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The Actuary The magazine of the Institute & Faculty of Actuaries

Competition in football

How has competitiveness changed in professional football? Is professional football more competitive than it was, for example, in the 80s? An objective answer to such questions might seem rather difficult. However, economic theory can be used to investigate such questions.

To analyse competitiveness, I calculated a measure called the Herfindahl-Hirschman index (HHI). I then manipulated the index to measure the ‘competition level’.

The Herfindahl-Hirschman index
The HHI is a well-known measure of industrial competition and it helps gauge how competitive an industry is.

The HHI is calculated as the sum of the squares of market share. For example, a monopoly has a market share of 100%, and so the HHI for a monopoly is 10,000. For a very competitive industry, each firm has a very small market share and the HHI is close to zero. For identical firms in a duopoly, the HHI is 502 + 502 = 5,000.

As an intuitive guide, HHI levels below 1,000 indicate relatively strong competition. The competition authorities in the US use the 1,000 points benchmark when investigating market structure.

The HHI is calculated for the final distribution of points on the closing day of the football seasons (see table 1). Market share was taken to be the proportion of points that each team earned as a fraction of the total points that all teams earned.

Other measures of competition
An alternative measure to calculate is the standard deviation of the final distribution of points. For example, if the league is very competitive, we would expect that many teams would cluster around an average number of points and so the standard deviation would be low. If the league is less competitive, we would expect a higher spread of points (and a higher standard deviation). A less competitive league would be apparent if there were ‘runaway winners’ and teams which were convincingly relegated.

There are mathematical associations between the standard deviation and the HHI. This occurs because both measures involve the process of squaring. However, the primary weakness with the standard deviation is that the measure is influenced by the total number of teams in the league. The total number of teams in the top division of English football has varied between 20 and 22.

Nevertheless, the standard deviation does have a strong advantage. To gauge extreme outcomes, in principle it is possible to calculate the ‘confidence interval’ of the standard deviation. Some back-of-the-envelope calculations suggest that the 95% confidence interval for the standard deviation (when 20 teams play in the league) is between 9.7 and 18.6 points.

One feature I control for is the fact that the Football Association sets the number of teams participating in the top division. The HHI is influenced by the number of teams within the league. It is possible to calculate the theoretical minimum and maximum HHI given the participation of a particular number of teams. Table 1 provides the theoretical minimum and maximum HHI scores.

Table 1 also provides the ‘competition level’ and figure 1 is a plot of the ‘competition level’. The competition level is calculated by a linear interpolation of the actual HHI with respect to the theoretical maximum and minimum. The closer the actual HHI is to the theoretical minimum, the higher is the competition level.

Table 1 suggests that 1983 and 1993 were the most competitive years in the sample period. In these years Liverpool and Manchester United (respectively) were crowned English champions. In 1984 Liverpool went on to retain the championship and also become European champions. In 1994 Manchester United also retained the championship.

The least competitive years in the sample period were 1986 (when Liverpool became champions) and 2002 (when Arsenal was crowned champions). In the subsequent years of 1987 and 2003, Everton and Manchester United (respectively) won the league championship. Such history gives the intuitive explanation that higher levels of competition foster stronger teams.

Inspection of figure 1 suggests that competition in the top division of English football shows no obvious trend. There is some weak evidence to suggest that competition increased between the mid 1980s to the early 1990s and that competition began to fall from the mid-1990s. Competition can also be analysed from other angles. The top division of the football league may contain within itself -’top’, ‘middle’, and ‘bottom’ parts and such ‘mini-leagues’ need separate investigation. The Economist newspaper (April 2004) reported that in the 1990s the league had become ‘stickier’. Stickiness in the league position indicated that there had been a fall in competition levels because a football team’s relative success had become more predictable.

Data for football league championship results is available at www.krysstal.com.

The minimum HHI is calculated assuming all teams finish on equal points.

The maximum HHI is calculated assuming that one team wins all matches and all the other teams finish the season on the minimum number of points.

Hiten Nandha supports Liverpool Football Club and works for the Government Actuary’s Department