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in international competition seems to have stagnated in
recent years. Nonetheless, these results still suggest that
over the last four or five decades, the emerging nations of
Asia and Africa appear to have improved relative to the
established powers of Europe and
South America – consistent with
convergence.
Formal testing for convergence
usually relies on a simple statistical
model. If there is convergence, we
should observe that changes in performance (“growth”) are inversely
related to historical levels of performance. In the context of soccer
results, this should mean that teams
with low win percentages in the past
should increase their win percentage,
while teams with high win percentages in the past should stagnate and
decline. An alternative measure
of performance is goal difference.
Winning teams have a positive goal
difference on average and losing
teams a negative goal difference,
but even a losing team can be getting better if the absolute size of
the goal difference is diminishing.
To estimate this effect, the average performance of national teams
across seven eight-year cycles is
calculated, starting from the years
from 1955-1962 up until 20032010 (these cycles coincide with
two FIFA World Cups). Eight year
cycles ensure that enough games
are captured in each measure of
performance to provide a reasonable estimate.
Figure 3 charts the relationship
between the level (on the horizontal
axis) and the change(on the vertical
axis) of win percentage and of goal
difference for each country.
The solid lines in each chart represent the regression line, the most accurate summary of
the relationship between the level and the change in the
variable. The fact that in both charts the regression line
slopes downward from left to right implies that there is
indeed convergence in international soccer results for both
win percentage and goal difference. The further to the
left on the chart (the worse results were in the past) then
the higher up the chart the country will be (the better the
improvement in results).
Further analysis shows that these patterns hold up
when the data is broken down into subperiods, when only
games played between teams from different federations
are considered, and when only competitive games (e.g.
44
in the World Cup) are included and “friendly” games
are excluded. Recall that this data suggests that there is
unconditional convergence-the weaker teams appear to
be catching up regardless of the underlying conditions of
Figure 3
the nations concerned.
These results seem to lend strong support to the notion of convergence in international soccer results. However, this approach has been strongly challenged by several
researchers e.g. Quah (1996). They argue that results of
this type may simply be examples of Galton’s fallacy, or
regression to the mean. Galton, a biologist and statistician
of the 19th century, noted that tall fathers tended to have
shorter sons and short fathers tended to have taller sons.
The fallacy is to think that this result necessarily implies
convergence – it can be the case that the tallest fathers
have shorter sons, but their sons in turn may still be tall
– while the sons of short fathers may be taller, but their
H A R V A R D I N T E R N A T I O N A L R E V I E W • Summer 2014