Convergence vs. The Middle Income Trap: The Case of Global Soccer

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ECINEQ WP 2017 - 453
Working Paper Series
Convergence vs. the middle income trap:
The case of global soccer
Melanie Krause
Stefan Szymanski

ECINEQ 2017 - 453
December 2017
www.ecineq.org
Convergence vs. the middle income trap:
The case of global soccer∗
Melanie Krause†
Hamburg University, Germany
Stefan Szymanski
University of Michigan, USA
Abstract
Unconditional convergence across countries worldwide is typically rejected in terms of GDP
per capita. But when focusing on a specific internationally competitive industry, such as
manufacturing, rather than the overall economy, unconditional convergence has been found
to hold. As the epitome of competition and globalization, this paper uses the performance of
national soccer teams as a further test case. We rely on data of more than 25,000 games between
1950 and 2014 and find clear evidence of unconditional β- and σ-convergence in national team
performance, as measured either by win percentages or goal difference. We argue that transfer
of technologies, skills and best practices fosters this catch-up process. But there are limits: we
show that good teams from Africa and Asia are failing to close the gap with top European or
South American teams for reasons that are analogous to the ”middle income trap”. Lessons
for other sectors include the virtues of internationally transferable human capital as well as
the mixed blessings of regional integration for worldwide convergence.
Keywords: unconditional convergence, global competition, soccer, middle income trap.
JEL Classification: O47, L83, F20, Z2.
∗We thank Dani Rodrik, Ruud Koning, Wolfgang Maennig, Rob Simmons, Sebastian Kripfganz, and sem-
inar participants at the University of Groningen for helpful comments on earlier drafts
†Contact details: M. Krause (corresponding author) Department of Economics, Hamburg University,
Von-Melle-Park 5, 20146 Hamburg, Germany; email: melanie.krause@wiso.uni-hamburg.de. S. Szymanski,
Department of Kinesiology, University of Michigan, 3118 Observatory Lodge 1402 Washington Heights, Ann
Arbor, MI 48109-2013, United States; email: stefansz@umich.edu.

1 Introduction
The convergence debate - whether poorer countries are catching up with richer ones
- is as old as economics itself. Neoclassical growth theory suggests that countries
facing a common technology should converge in terms of income, with poorer ones
growing faster than richer ones thanks to the higher marginal productivity of capital in
earlier stages of development. However, the empirical evidence regarding unconditional
convergence across the worldwide distribution of income per capita is not supportive
(Barro,1991;Mankiw et al.,1992;Islam,2003;Acemoglu,2009). The literature has
therefore focused on conditional convergence and club convergence, arguing that countries
tend to converge towards different steady states (Quah,1993a,1996;Durlauf et al.,2009).
Nevertheless, the concept of unconditional convergence may be alive and well. Rodrik
(2011, p. 45) comments: “The good news is that there is unconditional convergence
after all. But we need to look for it in the right place: in manufacturing industries
(and possibly modern services) instead of entire economies.” When examining the
productivity of manufacturing plants across a global sample of countries, Rodrik
(2013) finds unconditional convergence. These results have been confirmed by various
other studies with different manufacturing data, including B´en´etrix et al. (2012) and
Levchenko and Zhang (2011). In many countries the manufacturing sector is small, and
different industries may or may not exhibit convergence (Bernard and Jones,1996),
which explains the lack of convergence at the level of the entire economy. Rodrik
(2013) argues that the manufacturing sector has a number of features which make it
particularly susceptible to unconditional convergence: it produces tradeable goods and
is integrated into the global production chain, which leads to global competition and
fosters technological transfer across borders. Thinking along these lines, we will here
focus on another sector which might be considered the embodiment of global competition.
We examine convergence in performance in competitive international soccer,1
arguably the world’s most popular modern service. Soccer exhibits several features
Rodrik (2013) has highlighted about the manufacturing industry. First, it is a
truly global activity; the world governing body of soccer, FIFA, currently has more
members (211) than the United Nations (193). Second, the service is standardized and
internationally comparable. At the level of national team competition, performance in
soccer is far more accurately measured than most other data series; the game is always
the same (rule changes are infrequent and regulation is strict) and large numbers of
1”Soccer”, widely thought to be a contraction of ”Association football” (which is the proper name
for the game in English), is generally known outside of the US as simply ”football”. However, since
there are many other codes of football (American football, Australian Rules football, rugby football and
Gaelic football), we here prefer the term soccer, which is unambiguous.
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games are played (currently around 2000 per year). Comparable data on this scale is
simply not available for other industries, and services in particular. Third, international
soccer is by definition very competitive, so that small differences in skills, line-ups and
preparations can have a big influence on the performance. Apart from the monetary
rewards, success in international tournaments is often a source of national pride and
well-being, providing a strong incentive to perform well. Fourth, the global nature of
soccer facilitates the transfer of technology and skills. Weaker teams can catch up by
adopting stronger nations’ training and talent selection techniques and by investing in
their sports infrastructure. Furthermore, there are direct spillovers when individual
players from weaker nations are contracted to play for the world’s top leagues and at
the same time remain on their national teams. Finally, National soccer associations
are organized into continental federations representing Europe, North/Central America,
South America, Asia, Oceania and Africa. These play a significant role in organizing
competition and represent natural groups around which performance levels may coalesce.
Interestingly Africa, whose economic difficulties have been so widely discussed (Easterly,
2009;Sala-i-Martin and Pinkovskiy,2010), has in recent decades started to emerge as a
soccer power, culminating in the hosting of the 2010 FIFA World Cup.
The data used in this paper consists of the results of recorded national teams’ soccer
games between 1950 and 2014, matched with the Penn World Tables data for GDP and
population. Based on more than 25,000 games, our main findings are as follows:
(i) There is consistent evidence of unconditional convergence in national soccer team
performance, both β- and σ-convergence. This applies to the percentage of games won
as well as the goal difference between the teams. While a country’s income per capita,
population size and experience help predict the national team’s performance, the strong
evidence of unconditional convergence in the absence of these factors is striking and
robust to different econometric specifications. Apart from manufacturing, this has not
yet been found for any other economic sector - and certainly not for a service based on
a worldwide comparable dataset.
(ii) Despite this move towards more equal performances in soccer, our rank mobility
analysis also shows that the top of the distribution continues to be dominated by a few
teams from Europe and South America. Weaker teams from these stronger continents
are among those that have made the biggest improvements. While many of the weakest
teams from Africa and Asia have also advanced from a low base, the best teams from
these continents have failed to catch up with top European and South American teams.
We explain these findings with an analogy to the middle income trap: Thanks
to the global nature of soccer, countries with weaker teams can, up to a point,
achieve unconditional convergence by adopting the same technology in a broad sense.
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The transfer of best practices as well as insights from abroad is fostered by global
labor markets for coaches and players, which in the case of soccer are comparatively
frictionless thanks to human capital portability and the observability of performance.
But the process of catch-up by adoption reaches its limits at the transition to world-
class performance levels, when teams have to build up their own long-term talent
development techniques and playing styles. Among various lessons for other sectors,
we highlight the mixed blessings of regional integration for worldwide convergence.
In soccer, as well as in other industries, those countries that find themselves in the
same organizational group (here continental federations) as the world’s best performers
can catch up more quickly, while the gaps with other regional groups might even increase.
The remainder of this paper is organized as follows: Section 2 examines the structure
of competitive soccer in light of macroeconomic convergence models. Section 3 presents
some summary results of the dataset, while section 4 contains the empirical results on β-,
σ-, and club convergence as well as the distributional analysis. Section 5 focuses on the
limits of convergence with the analogy to the middle income trap. Section 6 concludes and
outlines some lessons for convergence in other globalized industries. Additional tables of
results are contained in the Appendix, while an Online Appendix provides supplementary
information.
2 Soccer in the Light of Convergence Models
The notion of unconditional convergence, both across entire economies and within specific
industries, is based on the idea that entities exhibit a higher marginal productivity
of capital at lower level of capital accumulation, and that there exist incentives for
cross-border adoption of technology, ideas and best practices. The first point is a simple
implication of standard neoclassical growth theory, the second emerges from endogenous
growth theory. To see how soccer makes for an insightful case study of the unconditional
convergence hypothesis, we have to take a closer look at its structure and organization.
With 211 countries affiliated to FIFA in 2017, it can safely be argued that every
nation on the planet participates in international soccer team competition. In many
other sectors, tests for convergence in performance across a worldwide sample are
troubled by data reliability and comparability problems. Measurement error can be
large and potentially correlated with other variables of interest. Soccer is not afflicted
by these problems. The result of each international game is a matter of official record
and not subject to dispute.2National teams play many games a year against different
2Fans often dispute whether their team should have lost, but not whether it did lose.
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opponents providing a rich sample of performance in a relatively short time frame.
Soccer has standardized regulations and a long tradition in terms of institutional
organization, as the Online Appendix describes in detail.3The first “international”
match took place between England and Scotland in 1872, but the growth of international
competition accelerated significantly in the second half of the 20th century. The end of
colonialism in the 1950s and the break-up of the Soviet Union in the 1990s increased the
number of countries with national teams. At the same time, the drivers of globalization,
which affected many economic sectors, impacted soccer in particular (Sugden and
Tomlinson,1998). Improvements in transport have reduced the time and cost involved
in organizing international matches, while the development of international broadcasting
enabled matches to be shown live around the world.
Despite the truly global nature of soccer, regional confederations, such as UEFA in
Europe and CAF in Africa, play a vital institutional role in the organization of the
game. They promote regulations, schedule games and continental cups (the UEFA
Euros or CONMEBOL’s Copa America) with the consequence that national teams
from the same continent play against each other more often than against teams from
other continents. There are analogies to the trade literature, where both geography and
membership of regional trade deals help to predict bilateral import and export flows
between countries (Bergstrand,1985;Frankel et al.,1995). The interplay between the
continental associations and FIFA as the global governing body is embodied in the
organization of the FIFA Men’s World Cup, the four-yearly pinnacle of international
competition.4As the Online Appendix describes in more detail, FIFA has expanded
the opportunities for the weaker regional federations in order to promote the game in a
global context. Yet, European and South American teams have continued to dominate
the tournament and no country from outside these associations has ever won it.
In our analysis, however, we will not only look at these few most prestigious matches
but at all games between national teams from 1950 to 2014, consisting of (i) competitive
games (mostly tournaments such as the World Cup, continental cups and their qualifiers)
and (ii) games played outside the framework of competition, termed “friendlies”, which
are often used as a way of preparing players for formal international competitions.
3In this paper we will focus on men’s soccer because for women’s soccer the time period is too
short and the number of countries too few to conduct a meaningful convergence analysis. Women’s
international soccer was largely ignored or actively discouraged for a long time; for example, the English
Football Association rule prohibited members from supporting women’s soccer until 1971. The first
women’s world cup only took place in 1991. Even today, there is a strong correlation between countries’
performance in women’s soccer and measures of gender equality (Bredtmann et al.,2016), which would
point to a selection effect in terms of a global sample.
4Organizing the FIFA World Cup is a huge social event for the host country, even if the significance
of the economic effects are contested (Feddersen and Maennig,2012).
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We test for unconditional convergence by analyzing national teams’ performance over
time. For our purposes the industry here can be defined as the national soccer team
organization and the measure of industry performance is success in competition against
other national teams. In this industry the output of one nation cannot be produced
independently of any other nation. Our study is therefore analogous to an assessment
of convergence of national education systems by comparing scores in standardized global
tests. We posit a conventional production function to define the process by which the
skills necessary for soccer competition are created:
Y=f(A, K, L) (1)
with capital K, labor Land a broadly defined technology A. The country’s capital
provides the sports infrastructure - stadiums, equipment, medical support and so on -
countries with a higher GDP per capita can devote more resources to soccer. A large
population Lis similarly helpful because soccer talent is drawn from the top end of
population distribution. While it might be natural to think of increasing returns to
scale (the larger the population, the larger the chance of finding top soccer talent), the
world’s most populous countries have not proven particularly successful - think of India,
China, Pakistan, Indonesia or even the US. In fact, in some of these countries soccer is
trumped in popularity by cricket (India, Pakistan), or baseball and American football
(the US), which underlines the importance of widespread public support in developing
successful national teams. Total factor productivity A, defined in a broad sense, therefore
subsumes all cultural and institutional factors fostering a national team’s performance,
from establishment as a national pastime and young talent development systems to best
practices in training, and well-functioning institutions running the game at all levels.5
Many of the ingredients of technology spread easily across borders and we argue that
the globalized and competitive nature of soccer makes it amenable to a best-practice
adoption. For the economy in general, Barro and Xavier Sala-i-Martin (2004), Caselli and
Coleman (2001) as well as Howitt (2000) discuss the factors facilitating and hindering the
technology diffusion across countries. In the context of soccer the following seem relevant:
(i) Technology in the strict sense. Match recording and slow-motion replay, satellite
TV live broadcasting and information availability via the internet has allowed teams to
analyze their own games more thoroughly, but also those of other countries. Specialized
software can help to break down the tactical behavior into individual actions (Kempe
5China has remained stuck at middling performance results in recent decades; as of 2017 it was 77th
in the FIFA national team rankings. But the country is investing heavily, and in 2015 President Xi
Jinping announced a series of initiatives aimed at turning China into a soccer superpower in the same
way the nation has reached the top of the Olympics medal table.
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et al.,2014). Consequently, a team can anticipate its opponents’ tactical set-up and
better prepare for games. This spread of information allows teams to adopt the successful
strategies of others, so that weaker teams learn from the best.
(ii) Institutions. The convergence debate has long focused on the role of countries’
institutional quality, including property rights and the rule of law (North and Thomas,
1973;Hall and Jones,1999;Acemoglu et al.,2005). In soccer, institutions in a broad
sense range from the continental associations to the organization of soccer at all
competitive levels on the ground. There have been scandals of corruption in associations’
governing bodies; see Maennig (2002) and Manoli et al. (2017) for discussions from an
economic point of view. Nevertheless, institutions play a vital role in the process of
technology diffusion by setting standards and spreading best practices across countries
in the whole organizational process, from game scheduling to resource distribution.
(iii) Human Capital (coaches). A good coach can help to improve the performance
of the players as a team (Frick and Simmons,2008). While players need to have the
nationality of the country in order to play for a national team, no such rules apply to
coaches. Therefore, there is substantial international mobility in what is a global labor
market for coaches. FIFA data show that 14 of the 32 national teams participating in
the 2014 World Cup had a foreign coach and these include many of the comparatively
weaker teams, see Table A-1. Coaches from abroad can bring in new training techniques,
change the tactical set-up and, more generally, spread insights gained in other countries.
(iv) Human Capital (players). While our interest is in the results of national teams’
games, most players make a living from playing for clubs in a national league, some of
which have become substantial enterprises in recent years. Since the Bosman ruling from
1995 delivered freedom of contract to professional soccer players in the EU irrespective
of their home country, European leagues have experienced a huge internationalization
(Szymanski,1999;Antonioni and Cubbin,2000). Club soccer plays a vital role in the
development of talent, transfer of skills and the adoption of best practices. Most of the
world’s best players play 50-60 competitive games per season, typically for clubs located
in the wealthiest European leagues (Spain, England, Germany and Italy) and only 10 or
so of these games are played for the national team. Thus when a player join a foreign
club, his national team may directly benefit from the skills he acquires while working
for his employer. Indeed, FIFA rules require every club to release their employees to
represent their national team in all forms of international competition.6Table A-1 gives
6FIFA Regulations on the Status and Transfer of Players 2016, Annexe 1, Paragraph 1: ”Clubs are
obliged to release their registered players to the representative teams of the country for which the player
is eligible to play on the basis of his nationality if they are called up by the association concerned. Any
agreement between a player and a club to the contrary is prohibited.”
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some evidence of the internationalization of top players by listing how many players of
each 2014 World Cup squad played in their home league or a European league. In only
eight of the thirty-two countries did more than half of the squad members play for a
club in their country, and four of these were countries with top national leagues.7At the
other extreme, only one player from each of Bosnia-Herzegovina, Uruguay, Ivory Coast
and Ghana played for domestic clubs. Generally, it has been shown that the share of
foreign players is the highest in the leagues that pay the highest wages, which are also
the leagues considered to play the highest quality soccer (Besson et al.,2008).
While knowledge transfer and skill development resulting from migration is in general
a significant transmission mechanism among economies, there are reasons to think it is
especially important in the soccer world, see e.g. Milanovic (2005). There are three key
features to note:
(a) Because the player remains on his national team while playing for a club in the
foreign league, the skill transfer effect can be thought to be much stronger and more
immediate than that of migrants returning to their country of origin (see Dustmann
(2003) and Wahba (2014) on return migration). There is a discussion whether this
so-called ’foot drain’ of the best national players, analogous to the ’brain drain’ in other
industries, hampers the development of domestic leagues.8But for the performance of
the national team, the skill transfer effects of migration are unambiguously positive.
For instance, Bauer and Lehmann (2007) provide evidence that teams with a higher
percentage of players under contract abroad performed better in the 2006 World Cup
than others, and Berlinschi et al. (2013) use 2010 FIFA rankings to find that migration
of national team players improves international soccer performance for weaker national
teams.
(b) The labor market for players exhibits hardly any information asymmetries. In
contrast to other global labor markets, workers’ performance is very transparent and
is measured almost exclusively in the objective terms of game success (Kahn,2000).
Comparability is facilitated with match analysis technology, continuously adding
information to databases on player characteristics and individual performance statistics
over time (Kempe et al.,2014).
(c) Finally, it is a particular feature of soccer that the skills acquired in one country
are directly transferable, whereas human capital might not be portable for many other
industries and jobs (Friedberg,2000).
7Cases such as Russia, whose national team players exclusively play domestically, underlines the
importance of political and institutional factors in player migration, see Leeds and Leeds (2009).
8Beine et al. (2001) argues that the migration prospects provide incentives for a skills investment
which might mitigate the actual loss due to migration. In soccer, top players which stay on the national
team continue to act as a role model and can therefore show a possible way out of poverty for talented
children in poorer countries (Berlinschi et al.,2013).
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Our hypothesis is therefore that the global transfer of skills and technology in the
soccer industry will lead to unconditional convergence in teams’ performance over time
which should be visible in the data.
3 The Dataset
Our original dataset contains more than 32,000 results of all the matches played between
national teams from 1950 to 2014.9We have information on the date and the venue
of the game, the number of goals scored by each team as well as the type of the match,
ranging from ’Friendly’ to World Cup. Such a worldwide dataset of industry performance
is unique to soccer.
In the convergence literature, the economic growth performance of a nation is typically
judged relative to that of other countries, with the ’productivity gap’ (Rodrik,2011) or
’distance to the technological frontier’ (Acemoglu et al.,2006). In sporting competitions
such as soccer, the agreed performance benchmark is also a relative measure of success:
Winning is everything. The inherent zero-sum nature makes our study more akin to
a comparison of countries’ relative rather than absolute income or productivity levels,
in line with the literature. Whether at the individual game level or at the multi-year
aggregate, we will work with two relative performance measures for national teams: (a)
the winning percentage (in terms of points with 1 for a victory, 0.5 for a draw and 0
for a loss), and (b) the average goal difference. The two measures can be thought to
be complementary: The winning percentage reflects the decisive outcome (win, lose or
draw), while the goal difference gives an indication of the scale of the victory (Koopman
and Lit,2014).
Following the discussion of the previous section, we can identify a number of factors
contributing to the outcome of the game between countries iand jat time t:10
outcomeijt =dummyi+homeit +awayit+lpopratioijt +lgdpratioijt +lexpratioij t +ijt (2)
homeit is a dummy for the home advantage for country iif the game takes place in
their country in front of their own supporters, awayit is equal to 1 if the game takes
place in country j, with neutral ground serving as the reference category. lpopratioijt
and lgdpratioijt denote the logarithms of, respectively, the population ratio and GDP
9The data for this paper is based on a database of international games from 1871 to 2001
compiled by Russell Gerrard (http://www.staff.city.ac.uk/~sc397/football/aifrform.htm) and
updated using data kindly provided by Christian Muck (http://laenderspiel.cmuck.de/index.php?
2e2abc971121d3382a78a6f5fbccea2e).
10This is also in line with the statistical literature on forecasting soccer results of clubs within national
leagues, which assumes, for instance, that match results come from a bivariate Poisson distribution
dependent on clubs’ latent attack and defense strength as well as the home advantage (Maher,1982;
Koopman and Lit,2014).
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per capita ratio between the two countries, with GDP per capita serving as an indicator
of a country’s potential spending power on soccer (Hoffmann et al.,2002). Population
and GDP per capita data are taken from the from the Penn World Tables, version 9.0
(Feenstra et al.,2015). Finally, lexpratioijt is the logarithm of the countries’ ratio of the
experience proxies. Experience reflects the familiarity with the competitive environment,
but also the extent to which soccer is established as a national pastime (Macmillan and
Smith,2007). Our proxy for experience at time tis the number of international games
played by the country since 1872, the year of the first recognized international soccer
game.11 After this matching process of the explanatory variables, about 25,000 games
are still left.12
Table A-2 presents summary statistics of the outcome and explanatory variables for
the whole sample period as well as various sub-periods. Overall, the variables look stable
over time; only the slight increase in the standard deviation of the population and GDP
per capita ratios indicate that in later years larger and richer countries played more often
against smaller ones. We will see if convergence in performance holds nevertheless. In fact,
if our hypothesis of absolute convergence is correct, the importance of the explanatory
variables should have decreased.
We start by estimating (2), using the win percentage as a measure of outcome, for all
games from 1950 to 2014 with clustered standard errors at the team level. Column 1
of Table 1 shows that all the explanatory variables are statistically significant at the 1%
level and enter with the expected sign in explaining the winning percentage. For instance,
a 100% increase, hence a doubling, of the population ratio of the two countries increases
the win percentage by 3.4 percentage points. Columns 2 to 5 of Panel A divide the games
by competitiveness into ’friendly’ and ’competitive’ games, with the latter consisting of
the qualifiers for World and Continental Cups (Column 4) as well as the tournaments
themselves (Column 5). There are slight differences between specifications; for example,
home advantage is most pronounced for World and Continental Cup tournament games
and it is stronger than the disadvantage of playing in the opponent’s country. The
converse holds for the qualifiers. In World and Continental Cups, population size also
plays less of a role than for friendlies or qualifiers, and the fit of the regression is less good.
Overall, however, we conclude that across all types of games the explanatory variables
are highly significant and of comparable importance. This is corroborated by Table A-
11Our reasoning builds upon Macmillan and Smith (2007), who conduct a cross-sectional regression
of countries’ soccer performance and who use the year of a country’s first international football match as
a proxy for experience. The two indicators are highly correlated. However, the total number of matches
played can better capture the activity throughout the years and produces fewer outliers.
12Note that the matching process with GDP per capita results in this loss of 7000 of the 32000 matches.
These involve (i) small territories with national FIFA status but without national income accounts, e.g.
several Caribbean islands, Scotland and Zanzibar, (ii) nations which no longer exist, e.g. West Germany,
Czechoslovakia and the USSR. Given these nations were also strong soccer nations (especially West
Germany), their omission is likely to understate the variance of performance in the early decades and
therefore understate any tendency toward convergence.
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Table 1: Game Outcome (Win Percentage) Regressed on Explanatory Factors
Panel A: By Types of Games
Dependent Var: (1) (2) (3) (4) (5)
Win Percentage All Games Friendlies Competitive Qualifiers World + Cont. Cup
home 0.121∗∗∗ 0.102∗∗∗ 0.152∗∗∗ 0.093∗∗∗ 0.167∗∗∗
(0.007) (0.009) (0.010) (0.015) (0.023)
away -0.122∗∗∗ -0.120∗∗∗ -0.116∗∗∗ -0.173∗∗∗ -0.131∗∗∗
(0.006) (0.008) (0.010) (0.014) (0.022)
lgdppcratio 0.031∗∗∗ 0.027∗∗∗ 0.035∗∗∗ 0.032∗∗∗ 0.045∗∗∗
(0.003) (0.004) (0.004) (0.004) (0.006)
lpopratio 0.034∗∗∗ 0.031∗∗∗ 0.038∗∗∗ 0.040∗∗∗ 0.025∗∗∗
(0.003) (0.003) (0.003) (0.004) (0.005)
lexpratio 0.100∗∗∗ 0.100∗∗∗ 0.093∗∗∗ 0.089∗∗∗ 0.098∗∗∗
(0.005) (0.005) (0.006) (0.006) (0.012)
Constant 0.451∗∗∗ 0.537∗∗∗ 0.397∗∗∗ 0.449∗∗∗ 0.372∗∗∗
(0.006) (0.006) (0.010) (0.015) (0.007)
Country Dummies Yes Yes Yes Yes Yes
R2 0.215 0.171 0.277 0.313 0.163
Obs. 50804 27708 23096 17784 5312
Countries 182 181 182 182 132
Panel B: By Time Period
Dependent Var: (1) (2) (3) (4) (5)
Win Percentage All Games 1950-1966 1967-1982 1983-1998 1999-2014
home 0.121∗∗∗ 0.122∗∗∗ 0.129∗∗∗ 0.138∗∗∗ 0.112∗∗∗
(0.007) (0.026) (0.018) (0.011) (0.008)
away -0.122∗∗∗ -0.120∗∗∗ -0.159∗∗∗ -0.126∗∗∗ -0.103∗∗∗
(0.006) (0.025) (0.015) (0.010) (0.008)
lgdppcratio 0.031∗∗∗ -0.024∗0.031∗∗∗ 0.040∗∗∗ 0.033∗∗∗
(0.003) (0.013) (0.008) (0.005) (0.004)
lpopratio 0.034∗∗∗ 0.035∗∗∗ 0.029∗∗∗ 0.036∗∗∗ 0.035∗∗∗
(0.003) (0.008) (0.005) (0.004) (0.003)
lexpratio 0.100∗∗∗ 0.126∗∗∗ 0.117∗∗∗ 0.086∗∗∗ 0.117∗∗∗
(0.005) (0.012) (0.007) (0.006) (0.007)
Constant 0.451∗∗∗ 0.510∗∗∗ 0.515∗∗∗ 0.376∗∗∗ 0.486∗∗∗
(0.006) (0.022) (0.019) (0.011) (0.007)
Country Dummies Yes Yes Yes Yes Yes
R2 0.215 0.221 0.245 0.245 0.216
Observations 50804 2970 7990 14866 24978
Countries 182 86 130 175 182
Notes: The table presents OLS regression results of (2) with the winning percentage as the dependent
variable. Standard errors clustered at the country level are given in parentheses: *** p<0.01, ** p<0.05,
* p<0.1. In terms of observations, every game is counted twice, once from the perspective of country
iand once from country j, to capture both the home advantage and disadvantage of playing in the
opponent’s country. Neutral venue serves as the reference category. Columns 2 to 4 in Panel A break the
games down by type, friendly and competitive, with the latter consisting of World Cup and Continental
Cup qualifiers (col 4) and tournaments (col 5).
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3, which uses the goal difference rather than the winning percentage as the outcome
variable. In the main specification of our convergence analysis, we will therefore pool all
these games.
Panel B of Table 1 and Table A-3 shows how the explanatory factors have influenced the
performance variable in different time periods. The sample from 1950 to 2014 is split into
four sixteen-year periods.13 In particular since 1982, when the impact of globalization
on soccer has become stronger (Sugden and Tomlinson,1998), the importance of the
variables home and away decreased, as has the impact of countries’ GDP per capita. By
contrast, the population and experience ratios remain as game-decisive as ever and might
even have become more important. The fact that we are working with an unbalanced
panel, with many new nations entering international competition in recent decades, may
account for these mixed results. The decrease in the model R2- for the goal difference it
decreased from 0.32 to 0.28 in the last two sample periods - is in line with our convergence
prediction of explanatory factors becoming less important. Let us therefore now subject
this hypothesis to a plethora of formal tests.
4 Empirical Results on Convergence
To investigate convergence between countries, we now turn from the individual game to
national team level. We will work with four-year World Cup cycles (i.e. four-year periods
ending in a FIFA World Cup year, for instance 2011-2014) to average out seasonal and
cyclical effects as well as one-off events such as playing against a particularly strong
opponent. Hence, we define the performance of country iin cycle tas the average
outcome, in terms of either win percentages (points) or goal differences, over the four-
year cycle.14 At the country and cycle rather than game level, the ratio variables of GDP
per capita, population and experience refer to the ratio between the given team and its
average opponent over the cycle. Countries playing fewer than five games over the cycle
were omitted to avoid a small sample bias. At this level, we are left with an unbalanced
panel of 1,644 country-cycle observations, roughly 15 games per country per cycle.
13Different cutoff years yield very similar results, as does a regression which interacts the explanatory
variables with a time trend.
14When averaging across win percentages, draws are treated as half a win. Note that starting in 1950
means that the first cycle comprises five years (1950-1954). Robustness checks with other periods than
four-year cycles, such as eight-year periods spanning two FIFA World Cups, lead to comparable results.
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4.1 Beta-Convergence
In the economic growth literature, β-convergence is defined as a negative coefficient of
the lagged level term in a growth rate regression
∆yit =α+β·yi,t−1+it,(3)
where the error term it fulfills the usual assumptions. Based on country i’s performance
in cycle t,yit (win percentage and goal difference), we calculate lags and changes.
If unconditional convergence holds, weaker teams in the previous cycle should show
performance increases even in the absence of other explanatory variables. The scatter
plots in Figure 1 suggest that this is indeed the case: The plot of changes versus lagged
performance levels across all 1,644 country-cycle observations exhibits a negative slope,
slightly more strongly for goal differences than for win percentages.
Figure 1: Changes vs. Lagged Levels of Win Percentages and Goal Differences over 16
World Cup Cycles (1950-2014)
(a) Win Percentage
−1 −.5 0 .5 1
Changes in Points
0 .2 .4 .6 .8 1
Lagged Points
(b) Goal Difference
−5 0 5 10
Changes in Goal Difference
−15 −10 −5 0 5
Lagged Goal Difference
Using the win percentage (points) per cycle as the performance variable, Table 2
shows the regression results. The main unconditional convergence regression (3) in Panel
A, col. (1) shows a negative coefficient of -0.435, which is statistically significant at the
1% level. This is a striking result. Unconditional convergence in a particular industry
has until now only been found in manufacturing (Rodrik,2013;B´en´etrix et al.,2012),
but, to our knowledge, it has not yet been empirically established in any other sector,
and certainly not for any activity in which the performance of all nations is measured
and compared.
The rest of Table 2 tests this results with various econometric specifications and
robustness checks. By including the ratios of GDP per capita, population and experience
of country iagainst its average opponent in that cycle in Panel A, col. (2), we can test for
conditional convergence. The R2increases from 0.29 to 0.39, but the β-coefficient becomes
13
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even larger in absolute value. This is robust to the inclusion of regional confederation
dummies in col. (3), implying that the development is not confined to one particular
continent. We then include country fixed effects to examine the unconditional (4) and
conditional (5) convergence hypothesis. The ˆ
β-coefficient stays highly significant and
doubles in size to -0.82 (-0.87).
A possible concern with these fixed effects estimations is the relatively short Tsetting,
given that the number of four-year cycles a country has played is at most 16. With the
model specification being dynamic by construction, the estimation might suffer from the
Nickell bias (Nickell,1981). Rewriting (3) (with fixed effect αi) as
yit =αi+ (β+ 1)
| {z }
ρ
·yi,t−1+it,(4)
we employ specific short Tdynamic panel data model estimation methods in Panel B.
The Arellano-Bond GMM results (Arellano and Bond,1991) in col. (1) and col. (2)
show a ˆρ-parameter of close to 0, which suggests a ˆ
β-coefficient of close to -1.15 Similarly,
the Unconditional Quasi-Maximum Likelihood results (Hsiao et al.,2002) in col. (3) and
col. (4) are around 0.2 for ˆρ, hence -0.8 for ˆ
β, and therefore of the same magnitude as
the fixed effects results in Panel A.
There might still be other concerns. In the dataset, there is a lot of heterogeneity
across time periods and countries in terms of the number of games played and average
opponent strength. Panel C therefore conducts two different weighted regressions.
The first addresses the problem that the number of games per team has increased
over time, contributing towards a decreasing variation. In col. (1) and col. (2), we
control for this by running regression (3) with time weights wit = (¯ni/nit)1/2, where nit
is the number of games played by country iin cycle tand ¯niis the average number
of games by iover all cycles. The regression coefficient remains negative and highly
significant. Finally, in col. (3) and col. (4) we use so-called dominance weights. With
the European and South American continental confederations generally presumed to be
the strongest ones, the weights reflect how often country iplayed against an opponent
from those two confederations.16 Even under this specification, we have a ˆ
β-coefficient
of -0.31 in the unconditional convergence regression and -0.49 for conditional convergence.
We conclude that all the results from the β-convergence analysis agree in their
prediction that weaker teams have caught up with stronger ones. In the Online Appendix,
15The residuals also pass the Arellano-Bond test for serial correlation in the first-differenced errors
and of no serial correlation in the second-differenced errors, see the reported test statistics AR1 and AR2
in Table 2, Panel B.
16This specification also addresses the possible concern that mediocre teams which barely manage to
qualify for the World Cup and lose against stronger opponents from other continents might potentially
show a worse average performance than teams that did not qualify at all.
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Table 2: Beta-Convergence Regression Results, Main Specification
Panel A: Panel Data Regression
Dep Var: ∆ points (1) (2) (3) (4) (5)
l.points -0.435∗∗∗ -0.590∗∗∗ -0.597∗∗∗ -0.818∗∗∗ -0.872∗∗∗
(0.027) (0.031) (0.030) (0.032) (0.032)
lgdppcratio 0.012∗∗ 0.012∗∗ 0.017∗
(0.005) (0.005) (0.010)
lpopratio 0.018∗∗∗ 0.019∗∗∗ 0.006
(0.004) (0.004) (0.009)
lexpratio 0.057∗∗∗ 0.056∗∗∗ 0.073∗∗∗
(0.007) (0.007) (0.010)
Constant 0.208∗∗∗ 0.288∗∗∗ 0.280∗∗∗ 0.383∗∗∗ 0.417∗∗∗
(0.013) (0.016) (0.018) (0.015) (0.015)
Confed Dummies No No Yes No No
Country FE No No No Yes Yes
R2 0.291 0.394 0.395 0.503 0.543
Observations 1644 1644 1644 1644 1644
Countries 178 178 178 178 178
Panel B: Fixed Effects Short TDynamic Panel Estimation
(1) (2) (3) (4)
Dep Var: points (GMM) (GMM) (QML) (QML)
L.points -0.043 0.021 0.254∗∗∗ 0.189∗∗∗
(0.048) (0.049) (0.039) (0.033)
lgdppcratio 0.031∗∗ 0.026∗∗
(0.012) (0.011)
lpopratio 0.029∗∗∗ 0.008
(0.009) (0.009)
lexpratio 0.055∗∗∗ 0.064∗∗∗
(0.013) (0.011)
Constant 0.486∗∗∗ 0.469∗∗∗ 0.361∗∗∗ 0.395∗∗∗
(0.024) (0.023) (0.022) (0.019)
AR1 -6.136 -7.076
AR2 -0.751 0.396
Observations 1484 1484 1372 1372
Countries 176 176 139 139
Panel C: Weighted Regressions
(1) (2) (3) (4)
Dep Var: ∆ points (Time W) (Time W) (Dom W) (Dom W)
l.points -0.454∗∗∗ -0.617∗∗∗ -0.306∗∗∗ -0.493∗∗∗
(0.028) (0.031) (0.040) (0.042)
lgdppcratio 0.010∗0.020∗
(0.005) (0.011)
lpopratio 0.019∗∗∗ 0.031∗∗∗
(0.004) (0.005)
lexpratio 0.060∗∗∗ 0.033∗∗∗
(0.008) (0.011)
Constant 0.214∗∗∗ 0.290∗∗∗ 0.163∗∗∗ 0.268∗∗∗
(0.014) (0.019) (0.022) (0.026)
R2 0.304 0.409 0.178 0.301
Observations 1644 1644 599 599
Countries 178 178 56 56
Notes: The table presents the regression results of (3) (Panels A and C) and (4) (Panel B). Standard
errors clustered at the country level are given in parentheses: *** p<0.01, ** p<0.05, * p<0.1. pointsit
denotes the average points country ihas obtained per game during the four-year cycle t. Panel C uses
observation weights as explained in the text.
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we repeat the complete analysis with other performance variables and subsamples. The
negative sign in the ˆ
β-coefficient is robust to (i) the use of goal difference rather than
winning percentages, (ii) limiting the sample to competitive games, (iii) considering only
teams that were active from the first cycle (1950-1954) onwards,17 (iv) splitting the
sample into the time periods 1950-1982 (the first eight cycles) and 1983-2014 (the last
eight cycles). While we find significant convergence results throughout time, there is no
indication that they have become stronger in later years. We will return to this point,
when we analyze limits of the convergence between weaker and stronger teams.
4.2 Sigma-Convergence
A negative β-coefficient in the growth-initial-level regression (3) is well-grounded in
growth theory and widely viewed as evidence for convergence (Islam,2003). However,
Quah (1993b) and Friedman (1992) argue that convergence must also be visible in a
declining dispersion of the cross-sectional distribution. This so-called σ-convergence
does not necessarily follow from β-convergence. Due to random shocks, a negative ˆ
βin
(3) might result from a general reversion to the mean and might not imply that poorer
or weaker individuals are systematically catching up (’Galton’s Fallacy’). With random
shocks playing an important role in an essentially unpredictable sport such as soccer, we
solidify our β-convergence result by checking for σ-convergence.
Figure 2: The Standard Deviation of (a) Win Percentage and (b) Goal Difference over
16 World Cup cycles 1950-2014
.1 .13 .16 .19 .22
Standard Deviation of Win Percentage
1954 1962 1970 1978 1986 1994 2002 2010
Years (End of Four−Year Cycle)
All Teams Only Teams Present Since 1950
Only Teams Present Since 1983
.6 .8 1 1.2 1.4 1.6
Standard Deviation of Goal Difference
1954 1962 1970 1978 1986 1994 2002 2010
Years (End of Four−Year Cycle)
All Teams Only Teams Present Since 1950
Only Teams Present Since 1983
Simple descriptive statistics suggest that σ-convergence, defined as a reduction in
the variance of the performance variable, is present. Figure 2 shows that the standard
deviation of both win percentages and goal differences decreased by one third to one half
over the sample period (1950-2014). This is true whether one considers all the countries
17 Obviously, the national teams entering the international stage and catching up has contributed to
the overall convergence effect, but we also observe unconditional and conditional convergence among the
teams which were present throughout the years.
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in each four-year cycle (the solid line), only the small group of football nations active
since 1950 (the dashed line), or the countries that have been continuously present in the
second half of the sample (since 1983, the dash-dotted line). The formal σ-convergence
test suggested by Carree and Klomp (1997) computes a test statistic
R=
√N(ˆσ2
0
ˆσ2
1−1)
2q1−(ˆ
β+ 1)2
,(5)
based on the adjusted ratio of estimated variances, ˆσ2
0and ˆσ2
1, at the beginning and end
of the sample. ˆ
βis the coefficient estimate from the β-convergence regression (3) for the
respective time period. Rhas asymptotically a standard normal distribution. In Table 3
we use it to test for σ-convergence across various time periods, both for the whole sample
and different sub-periods. Whether we look at the win percentages or goal differences,
the Rtest statistic is nearly always highly significant. The test is typically applied at
medium to long horizons, but even if we test for σ-convergence within each four-year
cycle in Table A-4 we obtain many significant results, in particular in cycles in the 1960s
and 1980s/1990s.18 Our overall conclusion is therefore not only in favor of unconditional
β-convergence but also σ-convergence in terms of national teams’ performance.
Table 3: Ratio Test Statistics for σ-Convergence in Win Percentage and Goal Difference
Period NWin Percentages Goal Difference
ˆ
βˆσ2
1R-stat ˆ
βˆσ2
1R-stat
Convergence over 65 years (16 cycles)
1950-2014 31 -0.7576 0.0144 7.1762∗∗∗ -0.8506 0.4081 11.9581∗∗∗
Convergence over 32 years (8 cycles)
1950-1982 30 -0.4357 0.0283 1.1147 -0.5065 0.8701 4.6002∗∗∗
1983-2014 111 -0.5574 0.0184 6.2461∗∗∗ -0.6072 0.5045 10.9664∗∗∗
Convergence over 16 years (4 cycles)
1950-1966 26 -0.7336 0.0261 1.8002∗∗ -0.7407 0.6785 5.6914∗∗∗
1966-1982 80 -0.5278 0.0219 2.5305∗∗∗ -0.5273 0.6878 2.9425∗∗∗
1983-1998 108 -0.4832 0.0229 3.5227∗∗∗ -0.4628 0.9621 3.2548∗∗∗
1999-2014 167 -0.3905 0.0227 2.0910∗∗ -0.5304 0.7318 6.8239∗∗∗
Notes: The table presents the variables and results of (5), computed for the respective periods.
*** p<0.01, ** p<0.05, * p<0.1.
4.3 Distributional Analysis
How has the shape of the performance distribution evolved over time, as weaker national
teams have caught up with stronger ones? In line with σ-convergence, the histograms and
kernel densities for the win percentage and goal difference in each four-year cycle have
18The lack of significance within the latest four-year cycles is mirrored in the flattening of the standard
deviation graphs in Figure 2.
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become taller and thinner, as described in the Online Appendix. But a full distributional
analysis has to abstract from the increasing number of teams and work with a balanced
panel. As a trade-off between the number of countries and the number of time periods
we construct our baseline Sample 1, which contains 76 countries across 10 four-year
cycles (1975-2014). It is restricted to countries with more than 1m inhabitants because
it can be argued that tiny countries lack the human and financial resources to make
significant performance improvements against their more populous peers (Hoffmann
et al.,2002). As robustness checks, the Online Appendix works with a shorter Sample
2 (127 countries and 6 four-year cycles, 1990-2014) as well as an extended Sample 3
(Sample 1 including countries with less than 1m inhabitants).19
Table 4: Distribution of Win Percentages and Goal Difference Sample 1 (76 countries)
Panel a) Distribution of Win Percentage
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Mean St.Dev. Skew Kurt JB pval. Unimod pval. CC Ind. Pola Gini
1975-78 0.5002 0.1683 -0.3445 2.8710 0.3564 0.6567 0.3024 0.1594 0.1885
1979-82 0.5134 0.1371 -0.1872 3.1298 0.5000 0.4733 0.3142 0.1059 0.1473
1983-86 0.5258 0.1316 -0.6700 3.1216 0.0436 0.9400 0.2265 0.1038 0.1379
1987-90 0.5159 0.1465 -0.5679 2.7126 0.0698 0.1533 0.4125 0.1180 0.1574
1991-94 0.5224 0.1341 -0.4842 2.4387 0.0812 0.5133 0.3499 0.1314 0.1442
1995-98 0.5326 0.1226 -0.3149 3.1776 0.4086 0.9633 0.2070 0.0971 0.1277
1999-02 0.5451 0.1001 -0.1941 2.1501 0.1514 0.5833 0.3563 0.0992 0.1045
2003-06 0.5432 0.1177 -0.2323 2.2168 0.1656 0.2200 0.4314 0.1181 0.1231
2007-10 0.5408 0.1188 0.1811 2.9808 0.5000 0.8733 0.2527 0.0980 0.1227
2011-14 0.5431 0.1052 -0.0154 2.3663 0.4338 0.3467 0.3781 0.0959 0.1099
Panel b) Distribution of Goal Differences
(1) (2) (3) (4) (5) (6) (7)
Mean St.Dev. Skew Kurt JB pvalue Unimod pvalue CC Ind.
1975-78 0.0352 0.9450 -1.1445 5.4890 0.0010 0.7733 0.2466
1979-82 0.0708 0.7895 -0.6210 4.1080 0.0205 0.8200 0.2422
1983-86 0.1985 0.6819 -0.4944 3.0985 0.1217 0.3933 0.3525
1987-90 0.0637 0.7217 -0.7806 3.5111 0.0215 0.5400 0.3127
1991-94 0.1647 0.7554 -1.0087 5.2635 0.0014 0.6467 0.2844
1995-98 0.2251 0.6279 -0.1753 3.1777 0.5000 0.9533 0.2167
1999-02 0.2837 0.5343 0.0838 2.6192 0.5000 0.3067 0.3798
2003-06 0.2494 0.5706 -0.1930 2.6359 0.5000 0.3633 0.3698
2007-10 0.2084 0.5749 -0.3756 3.3441 0.2289 0.7600 0.2539
2011-14 0.2108 0.5273 0.0416 2.5391 0.5000 0.8233 0.2614
Notes: The analysis is based on a balanced sample of 76 countries (Sample 1) with more than 1m
inhabitants throughout the sample period. Columns 1-4 report the distributional moments mean,
standard deviation, skewness and kurtosis. Column 5 contains the p-values of the Jarque Bera test
with the null hypothesis as the Gaussian distribution. Column 6 shows the p-values of Silverman’s
(1981) multimodality test with the null hypothesis as a unimodal distribution. Column 7 presents the
club convergence indicator by Krause (2017), Column 8 the bi-polarization index by Wolfson (1994) and
Column 9 the Gini coefficient as a measure of inequality. Due to the presence of negative values in the
goal differences, the latter two cannot be computed for this data.
19All samples are restricted to countries which played more than 5 games in every cycle in order to
avoid a small sample bias in calculating win percentage averages.
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The evolution of various distributional statistics for Sample 1 in Table 4 underpin
the convergence evidence. Apart from the large decreases in the standard deviation of
win percentages and goal differences (column 2), we also note decreases in, respectively,
skewness and kurtosis (columns 3 and 4), particularly since the 1990s. This makes
the distribution less skewed and flattens the tails, specifically the left one where the
worst performing teams are located. Countries’ positions move closer together as weaker
teams catch up. According to the Jarque-Bera p-value (column 5), in recent years we
cannot reject the hypothesis that win percentages and goal differences follow a Gaussian
distribution, which is symmetric and light-tailed. This is also illustrated in Figure 3a
for win percentages and Figure 3b for goal differences: the distributions clearly appear
less skewed, less dispersed and more Gaussian since the 1980s. The disappearance of
the long left tails of weak countries in the distribution of goal difference is particularly
striking.20
Figure 3: Densities of Performance Measures in Various Years, Sample 1 (76 Countries)
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
2
2.5
3
3.5
Win Percentage
Density Value
1975−78
1991−94
2011−14
−5 −4 −3 −2 −1 0 1 2 3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Goal Difference
Density Value
1975−78
1991−94
2011−14
That the distribution of countries’ soccer performance has moved towards a Gaussian
distribution stands in stark contrast to the evolution of countries’ (relative) GDP per
capita distribution, which is characterized by continued asymmetry and multimodality.
For GDP per capita, the literature has failed to find unconditional convergence in the
global distribution and attention has focused on the narrower notion of club convergence,
which denotes convergence only within certain groups of countries (Baumol,1986;Quah,
1993a,1996). If the distribution is multimodal, one can test for club convergence by
measuring if the various peaks become more pronounced over time (Krause,2017).
20Only for Sample 3, which includes tiny country with less than 1m inhabitants, the left tail stays
rather long, as the Online Appendix explains. This suggests that while there is convergence, very small
nations face significant obstacles to improving their performance due to scarce resources in terms of
population and wealth.
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However, we find little or no evidence of multimodality at any point in time either for
the distribution of win percentage or goal difference. Even for the years before the move
towards a symmetric, Gaussian distribution, the continental groupings do not become
visible in multiple modes in the performance distribution. Silverman’s (1981) test never
rejects the unimodality hypothesis at any reasonable significance level; the p-values never
go below 0.15 for the win percentage distribution (column 6 of Table 4).21 Accordingly, the
dynamic club convergence indicator shows no clear pattern across time periods (column
7). While the relative GDP per capita distribution has gone through various periods
of club convergence and de-clubbing (Krause,2017), in terms of soccer performance
countries have clustered more and more around a 0.5 win percentage and a goal difference
close to zero. We conclude that the convergence results in countries’ soccer performance
holds across the worldwide distribution. This is further underlined by a steady decrease
in Wolfson’s (1994) bi-polarization index (Column 8), which measures the size of the
distribution at both ends compared to the middle. Lastly, the Gini coefficient of inequality
in performance (Column 9) also decreases significantly across all time periods.
5 The Limits of Convergence and the Middle Income
Trap Analogy
5.1 Country Analysis
While our evidence strongly suggests that there has been convergence in men’s soccer
national team performance since 1950, it is also obvious that significant differences
remain. The prediction by the celebrated Brazilian player Pele in the 1980s that “An
African nation will win the World Cup before the year 2000” has proved to be wide of
the mark. Only European and South American teams have achieved this feat so far.
This leads us to question how teams from other continents have fared against European
and South American teams: are they catching up and winning more often in direct
encounters? Figure 4 reports the average win percentage per 4-year cycle of the newer
confederations (Asia, Africa and Central/North America) against the established powers
of Europe and South America since the 1970s.22 The graph suggests that each continent
has enjoyed some periods of catch-up, but that in all three cases convergence toward the
elite confederations has stalled in the last decade and might even be going into reverse.
The win percentage seems stuck at just below the 40% level, significantly below equality
with European and South American teams.
21We follow the version of Silverman’s (1981) unimodality test with the sample variance adjustment
by Efron and Tibshirani (1993). For the bootstrap procedure we use 2500 replications.
22In the years before, there were rather few direct encounters between the particular confederations
per four-year cycle. Also note the sixth confederation, Oceania (OFC), is omitted here since it largely
consists of small Pacific islands struggling to compete outside of the confederation.
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Figure 4: Win Percentages of Countries from Other Continental Confederations Against
Teams from Europe (UEFA) or South America (CONMEBOL), per Four-Year Cycle
.1 .2 .3 .4 .5
Win Percentage
1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 2014
Years (End of Four−Year Cycle)
Asia (AFC) Africa (CAF)
North/Central America (CONCACAF)
Further evidence is provided by a decomposition of performance inequality into
inequality within and between continental confederations. Using the 76 countries from
Sample 1 (ten four-year cycles from 1975-2014), Table 5 shows that the Theil index
of global inequality in win percentage decreased markedly over the years (col 1), but
this evolution has been driven by the strong decrease in performance inequality within
continental confederations (col 2).23 This holds for inequality within all the individual
confederations except North/Central America; in particular, performance inequality
within Europe decreased by 75% (Table A-5). By contrast, between-continent inequality
in performance (col 4) stood at the same value as at the beginning of the sample. Its share
of global performance inequality has therefore increased considerably (col 5). While most
of the differences in performance can still be attributed to within-continent inequality
(col 3), the relatively increasing gaps between continents are worth investigating.
In order to square the results of unconditional convergence across the worldwide soccer
performance distribution with the remaining rift between the top national teams and the
rest, let us analyze which countries have caught up the most. For our mobility analysis,
we rank the 76 countries from Sample 1 based on their win percentage. The relatively low
correlation coefficients of 0.5-0.7 from cycle to cycle in Table A-6 shows that there is a lot
of mobility in the distribution, much more than is typically found in, say, the distribution
of countries’ income per capita. Nevertheless, there are clearly some limits to the catch-
up process and we see big differences across continental federations. This is revealed by
Table 6. Across the whole period (1975-2014), European countries had the highest rank
on average (32.1 out of 76), while the average Asian, African and South American teams
were on similar levels. But looking at changes from the beginning to the end, we see that
the average countries from Europe and South America managed to improve their ranks
23The Theil index of inequality is used because it can be decomposed into its within- and between-
group components, unlike the Gini index (Cowell,2009).
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Table 5: Inequality in Win Percentage and its Decomposition Within and Between
Continental Confederations, Sample 1 (76 countries)
Theil Index of Within Continents Between Continents
Inequality Theil-Index Share of Total Theil-Index Share of Total
(1) (2) (3) (4) (5)
1975-1978 0.0630 0.0604 0.9588 0.0026 0.0412
1979-1982 0.0373 0.0357 0.9551 0.0017 0.0449
1983-1986 0.0340 0.0324 0.9506 0.0017 0.0494
1987-1990 0.0440 0.0408 0.9285 0.0031 0.0715
1991-1994 0.0350 0.0324 0.9270 0.0026 0.0730
1995-1998 0.0277 0.0244 0.8793 0.0033 0.1207
1999-2002 0.0170 0.0145 0.8491 0.0026 0.1509
2003-2006 0.0240 0.0195 0.8140 0.0045 0.1860
2007-2010 0.0241 0.0223 0.9274 0.0017 0.0726
2011-2014 0.0188 0.0163 0.8638 0.0026 0.1362
(from 34.3 to 30.8 and 44.6 to 38.9).24 The average African team fell further behind
in relative terms (from 37.5 to 39.6). This becomes even clearer when focusing on the
countries starting out from the bottom half of ranks in the beginning (rows 6 to 9), which
therefore had the biggest catch-up potential: Both weak teams from Europe and South
America made big improvements - by 15 ranks for the average European bottom-half
team -, while the average African bottom-half team fell slightly further behind. This
leads us to conclude that the biggest beneficiaries of worldwide convergence have been
second-tier national teams from Europe and South America. Some African and Asian
teams have also advanced, but many are still struggling to close the continental gap.
Table 6: Countries’ Ranks in the Win Percentage Distribution over Four-Year Cycles
by Continental Federation, Sample 1 (76 countries)
Asia Africa America (N,C) South America Pacific Europe
Mean Rank 39.3 40.2 44.2 41.5 58.0 32.1
St.Dev. of Rank 16.7 14.2 14.5 12.2 23.6 14.6
Rank in 1975-86 41.8 37.5 38.9 44.6 35.0 34.3
Rank in 2003-14 41.4 39.6 47.3 38.9 75.0 30.8
No. of Countries 15 23 6 10 1 21
Bottom Half: Rank in 1975-86 57.1 50.9 45.6 55.3 52.7
Bottom Half: Rank in 2003-14 48.4 52.3 51.6 50.6 37.6
No. of Bottom Half Countries 9 11 4 7 0 9
Figure 5 illustrates some cases in point: The world’s dominant national teams like
Brazil kept an empirical winning percentage at 0.7 throughout the sample period. Turkey
in the left panel and Ecuador in the right panel are examples of formerly weaker European
and South American countries which showed big improvements. Bangladesh, the world’s
8th most populous country, was among the weakest teams overall with a win percentage
24The beginning (1975-86) and end (2003-2014) here encompass three four-year cycles to ease out
random variation in ranks over cycles.
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Figure 5: The Evolution of Selected Countries’ Win Percentages per four-year Cycle
1980 1985 1990 1995 2000 2005 2010
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Year
Win Percentage per four−year Cycle
Brazil
Turkey
China
1980 1985 1990 1995 2000 2005 2010
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Year
Win Percentage per four−year Cycle
Bangladesh
Nigeria
Ecuador
of 0.1 in the 1970s. With a huge catch-up potential, it has shown performance increases.
But the better national teams from Africa and Asia, such as China and Nigeria, have
failed to make long-lasting improvements and remain at middling performance levels. In
order to understand why, we will consider the parallels to an empirical phenomenon in
the GDP per capita growth literature: the Middle Income Trap.
5.2 The Middle Income Trap Analogy
Coined by two World Bank economists (Gill and Kharas,2007), the term ’middle
income trap’, refers to the challenge countries face after prolonged periods of economic
catch-up growth. As the returns to capital diminish and wages rise, export-based
growth strategies based on abundant labor reach their limits. At the same time, they
do not yet have the technological and human capital resources to compete with richer
countries on innovation.25 Obviously, when drawing analogies to football performance,
the countries involved differ. In terms of income per capita, the Asian Tiger countries
(Korea, Taiwan etc), have been more successful in making the transition than some
stagnating Latin American countries. Brazil and Argentina owe their position in the
middle income trap partly to a resource-dependent economy, slow industrialization and
inefficient institutions (Lee,2013), while soccer has a long history in these countries, and
they are continually investing in their talent to stay among the top teams. Still, looking
at other teams which are failing to close the rift with these best European and South
American countries elucidates mechanisms of a ’middle performance gap’.
25Gill and Kharas (2015) lament that no economic growth model has yet been developed particularly
for middle-income countries to fill the gap been the Solow-Swan capital accumulation model for poorer
economies and endogenous growth theory for richer ones.
23
ECINEQ WP 2017 - 453 December 2017

First, it is obvious that for very weak teams, performance improvements are
easier to achieve than for teams in the middle. Starting at low levels, better sports
infrastructure, better nutrition and fitness plans, more effective training techniques,
expanded knowledge of tactics and insights from abroad, gained by players or a
foreign coach, can go a long way (Yamamura,2009). Directed initiatives reflecting the
soccer equivalent of foreign aid and foreign direct investment can also help to lay the
groundwork. For instance, FIFA gives grants to emerging continental associations paid
out of the profits generated by the FIFA World Cup; clubs from rich countries and
philanthropists support training and cooperation facilities in African countries.26 From
a low level, the win percentages of the world’s weakest teams can therefore increase
rather easily. But once these low-hanging fruits have been picked, sustained performance
improvements are harder, all the more so if their opponents have advanced in similar ways.
The development of new talent becomes decisive if teams aspire to be among the
world’s best. According to Acemoglu et al. (2006), the closer an economy gets to the
technology frontier, the more important it is not only to improve the performance
of existing firms and managers, but to broaden the talent pool. Applied to soccer,
maximizing the potential of the national population requires a national network of
scouting and training schemes for young players. It is well-known that the physiological
predictors for developing soccer talent have to be combined with the right sociological
factors in terms parental support, child-coach interaction and hours of training, see
Williams and Reilly (2000). Germany is widely admired for its youth development
system; 121 regional training centers allow every aspiring German teenager to have
access to intensive training programs within 25 km of their hometown. The creation
of a national league for players under the age of 17 further helps young talents to gain
competitive experience.27 Other countries are adopting these initiatives; in 2017 China
announced plans to create 50,000 football youth academies by 2025. Establishing a
talent development system can in the long run be expected to help countries escape the
’middle performance trap’.
For the continued growth of rich economies, innovation plays a vital role (Romer,
1990;Grossman and Helpman,1991). Eichengreen et al. (2013) find that countries
with more high-tech production were less likely to have growth slowdowns at the
26Examples are the Dutch clubs of Feyenoord Rotterdam and Ajax Amsterdam, which have established
youth training camps and cooperation facilities in African countries. George Weah, the FIFA World
Footballer of the Year in 1995, has invested considerably in soccer development of his native Liberia.
27For the discussion of the German youth development system by the international press,
see for instance https://www.theguardian.com/football/2015/sep/05/germany-football-team-youth-
development-to-world-cup-win-2014 .
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typical transition level of the middle income trap. In soccer, the adoption of best-
practices from abroad has helped many teams to catch up, but beyond a certain
point it might be important for a team to develop its own style. In fact, successful
playing styles which spread quickly across countries typically originate in the world’s
leading football nations, see Men´endez et al. (2013). One example is the ’Tiki Taka’
style of short passes and movements associated with the Spanish team’s victory in the
UEFA Euro 2008 and 2012 as well as the FIFA World Cup 2010 (Gyarmati et al.,2014).28
A final, but crucial factor helping to explain the ’middle performance trap’ in soccer is
the network effect from regional integration. According to Ayiar et al. (2013), countries
from Central and Eastern Europe, such as Poland and Hungary, have avoided the middle
income trap thanks to frequent interactions, via trade and technology spillovers, with
richer European neighbors. In soccer, regional blocks are particularly vital because teams
from the same federation most often play against each other (see Table A-7). Out of all
international pairings from 1950 to 2014, 82% pitted two teams from the same regional
federation against each other. European teams played against other European teams 84%
of the time. This is not only due to geographical proximity but underlines the role of the
continental confederations in organizing games and setting standards.
Our mobility analysis has revealed that weaker teams from Europe and South America
have improved their performance a lot. They are benefiting from playing against
the world’s best teams on a regular basis as well as sharing the same institutional
environment, which facilitates the technology transfer. By contrast, relatively good teams
from Africa or Asia can gain less from regional integration where they meet even weaker
peers. They simply have fewer opportunities to hone their skills against the world’s top
national teams, becoming stuck in the soccer analogue of the middle income trap. This
leads us to conclude that the strong role of regional associations in soccer has come with
a mixed blessing in terms of helping weaker teams to catch up.
6 Conclusion
Examining the performance of national soccer teams from 1950 to 2014, this paper
has found strong evidence of unconditional convergence. The results of the β- and
σ-convergence tests suggest that weaker teams have made improvements and caught up
with better ones. Unlike countries’ income per capita distribution, worldwide soccer
performance in terms of win percentages and goal differences has evolved towards a
28There is a big discussion among sports commentators to what extent the adoption of ’Tiki Taka’
by other teams is proving successful or long-lasting, see https://www.supersport.com/football/
blogs/sunday-oliseh/Why_Tiki_Taka_still_rules_the_world and http://bleacherreport.com/
articles/1391050-barcelonas-tiki-taka-4-teams-whove-tried-to-emulate-them.
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Gaussian distribution, as countries have moved towards each other. We identify the
biggest beneficiaries as (i) the world’s weakest teams with huge catch-up potential
and (ii) second-tier teams from Europe and South America, benefiting from regional
integration into the world’s top soccer continents. By contrast, the stronger teams from
Africa and Asia are failing to close the gap with the world’s best national teams and,
with continued middling performances, remain in the soccer analogue of the middle
income trap.
Our study is the first to find unconditional convergence in a particular sector other
than manufacturing and the first of its kind to use a truly global dataset. Conducting
a similar exercise in other service industries, from banking to tourism, would be more
difficult, given the challenge of constructing a consistent measure of performance across
countries. While international soccer obviously has some unique idiosyncracies, the fact
that we find unconditional convergence in such a competitive and regionally-integrated
service has implications for other sectors. Two conclusions are particularly noteworthy:
(i) Technological transfer by way of best-practice adoption can facilitate convergence if
the product/service involved is standardized, globally traded and performance is easily
observable. Global labor markets for soccer players and coaches ensure the transfer of
skills and insight, which is helped by the portability of human capital and low information
asymmetries (Kahn,2000;Milanovic,2005). It has been shown before that national teams
with more players contracted by foreign leagues do better than their peers (Bauer and
Lehmann,2007;Berlinschi et al.,2013); this paper provides the link to global convergence.
Obviously, labor markets function differently and with more frictions in other sectors.
However, our results can be seen under the light of general discussions about how to
better recognize migrants’ skills, to foster industry-specific experience abroad and to
internationalize the talent pool of skilled workers.
(ii) Regional integration fosters trade, common standards and the diffusion of best
practices between the countries involved. Regional associations are important in soccer,
but they have played an ambiguous role for worldwide convergence in performance: Our
results show that weaker teams from Europe and South America have gained from the
continued exposure to top teams and their institutional environment, at the expense of
teams from other continents. This calls for stronger integration not only within but also
between regions, an argument which can easily be made for other industries as well.
26
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Appendix A More Tables and Figures
Table A-1: Squads of 32 National Teams Participating in the 2014 FIFA World Cup
Team Coach Players (out of 23)
Foreign Home League (Other) European League
UEFA (Europe)
Germany No 16 7
Spain No 14 9
Italy No 20 3
England No 22 1
France No 8 15
Portugal No 8 15
Greece Yes 14 9
Russia Yes 23 0
Netherlands No 10 13
Belgium No 3 20
Switzerland Yes 7 16
Croatia No 2 21
Bosnia & Herzegovina No 1 22
CONMEBOL (South America)
Brazil No 4 18
Argentina No 3 19
Chile Yes 5 15
Colombia Yes 3 16
Uruguay No 1 16
Ecuador Yes 8 4
CONCACAV (North/Central American + Caribbean)
United States Yes 9 13
Mexico No 15 8
Costa Rica Yes 9 11
Honduras Yes 11 5
AFC (Asia)
Australia No 7 13
Japan Yes 11 12
Iran Yes 14 6
South Korea No 6 10
CAF (Africa)
Nigeria No 4 19
Cameroon Yes 2 21
Ivory Coast Yes 1 22
Ghana No 1 18
Algeria Yes 2 19
Notes: Each official squad consists of 23 players. Players which neither play in the home league nor in
a European league make up the difference to 23. The data are from http://resources.fifa.com/mm/
document/tournament/competition/02/36/33/44/fwc_2014_squadlists_neutral.pdf
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Table A-2: Summary Statistics of the Outcome and Explanatory Variables
All Years 1950-1966 1967-1982 1983-1998 1999-2014
Winning Percentages (Points)
Mean 0.5000 0.5000 0.5000 0.5000 0.5000
St.Dev. 0.4336 0.4490 0.4384 0.4297 0.4325
Min 0.0000 0.0000 0.0000 0.0000 0.0000
Max 1.0000 1.0000 1.0000 1.0000 1.0000
Obs 50804 2970 7990 14866 24978
Goal Difference
Mean 0.0000 0.0000 0.0000 0.0000 0.0000
St.Dev. 2.1868 2.5762 2.2716 2.1455 2.1326
Min -20.0000 -14.0000 -14.0000 -17.0000 -20.0000
Max 20.0000 14.0000 14.0000 17.0000 20.0000
Obs 50804 2970 7990 14866 24978
Log Population Ratio
Mean 0.0000 0.0000 0.0000 0.0000 0.0000
St.Dev. 2.0940 1.7661 1.9321 2.0823 2.1849
Min -9.1152 -6.9764 -8.6362 -9.1152 -8.4066
Max 9.1152 6.9764 8.6362 9.1152 8.4066
Obs 50804 2970 7990 14866 24978
Log GDP per capita Ratio
Mean -0.0000 -0.0000 0.0000 -0.0000 -0.0000
St.Dev. 1.2194 0.8994 1.1123 1.2150 1.2861
Min -5.7318 -3.4041 -5.1160 -4.9244 -5.7318
Max 5.7318 3.4041 5.1160 4.9244 5.7318
Obs 50804 2970 7990 14866 24978
Log Experience Ratio
Mean 0.0000 0.0000 0.0000 0.0000 0.0000
St.Dev. 1.0290 1.0613 1.0296 1.1804 0.9227
Min -6.4877 -4.0678 -5.5910 -6.4877 -6.1092
Max 6.4877 4.0678 5.5910 6.4877 6.1092
Obs 50804 2970 7990 14866 24978
Notes: The table presents summary statistics of the match-level data presented in the text. The years
from 1950 to 2014 can be divided into 4 four-year World Cup cycles. In terms of observations, every
game is counted twice, once from the perspective of country iand once from country j, to capture the
both the home advantage and the disadvantage of player in the opponent’s country in the subsequent
regressions.
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Table A-3: Game Outcome (Goal Difference) Regressed on Explanatory Factors
Panel A: By Types of Games
Dependent Var: (1) (2) (3) (4) (5)
Goal Difference All Games Friendlies Competitive Qualifiers World + Cont. Cup
home 0.589∗∗∗ 0.465∗∗∗ 0.766∗∗∗ 0.407∗∗∗ 0.774∗∗∗
(0.035) (0.042) (0.051) (0.090) (0.102)
away -0.629∗∗∗ -0.561∗∗∗ -0.675∗∗∗ -1.042∗∗∗ -0.582∗∗∗
(0.031) (0.037) (0.047) (0.083) (0.095)
lgdppcratio 0.136∗∗∗ 0.123∗∗∗ 0.147∗∗∗ 0.134∗∗∗ 0.192∗∗∗
(0.016) (0.019) (0.023) (0.025) (0.031)
lpopratio 0.168∗∗∗ 0.146∗∗∗ 0.205∗∗∗ 0.224∗∗∗ 0.111∗∗∗
(0.015) (0.013) (0.020) (0.022) (0.024)
lexpratio 0.657∗∗∗ 0.589∗∗∗ 0.675∗∗∗ 0.637∗∗∗ 0.716∗∗∗
(0.031) (0.030) (0.041) (0.042) (0.070)
Constant -0.016 0.346∗∗∗ -0.195∗∗∗ 0.145 -0.557∗∗∗
(0.033) (0.030) (0.053) (0.090) (0.039)
Country Dummies Yes Yes Yes Yes Yes
R2 0.274 0.213 0.356 0.388 0.252
Observations 50804 27708 23096 17784 5312
Countries 182 181 182 182 132
Panel B: By Time Period
Dependent Var: (1) (2) (3) (4) (5)
Goal Difference All Games 1950-1966 1967-1982 1983-1998 1999-2014
home 0.589∗∗∗ 0.693∗∗∗ 0.678∗∗∗ 0.617∗∗∗ 0.538∗∗∗
(0.035) (0.147) (0.088) (0.051) (0.035)
away -0.629∗∗∗ -0.694∗∗∗ -0.853∗∗∗ -0.633∗∗∗ -0.538∗∗∗
(0.031) (0.141) (0.073) (0.046) (0.040)
lgdppcratio 0.136∗∗∗ -0.142∗0.161∗∗∗ 0.198∗∗∗ 0.131∗∗∗
(0.016) (0.082) (0.041) (0.023) (0.019)
lpopratio 0.168∗∗∗ 0.214∗∗∗ 0.160∗∗∗ 0.182∗∗∗ 0.168∗∗∗
(0.015) (0.045) (0.023) (0.020) (0.017)
lexpratio 0.657∗∗∗ 0.892∗∗∗ 0.726∗∗∗ 0.552∗∗∗ 0.748∗∗∗
(0.031) (0.072) (0.036) (0.037) (0.052)
Constant -0.016 0.380∗∗∗ 0.675∗∗∗ -0.357∗∗∗ 0.093∗∗
(0.033) (0.127) (0.104) (0.053) (0.036)
Country Dummies Yes Yes Yes Yes Yes
R2 0.274 0.305 0.317 0.320 0.277
Observations 50804 2970 7990 14866 24978
Countries 182 86 130 175 182
Notes: Analogous to Table 1, the table presents OLS regression results of (2) with the goal difference
rather than the winning percentage as the dependent variable. See Table 1 for more details.
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Table A-4: Ratio Test Statistics for σ-Convergence in Win Percentage and Goal
Difference Within 4-year Cycles
Period NWin Percentages Goal Difference
ˆ
βˆσ2
1R-stat ˆ
βˆσ2
1R-stat
1955-1958 26 -0.4829 0.0393 -0.0473 -0.4169 1.6862 0.8472
1959-1962 29 -0.2975 0.0406 0.1944 -0.3812 1.2688 1.7653∗∗
1963-1966 44 -0.7092 0.0274 1.6663∗∗ -0.6390 0.6218 3.8155∗∗∗
1967-1970 61 -0.5349 0.0316 0.2524 -0.5413 0.9812 1.6188∗∗
1971-1974 80 -0.4409 0.0279 0.8135 -0.3567 0.9621 0.7557
1975-1978 88 -0.3801 0.0344 -0.2552 -0.2816 1.2167 0.0799
1979-1982 95 -0.4344 0.0268 1.8086∗∗ -0.4320 0.8802 2.7708∗∗∗
1983-1986 103 -0.2962 0.0310 -0.7965 -0.2788 1.1284 -1.5246
1987-1990 107 -0.2749 0.0307 1.0206 -0.2902 0.8378 5.5443∗∗∗
1991-1994 111 -0.3816 0.0287 0.3875 -0.1547 1.5515 -4.3673
1995-1998 146 -0.3783 0.0249 1.3643∗-0.4231 0.9565 4.4460∗∗∗
1999-2002 165 -0.4177 0.0260 0.2007 -0.3885 1.0789 1.3555∗
2003-2006 169 -0.3263 0.0246 1.3327∗-0.3764 0.9171 4.5074∗∗∗
2007-2010 169 -0.3059 0.0233 0.5907 -0.2509 0.8761 0.5310
2011-2014 172 -0.3390 0.0227 0.2989 -0.2992 0.7239 2.0603∗∗
Notes: The table presents the variables and results of (5), computed for the respective periods. ***
p<0.01, ** p<0.05, * p<0.1.
Table A-5: Theil-Index of Inequality in Win Percentage Within Continental
Confederations, Sample 1 (76 countries)
Asia Africa America (N,C) America (South) Europe
1975-1978 0.1430 0.0439 0.0081 0.0764 0.0358
1979-1982 0.0805 0.0259 0.0140 0.0423 0.0233
1983-1986 0.0437 0.0155 0.0290 0.0683 0.0311
1987-1990 0.0630 0.0160 0.0764 0.0809 0.0310
1991-1994 0.0509 0.0233 0.0122 0.0540 0.0254
1995-1998 0.0249 0.0199 0.0180 0.0459 0.0207
1999-2002 0.0121 0.0127 0.0104 0.0334 0.0114
2003-2006 0.0165 0.0218 0.0431 0.0216 0.0135
2007-2010 0.0206 0.0237 0.0123 0.0301 0.0217
2011-2014 0.0139 0.0175 0.0137 0.0334 0.0097
Notes: In this sample Oceania only consists of one country (New Zealand), so that within-continental
inequality in performance is zero.
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Table A-6: Correlation of Countries’ Ranks in the Win Percentage Distribution over
Four-Year Cycles, Sample 1 (76 countries)
Variables 1975-78 1979-82 1983-86 1987-90 1991-94 1995-98 1999-02 2003-06 2007-10 2011-14
1975-78 1.00
1979-82 0.54 1.00
1983-86 0.54 0.51 1.00
1987-90 0.50 0.36 0.61 1.00
1991-94 0.39 0.27 0.47 0.62 1.00
1995-98 0.53 0.36 0.53 0.43 0.61 1.00
1999-02 0.43 0.22 0.39 0.46 0.57 0.57 1.00
2003-06 0.52 0.33 0.52 0.57 0.60 0.57 0.73 1.00
2007-10 0.41 0.17 0.46 0.45 0.57 0.53 0.70 0.73 1.00
2011-14 0.48 0.37 0.48 0.59 0.63 0.58 0.55 0.68 0.65 1.00
Table A-7: Regional Matches Involving Teams from the Various Federations, 1950-2014
Asia Africa America (N,C) America (S) Oceania Europe
Asia 9586 691 161 202 130 788
Africa 691 12524 99 124 9 460
America (N,C) 161 99 4214 666 17 456
America (S) 202 124 666 3454 15 711
Oceania 130 9 17 15 32 26
Europe 788 460 456 711 26 11884
Notes: The table shows the number of international matches pitting Team 1 from the regional federation
in the row against Team 2 from the regional federation in the column. The continental confederations are
AFC (Asia), CAF (Africa), CONCACAF (North and Middle America and the Caribbean), CONMEBOL
(South America), OFC (Oceania) and UEFA (Europe).
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Appendix B Online Appendix
B.1 The Growth of International Competition
Association football (soccer) is a game whose rules were first written down in 1863 in
England. Originally played only between local clubs, the first “international” match
was played between England and Scotland in 1872. The game spread rapidly and by
the end of the nineteenth century most European and South American nations had
established national associations to administer the game, thus facilitating competition
between national teams. In 1904 FIFA was created as an organization to manage soccer
relations between countries, and in 1930 the FIFA World Cup was first played, with 13
national teams competing. In the first half of the 20th century, there were still rather few
international games; under 2,200 were recorded between 1900 and 1940, an average of 54
per year, and almost all of these involved European and South American countries. But
in the second half of the 20th century, this has changed, turning soccer into a truly global
industry: Since 1950 there have been over 36,000 games played between men’s national
soccer teams, an average of over 500 per year, see Figure B-1.
Figure B-1: The Growth of International Soccer Competition
0 200 400 600 800 1000
Total Games per Year
0 50 100 150 200
Teams
1950 1960 1970 1980 1990 2000 2010
Years
Teams Games
Notes: The graph shows yearly figures on the number of international games played between national
teams as well as the number of internationally active national teams. Apart from the steady increase
the graphs exhibit cyclical peaks in the years of a FIFA World Cup.
Table B-1 lists the years since 1950 in which a FIFA World Cup took place and
the number of participating teams from each continental association. Teams from
CONMEBOL, the South American association, and UEFA, the European one, where
the game first took root, have tended to dominate the World Cup; in fact, no team from
outside these associations has ever won the Cup. Teams from outside the big two regional
confederations have reached the semi-finals twice: the USA in the first World Cup in 1930
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(contested by only 13 nations), and South Korea in 2002. But FIFA has consciously tried
to expand opportunities for the smaller associations. While each continent controls its
own qualifying process, the number of slots allocated to each continental association is
agreed centrally. The share allocated to UEFA and CONMEBOL has shrunk considerably
over time, largely through expansion of the number of participating teams. A further
expansion of 16 teams has been agreed for the 2026 World Cup, which will reduce the
European and South American share further, possibly to as little as 46 %. Critics have
argued that the distribution remains unfair and should reflect global population shares
more accurately. The counter argument is that for a given quality of team it is harder to
qualify through UEFA or CONMEBOL than any other federation.
Table B-1: Number of Countries Qualifying for the FIFA World Cup 1950-2014
World Cup AFC CAF CONCA- CON- OFC UEFA Total UEFA + CONME-
CAF MEBOL BOL share
(Asia) (Africa) (Central+ (South (Oceania) (Europe)
North Am.) America)
1950 1 0 2 5* 0 7 15 0.800
1954 1 0 1 2 0 12* 16 0.875
1958 0 0 1 3 0 12* 16 0.938
1962 0 0 1 5* 0 10 16 0.938
1966 1 0 1 4 0 10* 16 0.813
1970 0 1 2* 3 0 10 16 0.813
1974 1 1 1 4 0 9* 16 0.813
1978 1 1 1 3* 0 10 16 0.813
1982 1 2 2 4 1 14* 24 0.750
1986 2 2 2* 4 0 14 24 0.750
1990 2 2 2 4 0 14* 24 0.750
1994 2 3 2* 4 0 13 24 0.708
1998 4 5 3 5 0 15* 32 0.625
2002 4* 5 3 5 0 15 32 0.625
2006 4 5 4 4 1 14* 32 0.563
2010 4 6* 3 5 1 13 32 0.563
2014 4 5 4 6* 0 13 32 0.594
Notes: For each FIFA World Cup, the table lists the number of participating teams by continental
federation. The * indicates the host federation. The CONCACAF federation includes Central and
North America as well as the Caribbean. Note that the table shows the number of teams that actually
qualified; in some cases the final slots were allocated by inter-continental play-offs.
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B.2 Beta-Convergence Results: Other Performance Variables
and Subsamples.
Analogous to the test for β-convergence countries’ winning percentages as explained in
Section 4.1 in the text, we here conduct the analysis with other performance variables
and subsamples. The following tables are all structured similarly and regress the change
in performance of country iin cycle ton its past performance:
∆yit =α+β·yi,t−1+it,(B-1)
Panel A, col. (1) runs this regression for unconditional convergence, col. (2) tests for
conditional convergence by including additional controls. Col. (3) includes regional
confederation dummies. Col. (4) and Col. (5) test for, respectively, unconditional and
conditional convergence using country fixed effects.
Panel B estimates
yit =αi+ (β+ 1)
| {z }
ρ
·yi,t−1+it,(B-2)
with specific short Tdynamic panel data model estimation techniques, Arellano-Bond
GMM in col. (1) and col. (2) and Unconditional Quasi-Maximum Likelihood in col. (3)
and col. (4).
Panel C conducts weighted regressions. Col. (1) and col. (2) use time weights
wit = (¯ni/nit)1/2, where nit is the number of games played by country iin cycle tand ¯ni
is the average number of games by iover all cycles. In col. (3) and col. (4) dominance
weights are used, reflecting how often country iplayed against an opponent from the
two confederations, Europe and South America.
In particular, we conduct the analysis with different performance variables and sub-
samples and compare the results to those in the main text. Using the goal difference
(Table B-2) yields very similar coefficients as the winning percentage. Concerns that
convergence results might be driven by stronger teams’ anecdotically worse performance
at friendlies, when they often give weaker players a chance, can be alleviated by Table B-
3: restricting the sample to competitive games gives even stronger convergence results,
in line with our previous analysis that ’friendlies’ and competitive games are mostly
decided by the same factors. In Table B-4 we consider only the teams that were active
from the first cycle (1950-1954) onwards, to exclude the effect of newcomers. Obviously,
the national teams entering the international stage and catching up has contributed to the
overall convergence effect, but we also observe unconditional and conditional convergence
among the 42 teams which were present throughout the years. Finally, we split the sample
into the time periods 1950-1982 (the first eight cycles, Table B-5) and 1983-2014 (the last
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eight cycles, Table B-6). While we find significant convergence results throughout time,
there is no indication that they have become stronger in later years. This is confirmed
by Table B-7, which shows that the regression coefficients are clearly negative in each
four-year cycle but their magnitude has slightly decreased rather than increased.
We conclude from this analysis that our results of β-convergence in national teams’
performance is a result that is robust across econometric specifications, performance
variables, sub-samples and time periods.
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Table B-2: Beta-Convergence Regression Results, Goal Difference (GD)
Panel A: Panel Data Regression
Dep Var: ∆ GD (1) (2) (3) (4) (5)
l.GD -0.456∗∗∗ -0.587∗∗∗ -0.594∗∗∗ -0.796∗∗∗ -0.859∗∗∗
(0.030) (0.033) (0.033) (0.030) (0.032)
lgdppcratio 0.043 0.048 0.083
(0.029) (0.030) (0.054)
lpopratio 0.095∗∗∗ 0.098∗∗∗ 0.026
(0.024) (0.023) (0.063)
lexpratio 0.337∗∗∗ 0.334∗∗∗ 0.502∗∗∗
(0.044) (0.044) (0.065)
Constant -0.049∗-0.032 -0.113∗-0.140∗∗∗ -0.098∗∗∗
(0.026) (0.024) (0.066) (0.008) (0.011)
Confed Dummies No No Yes No No
Country FE No No No Yes Yes
R2 0.367 0.453 0.454 0.554 0.600
Observations 1644 1644 1644 1644 1644
Countries 178 178 178 178 178
Panel B: Fixed Effects Short TDynamic Panel Estimation
(1) (2) (3) (4)
Dep Var: GD (GMM) (GMM) (QML) (QML)
l.GD 0.234∗∗∗ 0.128∗∗ 0.267∗∗∗ 0.187∗∗∗
(0.057) (0.058) (0.045) (0.038)
lgdppcratio 0.062 0.148∗∗
(0.074) (0.057)
lpopratio 0.114∗0.045
(0.060) (0.047)
lexpratio 0.597∗∗∗ 0.433∗∗∗
(0.079) (0.066)
Constant -0.132∗∗∗ -0.077∗-0.055 -0.046
(0.047) (0.041) (0.045) (0.040)
AR1 -6.692 -6.072
AR2 2.596 1.807
Observations 1484 1484 1372 1372
Countries 176 176 139 139
Panel C: Weighted Regressions
(1) (2) (3) (4)
Dep Var: ∆ GD (Time W) (Time W) (Dom W) (Dom W)
l.GD -0.474∗∗∗ -0.068∗∗∗ -0.287∗∗∗ -0.463∗∗∗
(0.030) (0.005) (0.037) (0.043)
lgdppcratio 0.007 0.048
(0.005) (0.057)
lpopratio 0.012∗∗∗ 0.149∗∗∗
(0.003) (0.027)
lexpratio 0.046∗∗∗ 0.186∗∗∗
(0.007) (0.060)
Constant -0.065∗∗ -0.007 0.046 0.092∗
(0.029) (0.008) (0.028) (0.052)
R2 0.381 0.223 0.187 0.307
Observations 1644 1644 599 599
Countries 178 178 56 56
Notes: Analogous to Table 2 in the paper, the table presents beta convergence regressions of (B-1) (Panel
A and C) and (B-2) (Panel B) when the goal difference is used as performance variable. See the text in
this Online Appendix for more details.
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Table B-3: Beta-Convergence Regression Results, Competitive Games
Panel A: Panel Data Regression
Dep Var: ∆ points (1) (2) (3) (4) (5)
l.points -0.453∗∗∗ -0.609∗∗∗ -0.617∗∗∗ -0.918∗∗∗ -0.947∗∗∗
(0.029) (0.033) (0.033) (0.030) (0.029)
lgdppcratio 0.024∗∗∗ 0.024∗∗∗ 0.015
(0.006) (0.006) (0.010)
lpopratio 0.018∗∗∗ 0.018∗∗∗ 0.009
(0.005) (0.005) (0.008)
lexpratio 0.066∗∗∗ 0.067∗∗∗ 0.075∗∗∗
(0.008) (0.008) (0.011)
Constant 0.219∗∗∗ 0.294∗∗∗ 0.277∗∗∗ 0.431∗∗∗ 0.447∗∗∗
(0.016) (0.018) (0.021) (0.014) (0.014)
Confed Dummies No No Yes No No
Country FE No No No Yes Yes
R2 0.276 0.386 0.388 0.527 0.563
Observations 1530 1530 1530 1530 1530
Countries 176 176 176 176 176
Panel B: Fixed Effects Short TDynamic Panel Estimation
(1) (2) (3) (4)
Dep Var: points (GMM) (GMM) (QML) (QML)
l.points 0.045 0.101∗0.151∗∗∗ 0.116∗∗∗
(0.052) (0.052) (0.035) (0.033)
lgdppcratio 0.036∗∗∗ 0.017
(0.014) (0.010)
lpopratio 0.016∗0.005
(0.009) (0.007)
lexpratio 0.069∗∗∗ 0.068∗∗∗
(0.014) (0.011)
Constant 0.448∗∗∗ 0.427∗∗∗ 0.416∗∗∗ 0.431∗∗∗
(0.027) (0.025) (0.022) (0.020)
AR1 -5.742 -6.221
AR2 -1.130 -0.449
Observations 1354 1354 1292 1292
Countries 168 168 140 140
Panel C: Weighted Regressions
(1) (2) (3) (4)
Dep Var: ∆ points (Time W) (Time W) (Dom W) (Dom W)
l.points -0.479∗∗∗ -0.652∗∗∗ -0.349∗∗∗ -0.570∗∗∗
(0.031) (0.036) (0.048) (0.057)
lgdppcratio 0.023∗∗∗ 0.021
(0.007) (0.014)
lpopratio 0.019∗∗∗ 0.036∗∗∗
(0.005) (0.007)
lexpratio 0.073∗∗∗ 0.049∗∗∗
(0.010) (0.014)
Constant 0.230∗∗∗ 0.296∗∗∗ 0.185∗∗∗ 0.301∗∗∗
(0.017) (0.023) (0.029) (0.031)
R2 0.287 0.406 0.205 0.349
Observations 1530 1530 579 579
Countries 176 176 56 56
Notes: Analogous to Table 2 in the paper, the table presents beta convergence regressions of (B-1)
(Panel A and C) and (B-2) (Panel B) when the sample is restricted only to competitive games, excluding
’friendlies’. See the text in this Online Appendix for more details.
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Table B-4: Beta-Convergence Regression Results, Only National Teams Present Since
1950
Panel A: Panel Data Regression
Dep Var: ∆ points (1) (2) (3) (4) (5)
l.points -0.384∗∗∗ -0.537∗∗∗ -0.553∗∗∗ -0.753∗∗∗ -0.790∗∗∗
(0.058) (0.057) (0.053) (0.054) (0.057)
lgdppcratio -0.002 -0.001 -0.003
(0.011) (0.012) (0.016)
lpopratio 0.015∗∗ 0.020∗∗∗ -0.005
(0.006) (0.006) (0.019)
lexpratio 0.080∗∗∗ 0.077∗∗∗ 0.096∗∗∗
(0.012) (0.014) (0.019)
Constant 0.203∗∗∗ 0.262∗∗∗ 0.234∗∗∗ 0.392∗∗∗ 0.394∗∗∗
(0.033) (0.031) (0.037) (0.028) (0.026)
Confed Dummies No No Yes No No
Country FE No No No Yes Yes
R2 0.234 0.339 0.345 0.433 0.473
Observations 574 574 574 574 574
Countries 42 42 42 42 42
Panel B: Fixed Effects Short TDynamic Panel Estimation
(1) (2) (3) (4)
Dep Var: points (GMM) (GMM) (QML) (QML)
l.points -0.006 -0.011 0.265∗∗∗ 0.201∗∗∗
(0.059) (0.056) (0.056) (0.045)
lgdppcratio 0.018 0.014
(0.022) (0.017)
lpopratio -0.001 0.001
(0.015) (0.015)
lexpratio 0.084∗∗∗ 0.095∗∗∗
(0.025) (0.024)
Constant 0.521∗∗∗ 0.505∗∗∗ 0.397∗∗∗ 0.403∗∗∗
(0.037) (0.037) (0.037) (0.029)
AR1 -4.729 -4.885
AR2 0.116 -0.0618
Observations 538 538 483 483
Countries 42 42 34 34
Panel C: Weighted Regressions
(1) (2) (3) (4)
Dep Var: ∆ points (Time W) (Time W) (Dom W) (Dom W)
l.points -0.439∗∗∗ -0.778∗∗∗ -0.339∗∗∗ -0.583∗∗∗
(0.117) (0.129) (0.067) (0.063)
lgdppcratio 0.083 0.004
(0.045) (0.022)
lpopratio 0.069∗∗ 0.031∗∗∗
(0.020) (0.006)
lexpratio 0.028 0.077∗∗∗
(0.036) (0.019)
Constant 0.237∗∗∗ 0.295∗∗∗ 0.193∗∗∗ 0.308∗∗∗
(0.067) (0.046) (0.039) (0.037)
R2 0.193 0.365 0.187 0.318
Observations 112 112 398 398
Countries 8 8 27 27
Notes: Analogous to Table 2 in the paper, the table presents beta convergence regressions of (B-1) (Panel
A and C) and (B-2) (Panel B) when the sample is restricted to the countries which played matches from
the first four-year cycle onwards. See the text in this Online Appendix for more details.
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Table B-5: Beta-Convergence Regression Results, Period 1 (1950-1982)
Panel A: Panel Data Regression
Dep Var: ∆ points (1) (2) (3) (4) (5)
l.points -0.565∗∗∗ -0.735∗∗∗ -0.741∗∗∗ -0.993∗∗∗ -1.011∗∗∗
(0.043) (0.038) (0.040) (0.044) (0.045)
lgdppcratio 0.008 0.007 0.049∗
(0.010) (0.010) (0.026)
lpopratio 0.021∗∗∗ 0.022∗∗∗ 0.034∗
(0.007) (0.007) (0.019)
lexpratio 0.092∗∗∗ 0.093∗∗∗ 0.053∗∗
(0.012) (0.013) (0.021)
Constant 0.274∗∗∗ 0.362∗∗∗ 0.349∗∗∗ 0.474∗∗∗ 0.490∗∗∗
(0.023) (0.021) (0.027) (0.020) (0.022)
Confed Dummies No No Yes No No
Country FE No No No Yes Yes
R2 0.403 0.532 0.530 0.648 0.667
Observations 474 474 474 474 474
Countries 108 108 108 108 108
Panel B: Fixed Effects Short TDynamic Panel Estimation
(1) (2) (3) (4)
Dep Var: points (GMM) (GMM) (QML) (QML)
l.points -0.106 -0.045 0.093∗∗ 0.067
(0.076) (0.085) (0.045) (0.044)
lgdppcratio 0.032 0.038
(0.031) (0.029)
lpopratio 0.020 0.021
(0.018) (0.019)
lexpratio 0.074∗∗∗ 0.065∗∗∗
(0.027) (0.021)
Constant 0.527∗∗∗ 0.506∗∗∗ 0.441∗∗∗ 0.455∗∗∗
(0.038) (0.040) (0.027) (0.025)
AR1 -2.989 -2.998
AR2 -1.608 -1.081
Observations 386 386 425 425
Countries 100 100 87 87
Panel C: Weighted Regressions
(1) (2) (3) (4)
Dep Var: ∆ points (Time W) (Time W) (Dom W) (Dom W)
l.points -0.547∗∗∗ -0.734∗∗∗ -0.412∗∗∗ -0.740∗∗∗
(0.053) (0.047) (0.066) (0.081)
lgdppcratio 0.020∗0.007
(0.012) (0.019)
lpopratio 0.022∗∗∗ 0.039∗∗∗
(0.008) (0.011)
lexpratio 0.085∗∗∗ 0.094∗∗∗
(0.014) (0.019)
Constant 0.265∗∗∗ 0.354∗∗∗ 0.217∗∗∗ 0.375∗∗∗
(0.029) (0.038) (0.036) (0.044)
R2 0.388 0.512 0.237 0.420
Observations 346 346 215 215
Countries 78 78 36 36
Notes: Analogous to Table 2 in the paper, the table presents beta convergence regressions of (B-1) (Panel
A and C) and (B-2) (Panel B) when the sample period is restricted 1950-1982, the first eight four-year
cycles. See the text in this Online Appendix for more details.
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Table B-6: Beta-Convergence Regression Results, Period 2 (1983-2014)
Panel A: Panel Data Regression
Dep Var: ∆ points (1) (2) (3) (4) (5)
lagpts -0.355∗∗∗ -0.494∗∗∗ -0.503∗∗∗ -0.902∗∗∗ -0.959∗∗∗
(0.028) (0.038) (0.038) (0.040) (0.037)
(mean) lgdppcratio 0.012∗∗ 0.013∗∗ 0.019∗∗
(0.005) (0.005) (0.009)
(mean) lpopratio 0.015∗∗∗ 0.016∗∗∗ 0.021∗∗
(0.004) (0.004) (0.009)
(mean) lexpratio 0.041∗∗∗ 0.040∗∗∗ 0.066∗∗∗
(0.007) (0.007) (0.012)
Constant 0.170∗∗∗ 0.241∗∗∗ 0.238∗∗∗ 0.417∗∗∗ 0.456∗∗∗
(0.013) (0.019) (0.021) (0.018) (0.017)
Confed Dummies No No Yes No No
Country FE No No No Yes Yes
R2 0.223 0.304 0.305 0.516 0.558
Observations 1170 1170 1170 1170 1170
Countries 177 177 177 177 177
Panel B: Fixed Effects Short TDynamic Panel Estimation
(1) (2) (3) (4)
Dep Var: points (GMM) (GMM) (QML) (QML)
l.points -0.109 -0.019 0.230∗∗∗ 0.180∗∗∗
(0.081) (0.078) (0.051) (0.047)
lgdppcratio 0.024∗0.013
(0.014) (0.010)
lpopratio 0.031∗∗∗ 0.018∗∗
(0.011) (0.009)
lexpratio 0.049∗∗∗ 0.054∗∗∗
(0.016) (0.013)
Constant 0.510∗∗∗ 0.483∗∗∗ 0.363∗∗∗ 0.393∗∗∗
(0.036) (0.035) (0.026) (0.024)
AR1 -4.266 -5.528
AR2 0.459 1.211
Observations 897 897 1007 1007
Countries 175 175 161 161
Panel C: Weighted Regressions
(1) (2) (3) (4)
Dep Var: ∆ points (Time W) (Time W) (Dom W) (Dom W)
lagpts -0.353∗∗∗ -0.493∗∗∗ -0.259∗∗∗ -0.417∗∗∗
(0.027) (0.038) (0.038) (0.048)
(mean) lgdppcratio 0.012∗∗ 0.019
(0.006) (0.012)
(mean) lpopratio 0.015∗∗∗ 0.027∗∗∗
(0.004) (0.006)
(mean) lexpratio 0.040∗∗∗ 0.024∗∗
(0.008) (0.011)
Constant 0.168∗∗∗ 0.236∗∗∗ 0.138∗∗∗ 0.234∗∗∗
(0.013) (0.022) (0.021) (0.031)
R2 0.218 0.292 0.150 0.257
Observations 1170 1170 384 384
Countries 177 177 56 56
Notes: Analogous to Table 2 in the paper, the table presents beta convergence regressions of (B-1) (Panel
A and C) and (B-2) (Panel B) when the sample period is restricted 1983-2014, the last eight four-year
cycles. See the text in this Online Appendix for more details.
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Table B-7: Beta-Convergence Regression Results For Each Four-Year Cycle
Dep Var: ∆ points
1955-1958 1959-1962 1963-1966 1967-1970 1971-1974 1975-1978 1979-1982
lagpts -0.573∗∗ -0.643∗∗∗ -0.805∗∗∗ -0.572∗∗∗ -0.524∗∗∗ -0.429∗∗∗ -0.519∗∗∗
(0.208) (0.105) (0.087) (0.065) (0.081) (0.093) (0.073)
Constant 0.284∗∗ 0.319∗∗∗ 0.408∗∗∗ 0.284∗∗∗ 0.258∗∗∗ 0.196∗∗∗ 0.250∗∗∗
(0.127) (0.056) (0.050) (0.037) (0.045) (0.044) (0.034)
R2 0.214 0.537 0.582 0.431 0.343 0.248 0.428
Observations 29 39 50 74 91 92 99
Countries 29 39 50 74 91 92 99
1983-1986 1987-1990 1991-1994 1995-1998 1999-2002 2003-2006 2007-2010 2011-2014
lagpts -0.309∗∗∗ -0.336∗∗∗ -0.436∗∗∗ -0.369∗∗∗ -0.395∗∗∗ -0.326∗∗∗ -0.297∗∗∗ -0.339∗∗∗
(0.076) (0.068) (0.061) (0.051) (0.073) (0.067) (0.049) (0.060)
Constant 0.153∗∗∗ 0.160∗∗∗ 0.217∗∗∗ 0.178∗∗∗ 0.190∗∗∗ 0.150∗∗∗ 0.138∗∗∗ 0.160∗∗∗
(0.040) (0.036) (0.033) (0.025) (0.035) (0.034) (0.024) (0.031)
R2 0.134 0.214 0.335 0.261 0.238 0.190 0.172 0.191
Observations 105 110 119 155 170 169 170 172
Countries 105 110 119 155 170 169 170 172
Notes: The table presents the unconditional beta regression results of (B-1) analogous to Table 2, Panel
A, column (1), for each four-year cycle separately.
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B.3 Histograms and Kernel Densities
We plot the histograms and kernel densities of both win percentage and goal difference
for each four-year cycle. The scale is the same for comparison. As the Figure B-2 and
Figure B-3 show, the histograms mostly seem unimodal. Over time, they become taller
and thinner, which is in accordance with our finding on σ-convergence. Note that the
number of countries varies. For a complete distributional analysis with balanced samples
of countries, see the main text.
Figure B-2: Histograms and Kernel Density Plots: Win Percentage per World Cup
Cycle (varying numbers of countries)
0 1 2 3 4
0 .2 .4 .6 .8 1
1950−1954
0 1 2 3 4
0 .2 .4 .6 .8 1
1955−1958
0 1 2 3 4
0 .2 .4 .6 .8 1
1959−1962
0 1 2 3 4
0 .2 .4 .6 .8 1
1963−1966
0 1 2 3 4
0 .2 .4 .6 .8 1
1967−1970
0 1 2 3 4
0 .2 .4 .6 .8 1
1971−1974
0 1 2 3 4
0 .2 .4 .6 .8 1
1975−1978
0 1 2 3 4
0 .2 .4 .6 .8 1
1979−1982
0 1 2 3 4
0 .2 .4 .6 .8 1
1983−1986
0 1 2 3 4
0 .2 .4 .6 .8 1
1987−1990
0 1 2 3 4
0 .2 .4 .6 .8 1
1991−1994
0 1 2 3 4
0 .2 .4 .6 .8 1
1995−1998
0 1 2 3 4
0 .2 .4 .6 .8 1
1999−2002
0 1 2 3 4
0 .2 .4 .6 .8 1
2003−2006
0 1 2 3 4
0 .2 .4 .6 .8 1
2007−2010
0 1 2 3 4
0 .2 .4 .6 .8 1
2011−2014
Histogram and Kernel Density Estimates
Win Percentage by 4−year cycle
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Figure B-3: Histograms and Kernel Density Plots: Goal Difference per World Cup
Cycle (varying numbers of countries)
0 .2 .4 .6
−10 −5 0 5
1950−1954
0 .2 .4 .6
−10 −5 0 5
1955−1958
0 .2 .4 .6
−10 −5 0 5
1959−1962
0 .2 .4 .6
−10 −5 0 5
1963−1966
0 .2 .4 .6
−10 −5 0 5
1967−1970
0 .2 .4 .6
−10 −5 0 5
1971−1974
0 .2 .4 .6
−10 −5 0 5
1975−1978
0 .2 .4 .6
−10 −5 0 5
1979−1982
0 .2 .4 .6
−10 −5 0 5
1983−1986
0 .2 .4 .6
−10 −5 0 5
1987−1990
0 .2 .4 .6
−10 −5 0 5
1991−1994
0 .2 .4 .6
−10 −5 0 5
1995−1998
0 .2 .4 .6
−10 −5 0 5
1999−2002
0 .2 .4 .6
−10 −5 0 5
2003−2006
0 .2 .4 .6
−10 −5 0 5
2007−2010
0 .2 .4 .6
−10 −5 0 5
2011−2014
Histogram and Kernel Density Estimates
Goal Difference by 4−year cycle
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B.4 Distributional Analysis with Different Samples
Here we repeat the distributional analysis, which the main text conducted with Sample 1
(76 countries and 10 four-year cycles, 1975-2014). We consider the shorter Sample 2 (127
countries and 6 four-year cycles, 1990-2014) as well as an extended Sample 3 (Sample 1
including countries with less than 1m inhabitants, in total 86 countries).
Table B-8 and Table B-9 describe the evolution of the distribution of win percentages
and goal differences for both samples according to various characteristics. While Sample
2 behaves very similarly to Sample 1 from the main text in terms of the reduction of
standard deviation, skewness and kurtosis, we see that the higher moments remain high
for Sample 3. The distribution including tiny countries remains relatively skewed and
long-tailed so that the Jarque-Bera null hypothesis of Gaussianity is rejected. This is also
visible in the kernel densities Figure B-4. Still, we have observed convergence across all
countries, and also within Sample 3, there is a clear decrease in performance inequality
in terms of the Gini coefficient (last column of Table B-9 ). Our conclusion is therefore
that very small football nations face significant obstacles due to scarce resources in terms
of population and wealth. This effect is, however, not strong enough to affect the overall
result of worldwide convergence in performance.
Table B-8: Distribution of Points and Goal Difference Sample 2 (127 countries)
Panel a) Distribution of Win Percentage
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Mean St.Dev. Skew Kurt JB pvalue Unimod pvalue CC Ind. Pola Gini
1991-94 0.4752 0.1668 -0.5967 2.9474 0.0280 0.1433 0.3313 0.1482 0.1963
1995-98 0.4858 0.1480 -0.4899 3.3679 0.0460 0.9567 0.1948 0.1071 0.1686
1999-02 0.4986 0.1356 -0.7987 3.5606 0.0062 0.3633 0.3473 0.1110 0.1498
2003-06 0.4959 0.1394 -0.2458 2.2911 0.0941 0.3667 0.3403 0.1328 0.1602
2007-10 0.5007 0.1310 0.0276 3.2144 0.5000 0.5067 0.2732 0.1073 0.1459
2011-14 0.5003 0.1301 -0.2388 2.5107 0.2149 0.5300 0.2967 0.1168 0.1474
Panel b) Distribution of Goal Differences
(1) (2) (3) (4) (5) (6) (7)
Mean St.Dev. Skew Kurt JB pvalue Unimod pvalue CC Ind.
1991-94 -0.1545 1.0823 -1.4467 6.0484 0.0010 0.3267 0.3006
1995-98 -0.0451 0.8217 -0.7569 3.8306 0.0057 0.2700 0.3563
1999-02 0.0427 0.7578 -1.0645 5.1369 0.0010 0.4567 0.2709
2003-06 -0.0177 0.7381 -0.5354 3.2609 0.0379 0.8633 0.2246
2007-10 0.0188 0.6426 -0.5112 3.6708 0.0255 0.7667 0.2219
2011-14 0.0020 0.6497 -0.1382 2.3739 0.2141 0.4900 0.2899
Notes: The analysis is based on a balanced sample of 127 countries (Sample 2) with more than 1m
inhabitants throughout the sample period. Columns 1-4 report the distributional moments mean,
standard deviation, skewness and kurtosis. Column 5 contains the p-values of the Jarque Bera test
with the null hypothesis being the Gaussian distribution. Column 6 shows the p-values of Silverman’s
(1981) multimodality test with the null hypothesis being a unimodal distribution. Column 7 present the
club convergence indicator by Krause (2017), Column 8 the bi-polarization index by Wolfson (1994) and
Column 9 the Gini coefficient as a measure of inequality. Due to the presence of negative values in the
goal differences, Wolfson’s (1994) bi-polarization index and the Gini coefficient cannot be computed for
this data.
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Table B-9: Distribution of Points and Goal Difference Sample 3 (86 countries, including
those with less than 1m inhabitants)
Panel a) Distribution of Win Percentage
(1) (2) (3) (4) (5) (6) (7) (8) (9)
Mean St.Dev. Skew Kurt JB pvalue Unimod pvalue CC Ind. Pola Gini
1975-78 0.4690 0.1888 -0.3993 2.7193 0.1802 0.7333 0.2848 0.1807 0.2260
1979-82 0.4856 0.1573 -0.4490 3.4461 0.0988 0.6300 0.2738 0.1263 0.1781
1983-86 0.5045 0.1537 -0.9286 3.6328 0.0082 0.8933 0.2383 0.1183 0.1651
1987-90 0.4970 0.1582 -0.6722 3.0560 0.0359 0.4567 0.3186 0.1321 0.1757
1991-94 0.5074 0.1443 -0.6202 2.9253 0.0473 0.3700 0.3535 0.1385 0.1584
1995-98 0.5159 0.1341 -0.4774 3.2503 0.1045 0.9733 0.2086 0.1059 0.1437
1999-02 0.5292 0.1160 -0.8369 4.7137 0.0033 0.1967 0.3952 0.1061 0.1199
2003-06 0.5253 0.1360 -0.7245 3.7247 0.0182 0.1300 0.4101 0.1232 0.1431
2007-10 0.5222 0.1356 -0.3753 3.7377 0.0839 0.9900 0.1797 0.1048 0.1422
2011-14 0.5272 0.1232 -0.5948 3.4196 0.0450 0.4667 0.3361 0.1020 0.1289
Panel b) Distribution of Goal Differences
(1) (2) (3) (4) (5) (6) (7)
Mean St.Dev. Skew Kurt JB pvalue Unimod pvalue CC Ind.
1975-78 -0.1622 1.1141 -0.9871 3.8775 0.0053 0.2033 0.4277
1979-82 -0.0947 0.9184 -0.7554 3.9015 0.0130 0.3000 0.3348
1983-86 0.0685 0.8227 -1.0952 4.9705 0.0011 0.6333 0.2617
1987-90 -0.0241 0.7702 -0.8152 3.5144 0.0147 0.4600 0.3250
1991-94 0.1020 0.7827 -0.9667 4.7886 0.0020 0.7833 0.2518
1995-98 0.1257 0.7142 -0.5727 3.7947 0.0317 0.9633 0.1934
1999-02 0.1973 0.6291 -0.7496 4.9710 0.0028 0.2033 0.3495
2003-06 0.1614 0.6953 -1.0305 5.2054 0.0010 0.8167 0.2348
2007-10 0.1124 0.6660 -0.7816 4.0398 0.0099 0.4967 0.2991
2011-14 0.1359 0.6138 -0.5612 3.6389 0.0415 0.5800 0.2843
Notes: The analysis is based on a balanced sample of 86 countries (Sample 3), which, in contrast to
Sample 1 includes those with less than 1m inhabitants. See Table B-8 for more details.
Figure B-4: Densities of Win Percentage and Goal Differences in Various Years, Sample
3 (86 Countries)
0 0.2 0.4 0.6 0.8 1
0
0.5
1
1.5
2
2.5
3
3.5
Win Percentage
Density Value
1975−78
1991−94
2011−14
−5 −4 −3 −2 −1 0 1 2 3 4
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Goal Difference
Density Value
1975−78
1991−94
2011−14
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ECINEQ WP 2017 - 453 December 2017