Fort & Quirk, 1995). Hylan, Lage, and
Treglia (1996) found that pitchers in the free agency era with 7 or more years of
experience were less likely to move to another team than in the reserve era. Further-
more, although trades continue, the incidence of teams trading first-line players
who are likely to have the greatest effect on the outcome of games and therefore win
percentage has become even less frequent (Daly, 1992). Horrow (2001) reports that
Hall et al. / TEAM PERFORMANCE AND PAYROLL 157

during 1951-1976 an annual average of 4.7 players per team moved to a different
club via cash sales, trades, waivers, and other transactions, and during 1977-1994
that figure was 4.6.9
Although these market encumbrances may weaken the link between wages and
performance, they do not explain why causation might run from performance to
wages rather than wages to performance.
The explanation, in the case of baseball, may be associated with the long-term
nature of the employment contract and the impediments to trading star players. The
trading of top players in MLB is encumbered by two factors. First, since Commis-
sioner Kuhn prohibited the use of substantial cash in player transactions in 1976,
there is no clean or divisible mechanism for clubs to equalize the value of player
trades.10 MLB’s young stars who have not yet earned free-agent status generally
produce more value than they are paid. But unlike in European soccer, where cash is
commonly used in a trade to fill the difference between a player’s MRP and his sal-
ary, the best way for an MLB owner to extract surplus is to hold such a player until
he becomes a free agent. Second, unlike English soccer, MLB free agent stars fre-
quently have no trade clauses in their contracts.
Players on a winning team expect to be rewarded for the team’s success. Thus,
free agents on a winning team as well as players a year away from free agency often
earn handsome salary increases, whereas the salary of other players does not
respond to team performance in the short run. Many of these salaries were set years
earlier while the player was at a different performance level.11
In English soccer the situation is quite different. Traditionally, players have been
employed on relatively short-term contracts of between 1 and 5 years, and player
trading is an important part of the operation of the league. Carmichael, Forrest, and
Simmons (1999) report that, for example, 12.3% of players changed teams in the
1993-1994 season, which is not unusual. Moreover, the leading teams regularly
trade their top stars in search of a better lineup, whereas players frequently express
their ambition to play for a variety of clubs in a variety of leagues during their
careers. Thus, English league teams spent just under $2 billion (gross) on player
transfers during the seasons 1995-1996 to 1999-2000, an average of $400 million
per season and equal to around 70% of total spending on player salaries (see Annual
Review, 2001, p. 27).12
In English soccer, unlike MLB, young stars at the beginning of their careers have
mobility similar to the established stars. Importantly, “no trade” clauses are virtu-
ally unheard of in English soccer. Soccer fans are more likely to complain if their
team’s owners do not go after the best players than they are to grouse that their
team’s players rapidly turn over. In a league where the teams themselves are mobile
between divisions, mobility of personnel is accepted as part and parcel of the sys-
tem. Players, in turn, always seek to move up in division, league, and team to maxi-
mize their experience and income. The concentration of a large number of teams in
English soccer in relative geographic proximity to each other also makes it easier
for players to move among clubs without upsetting their social lives. Hence, both
158 JOURNAL OF SPORTS ECONOMICS / May 2002

for contractual and structural reasons there is much greater freedom in the labor
market of English soccer than in MLB. This allows for a closer match between sala-
ries and MRPs and for higher payroll outlays to be converted into performance suc-
cess more readily. It also means that players are in much less of a position to bargain
for any rents that accrue from unexpected success because players demanding unre-
alistic salaries (i.e., well in excess of their MRP) can be more readily traded.
Testing for Granger Causality
The problem of identifying economic causality from the statistical analysis of
data series has long been recognized as a fundamental problem in econometrics.
Causality in its most general sense is nebulous and nonoperational in a statistical
sense. We might think, for instance, of future expectations causing things to happen
now, which would suggest that the future in some way could cause the past. To
make the concept of causality operational we need to define a precise concept that is
clear, and this inevitably involves limiting the broad meaning of causality. In opera-
tional econometrics there are two broad definitions of causality currently being
used: Granger causality and long-run (sometimes weak) causality. Long-run cau-
sality is only operational for models containing nonstationary variables. In this case
we can divide the model’s properties into two parts: the long-run determination of
the system and the short-run adjustment. Long-run causality is defined only with
respect to the long-run determination of the model. Granger causality focuses on
any structural influence of one variable on another and is therefore operational in
the case of stationary and nonstationary data.
Granger (1969) proposed an operational definition of causality between two or
more variables in terms of the influence that one variable may have on another.
Consider the case of two processes, xand y, and the information on them contained
in their past behavior Xt(Xt=xt–1
,xt–2
,...xt–q
) and Yt(Yt=yt–1
,yt–2
,...yt–q
) for a
suitable lag length q.yGranger causes xif Ytprovides additional information for the
forecast of xtabove that provided by Xt. Granger causality is usually tested formally
within the framework of a stationary vector autoregression (VAR). In this simple
bivariate case, the test would involve the following system:
yt=αYt+βXt+νt
xt=χYt+δXt+εt,
where α,β,χ, and δare conformably dimensioned vectors of parameters. The test
of the hypothesis that xdoes not Granger cause yis given by the joint test that β=0
and the test of the hypothesis that ydoes not Granger cause xis given by the joint test
that χ= 0. Because this procedure is carried out for a reduced form VAR, it is impor-
tant to realize that two types of causality are actually being tested for at once. This is
the possibility that (a) in the structural form of the model yis simultaneously caused
Hall et al. / TEAM PERFORMANCE AND PAYROLL 159

by xor (b) in the structural form of the model yis caused by lagged values of x. This
may be fully appreciated if we state the above system in structural form that allows
for contemporaneous interactions:
yt=a12xt+α*Yt+β*Xt+νt
xt=a21yt+χ*Yt+δ*Xt+εt.
In matrix notation we can then write this system as
Azt=BZt,
where z=(yx)′,Z=(YX)′, and
Aa
aB=−
−




=




1
1
12
21
αβ
χδ
**
**
.
The Aand Bmatrices are the structural form parameters, and the parameters in
the reduced form VAR model above are derived as the reduced form of this system
(A–1B). So the test that β= 0 would be rejected if either a12 ≠0orifβ*≠0, that is, if in
the structural form there is either contemporaneous causality from xto yor lagged
causality.
Since the mid-1980s, a revolution has occurred in the analysis of time series data
with the development of the concepts of stationarity and cointegration. These meth-
ods have led to the development of statistical tests that can reject hypotheses consis-
tent with a particular direction of causality in the long run in isolation from the com-
plete dynamic response. However, we will not pursue this here as subsequent
testing of our data revealed it to be stationary. In team sports, as in much of indus-
trial organization, one is often concerned with panel data rather than simple time
series. In recent years, several researchers have begun to apply these techniques to
the analysis of panel data (e.g., see Hall & Urga, 2000) and one interesting result is
that a key feature determining how a panel should be treated is the source of the
nonstationarity in the panel. If a nonstationary variable in the panel is driven by only
one nonstationary common stochastic trend across the whole panel, this will affect
the properties of standard panel estimators in an important way to considerably
simplify the problem. In the case being considered here, payment costs are almost
certainly nonstationary. But if this nonstationarity comes from only one source (the
general rise in wages across all clubs), then this is the single source of nonstationarity
and it may be removed by considering a relative payroll variable, which is what we
use. It is theoretically possible, of course, that this transformation would not
remove the nonstationarity from the data, and this would imply that more than one
common stochastic trend underlies the complete panel. This is, of course, a testable
hypothesis in terms of testing the relative payroll variable for stationarity. The con-
160 JOURNAL OF SPORTS ECONOMICS / May 2002

ventional test of stationarity is a Dickey-Fuller test for a unit root. In the panel data
context, our regression equation was
∆yi,t =αi+ρyi,t–1 +ei,t,
i=1,2,...N,t=1,2,...,T, (1)
where the αiare fixed effects. The distribution for the t-statistic on the ρcoefficients
is asymptotically normal as the number of clubs goes to infinity; for a small sample
it would be closer to a standard Dickey-Fuller distribution, so assuming a critical
value close to 3 would be very conservative.
Note that for this analysis we have reverted to the full English League soccer
database, not the restricted Premier League sample. One difficulty with the using
the Premier League sample alone would be that due to relegation there is not in gen-
eral a complete series for lagged winning percentage. In any case, from the point of
view of testing for causality from wages to performance there is little sense in
excluding more than two thirds of the data.
Table 1 establishes that all of the variables considered appear to be stationary.
Our next step is to use a Granger causality test to examine the direction of causality.
In this context, our regression equation is
yi,t =αi+β1yi,t–1 +β2xi,t–1+ui,t,(2)
where yiis the dependent variable and xiis the independent variable. A variable z
can be said to Granger cause a variable wif the coefficient β2for the regression with
won the left hand side (LHS) is economically and statistically significant, whereas
the coefficient β2for the regression with zon the LHS is economically and statisti-
cally insignificant.13
These results tell a very different story for baseball and soccer (see Table 2). In
the baseball case, performance appears to Granger cause wages but wages do not
Granger cause performance. In the English soccer case, wages Granger cause per-
formance but performance does not Granger cause wages (the coefficient is very
small and not significant at the 1% level).
From an economic point of view, the implication of the Granger causality test is
that English soccer conforms to the efficiency wage model of sporting competition,
whereas baseball does not over these time periods. If wages do not cause better per-
formance in baseball, what does? In our model the only other explanatory variable
is past success, which diminishes in effect over time. The fixed effects are also
insignificant, so the statistical interpretation is that teams randomly achieve success
from time to time; this success persists for a while (and is translated into higher
wages) but eventually teams regress to the mean 0.50 winning record. Such an
interpretation is not economic nonsense but does seem to be at odds with the per-
Hall et al. / TEAM PERFORMANCE AND PAYROLL 161

ceived development of baseball and the sustained dominance of some teams. One
possibility is that other explanatory variables might account for success, thus
expanding the statistical model. Many such candidate variables (e.g., expendi-
tures—including signing bonuses—on player development, the extent of owner-
ship synergies with related businesses, and the depth of the pockets of the team
owners) should be closely correlated with the ability to pay high salaries and hence
to some degree have already been indirectly ruled out. Other variables, such as the
intensity of fan support, might have an effect on success but are hard to measure
directly. We experimented with the inclusion of local population variables for each
team; these had no significant effect on our results, which may not be all that sur-
prising because population tends to change only slowly and is thus similar to the
fixed effects. Of course, if tradition itself was an explanation of long-run success,
then the fixed effects would indeed be significant, which they are not. Within the
Granger framework, the causal influences of success in MLB during 1980-2000
remain difficult to identify unambiguously or at least such influences are not
readily quantifiable.
Testing for a Structural Break in Baseball
According to MLB’s Blue Ribbon Panel Report, the situation in baseball has
changed significantly since 1994, with differentials in economic status having a
much greater effect than hitherto. More generally, the argument of a structural shift
in the mid-1990s is premised on several factors. First, in 1994 baseball’s new
national television contract fell by more than 60%. At the same time, certain big
162 JOURNAL OF SPORTS ECONOMICS / May 2002
TABLE 1: Estimates of ρ
Dependent Variable Coefficient for ρt-Statistic Observation
Baseball winning percentage –0.62 –15.57 527
Baseball relative payroll –0.33 –9.81 527
Soccer logit of position –0.34 –14.04 975
Soccer relative payroll –0.059 –3.46 975
TABLE 2: Estimates of β2: 1980-2000 for Major League Baseball and 1974-1999 for Soccer
Dependent Variable Coefficient for β2t-Statistic Observation
Baseball winning percentage 0.003 0.24 527
Baseball relative payroll 0.823 5.18 527
Soccer logit of position 0.372 5.13 975
Soccer relative payroll 0.018 2.19 975

market teams (such as the Yankees) were earning more than $40 million a year in
unshared local media revenues, and the era of the new, big revenue–generating sta-
diums was ushered in by Camden Yards in 1992. With MLB’s centrally distributed
monies below $10 million per club, teams with a big market or new stadium found
themselves with a rapidly growing revenue advantage. Whereas the revenue dispar-
ity between the richest and poorest team was around $30 million in 1989, by 1999 it
was $164 million. Local revenues (including all stadium-related and local media
income) in 1999 went from a high of $176 million for the Yankees to a low of $12
million for the Montreal Expos.
Second, the 1990s witnessed the emergence of new franchise owners who also
own international communications networks or are attempting to build regional
sports channels. These owners value their ballplayers not only by the value they
produce on the field but what they produce for their networks. Presumably, when
Rupert Murdoch signed 33-year-old Kevin Brown to a 7-year deal worth an average
of $15 million annually, he was thinking about the News Corp’s emerging influence
via satellite television in the huge Asian market as well as his enhanced ability to
prevent the formation of a rival Disney-owned regional sports network in Southern
California. Similarly, when George Steinbrenner opened up his wallet for David
Cone ($12 million in 2000) or Roger Clemens ($30 million for 2001-2002), he had
in mind creating a new New York sports channel built around the Yankees. In these
and other instances, the owners of baseball teams do not treat their teams as stand-
alone profit centers; rather, the team is a cog in a larger corporate machine that is
used to maximize the long-term profits of a conglomerate.
Third, baseball’s expansion by four teams in the 1990s, although adding excite-
ment to the game, by decompressing talent makes the star players stand out more
and thereby makes it easier to buy a winning team.
Fourth, the selection of amateur players through the draft (introduced in 1965)
had served as an important leveler. In the 1990s, however, the selection of amateurs
began to favor the high-revenue teams, contributing to a greater imbalance on the
playing field. Sharply growing revenue disparities across the teams came to be
reflected in vastly different player development budgets across the teams. In 1999,
for instance, the Yankees spent more than $20 million on their player development
system, whereas the Oakland Athletics invested less than $6 million. This disparity
allows the Yankees, by offering far more handsome signing bonuses, to have
greater success in signing foreign players who come to the United States as free
agents. It also makes it more difficult for the bottom revenue teams to sign their top
draft picks of domestic players.14
The evidence presented in Table 3 provides prima facie support for a mid-1990s
structural break. It shows simple year-by-year regressions of winning percentage
on player payrolls.
From this table, it is apparent that in the 8 seasons between 1980 and 1992, pay-
roll spending was significant at the 5% level only thrice, and never at the 1% level.
In the 8 seasons between 1993 and 2000, payroll was always significant at the 5%
Hall et al. / TEAM PERFORMANCE AND PAYROLL 163

164 JOURNAL OF SPORTS ECONOMICS / May 2002
TABLE 3: Estimated Equation:
Win Pct
i
=α+β
Payroll
i
+
e
i
Year αβR2n
1980 .484 3.24 E-09 .006 26
(11.1) (0.38)
1981 .464 5.66 E-09 .002 26
(9.06) (0.73)
1982 .489 1.46 E-09 .005 26
(13.31) (0.34)
1983 .491 9.87 E-10 .003 26
(12.82) (0.26)
1984 .418 7.48 E-09* .166 26
(10.77) (2.18)
1985 .362 1.30 E-08 .149 26
(5.26) (2.05)
1986 .460 3.41 E-09 .029 26
(9.29) (0.84)
1987 .466 3.02 E-09 .022 26
(9.65) (0.74)
1988 .393 9.37 E-09* .181 26
(8.12) (2.31)
1989 .389 7.89 E-09* .232 26
(9.10) (2.69)
1990 .460 2.30 E-09 .028 26
(9.46) (0.84)
1991 .420 3.14 E-09 .151 26
(10.44) (2.07)
1992 .470 9.45 E-10 .020 26
(10.72) (0.70)
1993 .398 3.17 E-09* .195 28
(9.29) (2.51)
1994 .386 3.53 E-09* .203 28
(8.39) (2.57)
1995 .382 3.57 E-09** .319 28
(10.71) (3.49)
1996 .397 3.07 E-09** .396 28
(14.93) (4.13)
1997 .392 2.72 E-09** .450 28
(15.65) (4.61)
1998 .355 3.43 E-09** .554 30
(13.42) (5.89)
1999 .389 2.26 E-09** .475 30
(15.93) (5.03)
2000 .426 1.36 E-09** .284 30
(17.67) (3.33)
NOTE: t-statistics in parentheses.
*Two-tailed test, significant at 5%. **Two-tailed test, significant at 1%.

level and significant at the 1% in all but the first 2 seasons. This does seem to sug-
gest that payroll spending may have become more important for success after the
mid-1990s.
If this is so, we should also observe a structural break in our econometric model.
To test for this we ran our Granger causality regressions to allow for slope coeffi-
cients to change in either 1994 or 1995. We found that there did appear to be a
change and that the break was most plausibly fixed at the end of 1994. We report the
relevant coefficients for the Granger causality tests in Table 4.
From this it is apparent that lagged wages in the performance regression have
become statistically significant since 1994. At the same time, the wages regression
shows that the effect of past performance has declined, although it is still signifi-
cant. These results indicate that although it is still not possible to identify a unique
causal relationship from wages to performance, since 1995 it has also become
impossible to argue the reverse, that wages are determined by performance,
because causality no longer appears to flow in a single direction.
It is useful, perhaps, to consider the full Granger causality regressions to observe
more closely the apparent changes.
Prior to 1995, our two estimated relationships are
Wpci,t = 0.322 + 0.343 Wpci, t –1
Wagesi,t =αi+ 0.532 wagesi, t –1 + 0.864 Wpci, t –1
,
whereas since 1995 the relationships are
Wpci,t = 0.322 + 0.290 Wpci, t –1 + 0.034 wagesi, t –1
Wagesi,t =αi+ 0.674 wagesi, t –1 + 0.583 Wpci, t –1
.
Wages, as before, are expressed relative to the mean of all clubs in a given season. If
these estimates represented a trend in the underlying parameters that drive success
in baseball, the model would eventually come to resemble closely the efficiency
wage system observable in soccer.
Hall et al. / TEAM PERFORMANCE AND PAYROLL 165
TABLE 4: Estimates of β2: 1980-1994 and 1995-2000
Dependent Variable Coefficient for β2t-Statistic
Baseball winning percentage
1980-1994 0.006 0.52
1995-2000 0.034 2.21
Baseball relative payroll
1980-1994 0.864 5.38
1995-2000 0.583 2.87
NOTE: Number of observations = 527.

DISCUSSION AND CONCLUSIONS
The finding that player spending does appear, statistically, to cause improved
performance in English soccer confirms not only the earlier research of Szymanski
and Smith (1997) but also seems consistent with the more or less unfettered opera-
tion of the player market in soccer. Although baseball during 1980-1994 presents
no evidence of Granger causality from wages to performance, there appears to be a
shift in the mid-1990s. In our tests, since 1995 there is evidence that the causality
between performance and payroll runs in both directions. If our measurement of
expenditures on players and player development were more precise and complete,
it is possible that the causal link from player costs to performance would become
stronger.15
The cause of the differences in the way that the soccer and baseball markets
operate are to be found in the institutional rules that govern them. Restrictive agree-
ments that limit player spending, player mobility, roster sizes, the right to trade
players, and so forth have made it less likely that teams can fully use their financial
muscle to buy success in baseball. The absence of any of these restrictions in Eng-
lish soccer make it more likely that teams can buy success.
NOTES
1. Scully’s (1974) general method has also been used to test for discrimination through the perfor-
mance regressions. Limited evidence of salary discrimination has been found in baseball (see Kahn,
2000).
2. This finding is consistent with Major League Baseball’s (MLB’s) Economic Study Committee
Report of December 3, 1992, and the staff analysis on which it is based. See, for instance, Section III of
the Major League Baseball Economic Study Committee, Staff Analysis, December 1992.
3. Removing the Yankees from the regression reduces the coefficient of determination from .24 to
.21 in Figure 1 and from .71 to .65 in Figure 2. Clearly, the Yankees are strong contributors to the pay-
performance link, but the link is still healthy without them.
4. See Noll (2002 [this issue]) and Szymanski and Ross (2000) for a more detailed analysis of the
promotion and relegation system.
5. Here, payroll refers to all club salaries and not just players. This figure now accounts for more
than 50% of total costs. Transfer fees are not included. Transferfees are best viewed as long-term invest-
ment and would require a compelling amortization scheme to be employed. In any event,because it is the
most successful clubs that are the highest net transfer fee spenders, if this information were included it
would only strengthen the measured pay-performance link in British soccer.
6. This data set, together with other accounting variables until 1997, can be found in Szymanski and
Kuypers (1999).
7. It might be reasonably asked whether the improved fit for the soccer data is a result of the
loglinear specification. Accordingly,we also tested the baseball data using logit and loglinear specifica-
tions; the closeness of fit was almost identical.
8. The “idealized” standard deviation of winning percentages in a league where each team has an
equal chance of winning is .5/√m, where mis the number of matches in a season. For a 160-game season
it would be 0.0395 and for a 40-game season it would be 0.0791. Thus, the actual standard deviation of
the baseball winning percentages is 75% larger than the idealized, whereas for Premier League soccer it
is only 40% larger.
166 JOURNAL OF SPORTS ECONOMICS / May 2002

9. Our own review of the Sporting News’s Baseball Guide from 1960 through 2000 revealed the
following pattern of diminished cash sales and trades. From 1960 through 1975 there were 518 cash pur-
chases of players, representing 6% of all players in the major leagues at the time. During the 1980s there
were 157 cash purchases, representing 2.4% of major leaguers, and during 1990-2000 there were 9 cash
purchases, representing 0.1% of all major leaguers. In contrast, the share of players affected by trades
went from 9.0% during 1960-1976 to 11.3% during 1977-2000. Hence, the overall movement of players
from trades and cash sales fell from 15.0% during 1960-1976 to 12.2% during 1977-2000. The differ-
ence in the extent of cash trading in English soccer is striking. Sloane (1969) reports that in the 6 seasons
between 1961-1962 and 1966-1967 more than 5% of professionals were traded for a fee every season.
Because professional careers average 3 or 4 seasons in soccer, this implies a much higher degreeof turn-
over than 6% during a period as long as 16 years (1960 to 1975). Moreover, evidence from Dobson and
Gerrard (2000) suggests that turnover has increased. In the 4 seasons between 1990-1991 and 1993-
1994, they found that on average 10.3% of professionals were transferred for a fee every season.
10. In June 1976, Commissioner Bowie Kuhn disallowed Charlie Finley’s attempted sales of Joe
Rudi and Rollie Fingers from the Oakland A’s to the Boston Red Sox for $2 million and of Vida Blue
from the A’s to the New York Yankees for $1.5 million. Commissioner Kuhn set a rule of thumb that all
trades involving more that $400,000 in cash had to be approved by his office. Today, the threshold for
commissioner sanction is $1 million. According to the Sporting News’s Baseball Guide, the last time a
player moved teams as a result of a cash sale was in 1991.
11. Note that the correlation between success and payroll in baseball often results from the ability to
hold a winning team together rather than the initial purchase of a winning team. The 2001 Yankees were
composed mostly of players from their farm system or were acquired through trades. Of course, the Yan-
kee farm system itself benefits from annual player developmentexpenditures in excess of $20 million.
12. Although a high level of player mobility has always been an accepted part of the soccer system,
until recently clubs were able to place some obstacles in the way of players wanting to move. Most nota-
bly, until 1995 clubs could demand a transfer fee for players moving to a new club even when their old
contract had ended. The famous Bosman judgment of 1995 outlawed this kind arrangement within the
European Union, as well as prohibiting restrictions imposed by national governing bodies on the number
of foreign players permitted on a team. It is still too early to tell whether this ruling has further increased
the mobility of players, but there has certainly been a considerable influx of foreign players into the Eng-
lish Premier League in recent years.
13. Davies, Downward, and Jackson (1995) and Dobson and Goddard (1998) investigated Granger
causality between attendance and performance for the Rugby League and English soccer, respectively.
In both cases they found mixed evidence.
14. This point is treated in more detail in Zimbalist (2001).
15. Another possible factor here is that for most years the baseball salary data in our study reflects
end of year payroll, whereas for some years it reflects beginning of year figures. The effect of this is dis-
cussed (and illustrated for the National Hockey League) in Zimbalist (2002 [this issue]).
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Stephen Hall is in the School of Management at Imperial College in London.
Stefan Szymanski is a senior lecturer of economics in the School of Managementat Imperial Col-
lege in London.
Andrew S. Zimbalist is a professor of economics at Smith College in Northhampton,
Massachusetts.
168 JOURNAL OF SPORTS ECONOMICS / May 2002