The Gini Coefficient as a Measure of League Competitiveness and Title Uncertainty

This article looks at the Gini coefficient and asks whether it can serve as a measure of league competitiveness. Does a lower Gini coefficient indicate more uncertainty in a title race? Are there any applications to futures betting?

Table data from the English Premier League, the English Championship, La Liga and the A-League are used. Could the Gini coefficient have predicted that Leicester City had a realistic chance of winning the English Premier League?

What is the Gini coefficient?

The Gini coefficient is a measure of inequality within a data set. It’s most common application is to measure income inequality within a country. A higher value denotes more inequality. The coefficient takes a value between 0 and 1, where 0 denotes perfect equality (every citizen has the exact same income) and 1 denotes perfect inequality (one person has all of the income).

In real life no country comes anywhere close to 0 or 1, with calculated Gini coefficients ranging from 0.24 and 0.49 in OECD countries.1 Learn more about Gini coefficients.

Application of the Gini coefficient to league standings

In the context of sport, the Gini coefficient can be calculated using historical table standings. While the calculated values may provide little insight on their own, comparisons can be made between leagues providing they share the same points scoring system and a comparable number of teams. If a few teams dominate the league, as is the case in La Liga, then we would expect a higher Gini coefficient because the top sides accumulate more league points than table-topping teams in other leagues.

Another possible use of the Gini coefficient is to measure changes in league competitiveness over time. Looking at the English Premier League (EPL), Leicester City won the 2015/16 title, a feat that many thought was impossible given the prior dominance of a few major sides. Based on casual observation, it appears the dominance of the major clubs is on the decline in the EPL. Comparing the Gini coefficients for the league over time could provide a formal measure of this change in competitiveness.

Why use league points and not income?

League points are unambiguous and easily attainable. Income figures are harder to source, are less reliable and often inconsistent due to varying accounting practices. The same goes for player salaries and player transfer values. Also, accumulated league points can be seen as a proxy for the club’s transfer and wages expenditure. While there are obviously individual exceptions, on the whole a team with a larger wage bill will out-perform a lower spending club.

Gini coefficients for the EPL, Championship, La Liga & A-League

Using historical league tables, Gini Coefficients have been calculated each year for the English Premier League, English Football Championship (2nd division in England), La Liga and the A-League.

The points figures have been edited to give back any deductions for ineligible substitutions and insolvency/administration penalties.

Because the Gini coefficient is a measure of inequality, the lower the value, the more competitive the league. In the following analysis the phrase “more competitive” implies less inequality and more uncertainty.

Figure 1: Comparative League Gini coefficients over time

The following graph plots the Gini coefficients for four football leagues over time.

The calculated coefficients fit in well with expectations. The football Championship in England has been the most competitive league. The EPL has been the least competitive for most of the years, however in the last two seasons it has been more competitive than La Liga.

The A-League data is difficult to compare to the other leagues because it only features ten sides rather than twenty or more. More data will be required to determine if there is an upward trend in inequality.

Figure 2: Comparative League Gini coefficients over time – top 10 sides

A stylised fact about the English Premier League is that in the bottom half of the table the sides are primarily concerned with staying in the division. The teams in the top half of table are the ones who compete for titles and the chance to play European football. With this in mind, the following graph plots calculated Gini coefficients for the top 10 sides in the three European leagues over time. How does the competitiveness of the top ten sides compare between leagues?

The competitiveness of the top ten sides of the Championship has remained relatively stable in over time, with no discernible upward or downward trend. The English Premier League started out with a similar competitiveness as the Championship in the late 1990’s, however due to heavy investment by wealthy owners of larger clubs, the EPL became less competitive from 2000 onward, with a few clubs dominating the competition. From the 2013/14 season onward, however, the dominance of the major clubs in England has been in decline, making the league consistently more competitive each year since. In 2016 the top half of the EPL was actually marginally more competitive than the top half of the Championship.

Explaining the trends

How can we explain the trend of increasing competitiveness in the EPL? One answer is the UEFA financial fair play rules. Since 2013, clubs that have qualified for UEFA competitions are assessed against break-even requirements, which require they balance their spending with their revenues.2 Another answer lies in the EPL TV rights deals and the way those funds are distributed. Over the past few years the TV rights money for the EPL has skyrocketed. In 2013-16 the UK deal came to Â£3 billion while the 2016-19 deal is worth Â£5.1 billion.3

What stands out about the recent EPL rights deals is the equitable distribution of the money. In the 2015/16 season, first placed Leicester City received Â£93.0 million while Newcastle, who were relegated, received Â£72.7 million.4 The huge sums of money awarded to the lowest teams have enabled them to compete more effectively with the top sides.

Until now, La Liga has been much less egalitarian. The Spanish top division clubs have negotiated their deals independently, which resulted in a huge disparity in income. For the 2014/15 season Barcelona received an estimated \$173 million from worldwide TV rights while Eibar received only \$15 million â€“ a ratio of 11.5 to 1. For the same season in the Premier League, winners Chelsea received \$150 million while last placed QPR received \$98 million, for a top-to-bottom ratio of 1.5 to 1.5

The result of the previous La Liga TV deals has been the dominance of teams like Barcelona and Real Madrid over the rest of the league. This shows up clearly in the Gini coefficients for the top 10 sides. There is a clear upward trend, indicating the league has become less competitive over time. Since 2009/10, the top half of La Liga has been consistently less competitive than the top half of the EPL.

This is due to change, however.

In February 2016 the Spanish League announced a new three-year deal for domestic TV rights worth â‚¬2.65 billion. The deal will come into play from the 2016-17 season to 2018-19. The new domestic rights sale is more in line with the distribution model employed by the EPL.6 As part of the new deal, 10% will be distributed among division 2 teams while the rest will be distributed as follows:
Pot 1 â€“ 50% distributed equally among all 20 La Liga clubs
Pot 2 â€“ 25% is merit money, distributed on how the teams finished in league in last 5 years
Pot 3 â€“ 25% is distributed based on resources generation (club members, attendances, ticket sales, etc.)

Based on this we would expect the Gini coefficient for La Liga to trend downward in the next few years as the EPL has done.

Application of the Gini coefficient to futures betting

Picking the winner of the football Championship has always been tough, while historically, only a few teams were perceived as having a realistic chance of winning the English Premier League or La Liga. This fact shows up well their respective Gini coefficients, with the EPL and La Liga having consistently higher Gini coefficients than the Championship.

Not knowing anything else about a league, the Gini coefficient gives us a measure of competitiveness, and therefore a measure of uncertainty. The more competitive a league is, the more uncertainty there is about which club(s) can win it. Based on this you could surmise that it’s best to back the favourites in leagues with high Gini coefficients and consider longer-shot bets in leagues with lower Gini coefficients.

The Gini coefficient as a predictive tool

The Gini coefficients for the EPL have been in decline in recent years, which suggests the league has become more competitive each season. The 2015/16 season in particular saw a sizable drop in the Gini coefficient, which partially explains Leicester City’s triumph. Ignoring last year’s data, however, was it possible to predict that a 5000-1 odds outsider could have won the league in 2015/16? You would have to say no. The EPL was comfortably less competitive than the Championship the year before and the Gini coefficient for the top ten teams in 2014/15 was similar to figures in 2006/07, 2009/10 and 2010/11. The result in 2015/16 represented a staggering drop down to 0.076, the lowest level since 1997/98. Previous drops of this magnitude (0.024) occurred in the seasons following particularly high Gini coefficients.

The Gini coefficient serves as a good measure of league competitiveness in retrospect, but as a forecasting tool it is less effective. This is because of the high random deviation of the Gini coefficient each season. The Championship represents a league with no discernible trend in its Gini coefficient over time, yet it has a high standard deviation of 1.50% for the top ten teams and 1.95% when all 24 teams are included. This noise makes it difficult to pick out trends until they become obvious.

The Gini coefficients for La Liga have been trending upwards in recent years, however we know that this trend cannot be relied upon to continue into the future. This knowledge isn’t based on the Gini coefficient data, however, it is based on anticipation of the new TV rights deal and its implications for the league’s competitiveness going forward.

Conclusions

Gini coefficients have been traditionally used to measure income inequality in countries. They can be effectively applied to sports, however. By calculating Gini coefficients for sport leagues based on table standings we are given a formal measure for the competitiveness of each league. The figures themselves aren’t enlightening. It’s when they are compared over time and between leagues (that use the same point scoring system) that they become interesting.

This article looked at the Gini coefficient data for the EPL, English Championship, La Liga and the A-League. The results lined up well with expectations. The Championship is the most competitive league, the EPL has become more competitive in recent seasons, while La Liga has become less competitive. These trends can be partially explained by the contrasting TV rights deals between the leagues.

Gini coefficients serve well as a backward-looking tool to measure league competitiveness, but due to the high variation in the values due to random error, discerning trends in the data is difficult, which makes the Gini coefficient less valuable as a forecasting tool and therefore less valuable in the context of futures betting. It is certainly worth paying attention to, however. It provides an excellent means of comparing league uncertainty as well as measuring the changes of that uncertainty over time. The Gini coefficient also serves as a useful tool when analysing an unfamiliar league.

References and acknowledgements

The Gini coefficient calculations used in this article were made using a modified version of the Lorenz Curve Calculation Spreadsheet which is made freely available at PeterRosenmai.com. These figures were then verified here: http://www.wessa.net/co.wasp

https://en.wikipedia.org/wiki/Gini_coefficient

All final league standings were sourced from Wikipedia.

The EPL data set ranges from the 1995/96 season to the 2015/16 season. Prior seasons have been excluded because the league featured 22 rather than 20 teams prior to this period.

The Championship data set ranges from the 1995/96 season to the 2015/16 season to match up with the EPL data.

The La Liga data set ranges from the 1997/98 season to the 2015/16 season. Prior seasons have been excluded because the league featured 22 rather than 20 teams prior to this period.

The A-League data set ranges from the 2009/10 season to the 2015/16 season. Prior seasons have been excluded because the league featured 8 rather than 10 teams prior to this period.