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Measuring the Trend of Competitive Balance in Football

Zahie Hosain University of British Columbia Vancouver
"I believe only in sporting merit," stated former Arsenal manager Arsene Wenger in a 2009 interview.1 His sentiments are now being echoed by a larger cohort of football fans who have begun to notice irregularity in the quality of their beloved sport. In this case, the term 'quality' is a bit of a misnomer.

As nebulous as it may sound, old school football enthusiasts would interpret the use of this term here as the presence of world-class football players across multiple teams, as well as intense competition focused at the hands of a broader group of teams. On the other hand, this term would be interpreted by newer and younger football fans as the existence of world-class football players across only a few teams, as well as intense competition focused at the hands of a smaller set of teams.

More specifically, a few teams buying the best players in order to dominate other teams, winning all tournaments and trophies, hence disrupting competition. This has steadily evolved into a major source of concern among many involved in the sports sector, owing to a few overachieving teams disrupting competitive balance. Although, in terms of sporting merit, research-based empirical data hasn't always indicated why disruption in competitive balance is not troubling (Borland and Mc Donald, 2003), but in the footballing world, fans, players, and managers all seem to agree that this imbalance is harming the spirit of the sport.

https://amp.theguardian.com/football/2009/aug/17/arsene-wenger-european-super-league

Definition of Competition: Generally understood to be a process in which rivals compete in order to achieve some objective - Tragakes, Ellie. Economics for the IB Diploma. Cambridge University Press, 2000- Page 42

Competitive Balance and its Importance in Football

Competitive balance in football refers to maintaining a degree of parity between teams' sporting ability in order to reinforce the sport's aura of fairness. However, the theoretical understanding of ‘competition’ rests on the premise of consumers’ awareness about the product.

In the case of a game of football (product), or for that matter in any other sport, the fairness and the entertainment quotient relies on the spectators inability to predict the outcome of a match or a collective event. However, with parity, there will always be uncertainty in predicting the outcome of events, which will maintain spectator interest and increase their demand for watching events.

Therefore, the greater the parity between teams, the less predictable is the outcome, which increases the entertainment quotient.

From an economic standpoint, competition in sports is highly valuable because it generates more spectator attendance, which means higher revenue generation. Competition promotes fan welfare. The uncertainty in a game will always have a psychological tingling that drives a desire to experience thrill which is embedded in an unpredictable result. Therefore, it is widely believed that maintaining competition is critical to keeping the sport viable in the long run, because a lack of competition will ultimately reduce the number of spectators, resulting in these numbers not being maximised and the sport running the risk of losing spectators in the long run.

Other problems could arise as a result of this, such as certain teams going bankrupt, the development of stand-alone leagues, like the recently proposed European Super League4, to draw more spectators while decimating the competitive spirit of the sport, and so on.

Most football fans, however, recognise and accept a select teams' long-term dominance in footballing tournaments due to their historical achievements, such as Manchester United in England and Bayern München in Germany.

The presence of elite teams, which will continue to dominate leagues and be superior to other teams, does not entirely reflect the premise that the outcomes of any events in which they engage are predictable. Their presence has no bearing on the outcome of any single event, whether it is an individual match or a European championship, and uncertainty will always be a part of the game.

https://www.thequint.com/sports/football/what-is-the-newly-announced-european-super-league

Disruption of Competitive Balance: PSG in Ligue 1

The French football league, known as 'ligue 1,' is one of the most prominent examples of disturbances in competitive balance in sports. Ligue 1 is infamous for having one side that is PSG which dominates the whole league due to its recent change in ownership (QSI- Qatar Sports Investment) that brought in greater financial strength. After winning practically all domestic tournaments every season for the past ten years, and with PSG making huge moves in transfer market windows (time periods in a season meant for the purpose of buying players) almost every season, ligue 1 has become predictable. And it is assumed in this research that with greater predictability, there will be less competitive balance.

The new ownership of PSG have completely ignored the aspect of competition and almost made every event in which they are involved predictable. Why? They have bought the best players and won practically every trophy, thereby taking away the entertainment aspect of the sport.

An uncompetitive league will lead to spectator disinterest and thereby have an impact on the revenue generating potential of the sport. Let us assume that the number of matches played in a season remains the same. To keep the spectator interest alive in the sport, we are stating that the competitiveness of the sport is getting fueled by the entertainment quotient provided by the unpredictability of the event. So, in a competitive league, spectators will increase their demand for the sport from D1 to D2 at P2. This will increase the revenue to P2 Q2 - P1 Q1 because increasing spectator demand will increase subscription and matchday revenues.

Market cap of QSI is 2.761B

Graph 1. Increase in spectator demand due to competitive balance

An uncompetitive league may not maximise the revenue potential generated from spectator demand. Because predictability is thought to lower spectator demand as reasoned above, it can be extrapolated that PSG is not maximising its demand for spectator interest with increasing predictability. The heavy expenditure of PSG can be inferred as ‘allocative inefficiency’6 from a theoretical viewpoint. We have observed that usually there is a tendency of monopolies to restrict their output below a level that would be produced in a competitive market and charge a higher price. In this case, the predatory transfer market behaviour of PSG indicates monopolistic conduct.

PSG's Transfer Market activities

PSG competes in ligue 1, a ‘relegation-based’ competition in France. A relegation system would mean that the league is open, allowing teams from lower levels to enter and play at the top level but also relegating underperforming teams to lower tier leagues.

Allocative inefficiency occurs when marginal benefit is not equal to marginal cost. Monopolies are allocatively inefficient because at the monopolists’ equilibrium, the marginal benefits are greater than the marginal costs.

https://www.scottfujita.com/what-is-relegation-in-soccer/

In an open system, every team's primary goal is to maximise their wins in order to stay in the league. Over the past 20 seasons, PSG has remained in the top division, not relegating once to any of the lower tiers of french football. Therefore there is no doubt that the team is a win-maximising team. When compared to their league rivals, PSG has maximised their wins by spending a lot of money to buy the best players.

PSG has evolved from a team that was solely incentivized to maximise wins in order to remain in the top flight, to a team that is incentivized to maximise profits by buying the best players. Prior to the takeover, PSG had endured massive losses adding up to $340 million in season 2010/11 from 1989/99, as well as a ‘negative net spend’ (Income spent on buying players - income earned through selling players as reflected in chart 1.) only in the transfer market throughout this period.

To turn PSG profitable, the Arab ownership's initial game plan after taking over PSG was to wipe off PSG's debts and losses, allowing them to bring in a number of high-profile players, most notably Zlatan Ibrahimovic and David Beckham. The addition of these players to the squad increased their revenue streams because the team became more marketable and began doing better in the league. These initial investments resulted in sustained higher matchday, broadcast, and commercial revenues, allowing PSG to develop their squad and generate further revenue.

Despite having a negative net spend in the transfer market, the team has generated an annual revenue of $613 million since the takeover and has stayed profitable in three seasons. The team has also benefited from a soft-budget constraint imposed by the ownership in the transfer market.

Chart 1. Net Spend of PSG in the transfer market between 2010 and 2021

The chart shows a significant disparity between the money invested and the money made by offloading players on the transfer market. This graph corroborates the claim that PSG has a soft-budget constraint pampered by the ownership. Olympique Lyon and AS Monaco, two French league sides that compete with PSG, have also made substantial financial investments. However, the question is if these extravagant spending habits are justified in terms of sporting merit. In contrast, Olympique Lyon and AS Monaco have been able to finance their huge spending by selling players on the transfer market, and maintaining a positive net spend.

Charts 2 & 3. Net Spend of Olympique Lyon and AS Monaco in the transfer market between 2010 and 2021

The trendlines show a rationale in terms of sports merit for their heavy expenditure throughout the years. The teams did not enjoy soft-budget constraints like PSG imposed by their ownerships in order to meet their aspirations of winning titles, but they did it in a fair manner by producing talented players and selling them. This is in stark contrast to the practises promoted by PSG, who actually bought the players of AS Monaco like Kylian Mbappe among others, to see their way out of their incompetence to go on to win titles.

Evaluating the Impact of the New Ownership: QSI

Prior to QSIs' ownership of the now-French giants, which has been essential in the team's recent success, PSG had only won the French League title twice, and the team has enjoyed an era of extended domination at the top of the league ever since. PSGs’ success is all down to their ownership, which has allowed the team to buy players and form an unbeatable team.

PSG competes in three domestic tournaments in France, in addition to the league tournament, which are the French Supercup (Trophée des Champions), the French Cup (Coupe de France), and the French League Cup (Coupe de la ligue). PSG can compete in a variety of tournaments outside of France, but the main tournament that PSG or any other European would be concerned with winning is the UEFA Champions League. Due to their strong domestic league performance, PSG has comfortably qualified for the UEFA Champions League over the last 10 years.

Charts 4 & 5. Money spent in the Transfer Market by PSG (2000-2021) & ligue 1 top 3 appearances (2000-2021)

The team’s expenditure habits were altered following the new ownership takeover in 2011, as seen by a surge in spending and a more noticeable curve in chart 4. Between 2000 and 2021, PSG finished in the top 3 battle 10 times. Prior to 2011, PSG had only finished in the top 3 once, but since then, PSG has finished in the top three every season, bringing their total to 10 top 3 finishes due to a substantial shift in their spending habits after 2011. Not only has PSG been efficient in finishing the ligue 1 seasons in style, the team has also managed to practically win every French domestic title between 2011 and 2021.

Table 1. Titles won by PSG

When evaluating the trend of PSG's domestic success, what stands out is the consistency with which PSG has maintained their success after a significant gap. PSG have won the ligue 1 title seven times in the last ten years. And it is reasonable to say that their dominance has been steady, but before being crowned champions of the season 2012/13, they were crowned champions roughly 19 years earlier in the 1993/94 season, and before that season, they were crowned champions around 8 years previously in the 1985/86 season. Being named champions 19 years later is not a coincidence, but a concrete result of their new ownership.

The same is true for other domestic tournaments, such as the French Super Cup, which PSG won in 2013/14, nearly 15 years after their previous triumph in 1998/99. After that, they won the tournament every season following their triumph in 2013/14, which should definitely be linked to the Arab takeover. PSG has been able to retain a tighter gap in their winning run in the French Cup and the French League Cup, but the first two titles clearly indicate a favourable impact of the Arab takeover on PSG's road to success.

Table 2. Ligue 1 Champions from season 2005/06 to 2020/21

The team in question, PSG, did not win the title until 2012/13, a year after its new ownership took over. This can also be linked to the team's large spending habits and how efficient they have been with all of the players they have bought.

Measuring the trend of competitive balance in Ligue 1

A league's competitive balance can be assessed in both short and long terms. Static competitive balance focuses on the short term period, determining the competitive nature of a league in a given season, determining the evenness of teams, neck-to-neck competition articulated in tournaments, and if there are any dominating runaway teams or teams at the bottom of the league. Dynamic competitive balance, on the other hand, focuses on the long term period, which determines whether teams remain in the same position in the league over time.

The Noll-Scully measure is the static method, widely used by sports economists to determine competitive balance in many sporting leagues. The method divides the standard deviation of the winning percentage of all the teams in a league by the standard deviation calculated if the winning percentage was equal across all teams in the league. The formula that the method follows is:

In this formula, cb is the competitive balance and σ(wp) is the standard deviation of all teams' winning percentages in a league (represented by i) during a specified time period (represented by The denominator σ(wp)ideal it is 0.5 , where N is the number of games played at the end of the season (constant across all teams). This is because the standard deviation of a random sample of an individual team's wins is computed using binomial distribution (N,p), where N is the number of games played and p is the probability of winning. Therefore, the standard deviation of an ideal season takes this form. In a totally competitive league,' the value of p would be 0.5. In this hypothetical 'totally competitive league,' the Noll-Scully measure will have a value of 1 because both equating standard deviations cancel out and leave 1. The league's competitiveness is best defined by the value 1. Any value less than or greater than one indicates that there is competitive imbalance.

To understand if the competitive balance in ligue 1 h as deteriorated as a result of PSG's emergence, a broad timeline must be examined. Seasons from 2000/01 to 2020/21 will be considered in this situation. This stands to reason because PSG was an ordinary mid-table team prior to 2011, and a 20-year timeframe will allow for an examination of how its activities have changed the competitive balance in the league.

This league follows a win, draw, or lose system. Therefore, the following formula will be used to calculate the winning percentages of all teams in all seasons:

The winning percentages will then be used to calculate the mean winning percentage for each season using the formula below of:

The following table represents the winning percentages of all teams in a single season, 2002/03. The means of all the winning percentages are also shown in the table. The table is as follows:

Table 3. Sample calculation of mean of winning percentages of teams (season 2002/03)

The σ(wp) values will be calculated with the mean of all winning percentages from the 20 seasons. There will be 20 standard deviation values because there are 20 seasons. The standard deviation of all winning percentages in a season will be calculated using the formula:

The standard deviations of the winning percentages' means were calculated using MS Excel. Table 4 illustrates the mean winning percentages, alongside the standard deviation of those means. All figures have been rounded to three significant figures. The following is the table: The σ(wp) values will be calculated with the mean of all winning percentages from the 20 seasons. There will be 20 standard deviation values because there are 20 seasons. The standard deviation of all winning percentages in a season will be calculated using the formula:

The standard deviations of the winning percentages' means were calculated using MS Excel.

Table 4 illustrates the mean winning percentages, alongside the standard deviation of those means. All figures have been rounded to three significant figures. The following is the table:

Table 4. Mean and Standard Deviation of means of winning percentages of teams (season 2000/01 to 2020/21)

The CB values for all seasons will be calculated using the aforementioned formula after all standard deviation values have been determined. The figures have been rounded to three significant figures.

A scatter diagram is created using the CB values to examine the level of competitiveness and the trajectory of competitiveness over the last 20 years

Chart 6. Scatter diagram depicting the trend of competitiveness in Ligue 1 between 2000 and 2021

Interpretation

According to the model's assumptions, the value of p in a totally competitive league should be 0.5; however, in the case of ligue 1, the above scatter diagram shows that it is far from a perfectly competitive league, with Noll-scully values ranging from 1.1 to 1.9.

Since 2000/01, the league has had an upward trend in Noll-Scully values. In season 2000/01, ligue 1 had a N-S value of 1.19, and since then, the N-S values have followed a somewhat consistent climb. While keeping in mind that PSG was taken over in 2010/11, the average N-S value from season 2000/01 to 2009/10 is 1.3, which contrasts with the average N-S value from season 2010/11 to 2019/20, which is 1.6. An increase in these values cannot be directly linked to the takeover of PSG without taking into account the broadcast revenues as per TV deals and rights of ligue 1. Among the big-5 football leagues (La Liga in Spain, Bundesliga in Germany, Serie-A in Italy, and Premier League in England), ligue 1 of France has the lowest revenue from broadcasting rights (which in this case is being assumed as the revenue stream for teams to buy players). The Premier League has been the most successful of the big five leagues in terms of generating revenue from domestic television rights sales. The revenue generated by a single domestic match in the league is nearly triple that of a domestic match in the other big five leagues. Not only has the Premier League been highly successful in selling TV rights domestically, but also overseas.

When looking at recent foreign TV rights contracts, the EPL is the only league to generate more than €1 billion in a year, with €1.582 billion, trailed by LaLiga with €897 million, Serie-A with €371 million, Bundesliga with €240 million, and ligue 1 at just €80 million. These huge disparities in revenue generated may lead one to conclude that, of the Big-5 leagues, ligue 1 is the least appealing, with TV rights revenues almost 20 times lower than those generated by the Premier League. The league's inability to generate large broadcast revenues would imply that teams have less money to spend on players, which is a plausible assumption given the league's inability to attract famous players. Teams are less competitive in the league as they have less money to invest on players.

However, the league's inability to generate large revenue clearly has had little effect on PSG, who has been spending lavishly on players in the transfer market following its takeover, despite its operating losses due to its soft-budget constraint, as seen in chart 5, allowing the team to become extremely competitive. The team has become so competitive overtime that the rate at which it has become competitive has been too rapid for the other teams in the league to close the gap to, thereby disturbing the league's competitive balance, as seen by the increased N-S values in chart 6 after 2010/11.

The N-S values in chart 6 that had been steadily growing over time witnessed a startling decline with the 2019/20 season. This exceptional value can be linked to the COVID-19 pandemic, which caused many fixtures to be cancelled and teams to face huge losses owing to a lack of revenue generated from the various revenue streams. This is related to the notion that most teams, including PSG, cut their expenditure significantly, as indicated by chart 4, allowing them to be more competitive with one another and so strengthening the competitive balance of the league. Drops in N-S values in other contexts can also be connected to increased television revenue, which allows teams to spend more on players and strengthen their squads, thereby increasing competitiveness and consequently competitive balance.

An observational point is that before the 2002/03 season, ligue 1 operated with only 18 teams until it was expanded to 20 teams with the start of the 2002/03 season. This will have a statistical impact given that the number of matches played by teams is used to calculate the winning percentages, which is further used to calculate the competitive balance values. However, the basic premise of the argument will not be impacted by this.

Shortcomings of the Noll-Scully Measure

This model used to determine the competitive balance has shortcomings too, one of which is that it does not account for the dominance of a certain set of teams in a league overtime. The Noll-Scully measure is also considered to be biassed as referred to the article from the Journal of Quantitative Analysis in Sports, “Measuring competitive balance in sports” by Matthew Doria and Barry Nalebuff, which states that the Noll-Scully measure artificially inflates the imbalance for leagues with long seasons in comparison to those with short seasons. This study by Doria and Nalebuff provides a general model of competition that leads to unbiased variance estimates. Their model provides insight into the competitive balance at the game level.

Conclusion

The governing body of European football UEFA has implemented certain regulations that are made to ensure that european teams are not spending more than they earn. There is a very apparent yet veiled oration for the existence of these regulations, which is to look down on a tournament that is, according to prominent economist George Akerlof, analogous to a "rat race" which means, "The winner takes it all." This remark implies a self-perpetuating cycle of sports and financial success (“success breeds success”) resulting in an increasing degree of competitive imbalance and potential monopolisation. As a result, certain teams are incentivized to spend substantial sums of money to win this race in the hopes of initiating an upward cycle of success, thereby disrupting competitive balance.

In order to compete with teams that are already spending so much, other clubs will have to rely on substantial investments. Such teams may not have the financial resources to make such large investments, thus their long-term success will be determined purely by the size of the domestic or local market or their past success.

So, in order to maintain the competitive balance of football leagues, these regulations must be effectively implemented in order to prevent teams like PSG from undertaking large transfer market expenditures, thereby taking away the competitive sporting merit.

https://www.degruyter.com/document/doi/10.1515/jqas-2020-0006/html