I have blogged on concentration ratios before and currently covering it with my A2 class. This topic can be a multiple-choice question or part of a market structures essay/data response.
The concentration ratio is the percentage of market share taken up by the largest firms. It could be a 3 firm concentration ratio (market share of 3 biggest) or 5 firms concentration ratio. Concentration ratios are used to determine the market structure and competitiveness of the market. The most commonly used are 4, 5 or 8 firm concentration ratios which measure the proportion of the market’s output provided by the largest 4, 5 or 8 firms.
Example of a hypothetical concentration ratio. The following are the annual sales, in $m, of the six firms in a hypothetical market:
Firm A = 56 – Firm B = 43 – Firm C = 22 – Firm D = 12 – Firm E = 3 – Firm F = 1
In this hypothetical case, the 3-firm concentration ratio is 88.3%, that is 121/137 x 100.
HHI and European Football
However, we can apply a similar calculation to measure the concentration of football league championships. The Herfindahl-Hirschman Index (HHI) was originally developed to measure the concentration of firms in an industry, but it has been used in football. To work out the HHI (see equation) you count the number of championships a team won (Ci) within a given time period, dividing by the number of years in the period (N), squaring the fraction, and adding the fractions for all teams.
If the HHI is a maximum 1 this indicates a perfect imbalance and one team has been champion for all years. The minimum HHI value is 0.1 and this means that there has been a different winner each year. Below is the HHI in various European leagues between 2012-13 to 2021-22.
Distribution of championships in European Leagues – 2012-13 to 2021-22 (10 years)
From the above table this to the big football leagues in Europe we see that the distribution of championships is high skewed toward a few dominant teams. In all four leagues one team has won at least 5 championships over the 10 years with Bayern Munich being totally dominant in the Bundesliga winning all 10 – HHI = 1. In a lot of cases the runner-up in these leagues is also featured as a championship winner. La Liga and the EPL had two teams that were 1st or 2nd in most years – Barcelona or Real Madrid, Manchester City or Liverpool. To the extent that teams can ‘buy championships’ because they have more revenue than their competitors, differences in market size and team popularity may be to blame. The EPL is the most balanced of the league with a HHI = 0.32 with La Liga HHI = 0.38. This lack of competitive balance combined with the extraordinary popularity of European football provides additional evidence that fans may be less concerned with the competitive balance that one might think.
Source: The Economics of Sport (2018) – M. Leeds, P. Von Allmen and V. Matheson
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