Changing the hidden rules of football

We love sports for many reasons, from a cultural tradition that teaches each of us to respect and admire sports events, to professional reasons. One of these reasons relates to the ability of the best players and the best teams to hold our attention for lengthy periods. Deeply correlated with the quality of players and teams, it is important to have balanced sports competitions. Balanced competitions tend to disperse the probability of final victory across a large number of teams and thus maintain interest; in contrast, competitions whose winner is easily anticipated tend to lose interest, fans and financial sustainability.

This discussion is important with regard to football, especially in the professional European football competitions. Season after season, we observe a concentration of the probability of winning the European professional leagues on a few teams, usually the ones with the largest budgets at the beginning of the competition. However, various studies have claimed that certain adjustments to the competitions would produce more balanced professional football leagues.

In a recent paper (Teixeira et al. 2014), we claim that changing the system of reward for victory (2 points replacing the current 3 points in most competitions), the number of rounds or the relevance of random factors (such as referees’ influence or the effect of home advantage) could improve the competitive balance of European professional leagues. However, some of the organising institutions of football competitions (such as the national federations and UEFA) lack the software programs that can simulate the expected values of the measures of competitive balance for a given number of editions of a competition.

The main factors that our review of the literature identified as influencing the competitive balance of football leagues are: the number of competing teams and the number of journeys/rounds, the number of points awarded for a victory, home advantage, the size of the assistance (also considering the matches played as a visitor team), the influence of referees, and the influence of sport history.

Number of teams

There are two main models of sports leagues: closed and open. In the closed model, as seen in the North American, leagues have a fixed number of members (and the addition of a new team or removal of an existing team is rare). The open system is common in European sports leagues and is based on a system of promotion and relegation. Several authors have studied how restructuring a league’s format (i.e. modifying the number of teams and matches) can affect the annual assistance of stadiums and the competitive balance of the competition.

Points for a win

In 1981, the English Football League introduced the system of 3 points for a victory, 1 for a draw and 0 for a loss, which replaces the previous system of 2 points for a victory, 1 for a draw and 0 for a defeat. Starting in the 1990s, the new system became standard across most leagues and competitions. According to Newson (1984), the initial idea “was presumably that a greater reward for winning games would encourage more positive attitudes from teams and that the consequently more attractive and aggressive football would bring in bigger crowds”. If the teams are drawing near the end of the match, they will launch themselves to the attack in search of the winning goal that would guarantee them the two additional points. However, the critics of this system consider that if a team is winning near the end of the game, that team will adopt a negative and defensive strategy to preserve not only the victory but also the two additional points compared to a draw.

Other alternatives have already been studied in football leagues, such as the penalty shootout. Some leagues have tried penalties at the end of a drawn match: in 1987, the Norwegian First Division used three points for a win at the end of 90 minutes, two points for a shootout win, 1 point for a shootout loss and 0 points for a loss. Between 1996 and 2000, the Major League Soccer in the US used 3 points for victory, 1 point for a shootout victory and 0 points for a shootout loss or a loss at the end of 90 minutes.

Home advantage

The existence of home advantage in sports is a well-known and documented fact. For instance, Jamieson (2010) argued that the home team tends to win approximately 60% of all athletic contests. He studied several variables and concluded that the time era, season length, and game type all have a significant impact on home-field advantage. Carron et al. (2005) also noted that the home advantage appears to be universal across all types of sports.


There are many factors that might account for home advantage, but the social pressure exerted by the crowd is one of the major ones.
Various authors (referenced in our paper) have argued that crowd assistance produces a greater and more negative noise when visiting teams’ players tackle, which may potentially (and most likely) serve as a biased cue for the referee’s decision.


Referees are important agents in a football match, employed to interpret the rules in an impartial way. However, they can exercise a considerable discretionary power that can have a very important influence in the final result of a football match, in particular when adding extra time, awarding penalties, allocating yellow and red cards or deciding on free-kicks or offsides.

Team history

In addition to the previously identified dimensions, we have to account for what some authors argue is an even more influential factor: the team’s history, which is highly correlated with the budget size and with the probability of winning matches and competitions.

Tactical quality

Various authors also identify tactical quality as an important factor in winning. Lafuente (2008) developed an algorithm to ease the replacement of a player. Papahristodoulou (2012) studied the optimal formations of two football teams (AC Milan and Barcelona) and how this optimal formation maximizes the probability of winning matches.


In our template, we also considered ‘Luck’ as a factor. Although the previously identified factors can be considered as endogenous factors for competing teams, there is always space for ‘luck’, even at residual levels, to complement the explanation of the determinants of victory.


We constructed an Excel template as explained in our paper. We then ran some experiments using the template to observe how different combinations of parameters lead to different values for the competitive balance of football leagues.

We calculated an index of competitive balance that is essentially a Hirschman-Herfindahl Index, following the equation suggested by Kupfer (2002).

We observed that the highest mean value (9.21, interpreted as the most balanced simulation) obtained for our measure of the competitive balance of 20 simulated seasons was observed in a case in which each victory is awarded 2 points, each draw is awarded 1 point, and each defeat is awarded 0 points. This highest mean value is related to the combination of weights 30% (Teams’ budgets), 20% (Home advantage), 10% (Tactical quality), 10% (Referees), 15% (Assistance), and 15% (Luck). Figure 1 shows this combination among different experiments.

Figure 1. Competitive balance simulated for 20 seasons (win = 2 pts; draw = 1pt)

Notes: 16 teams, round-robin, 30 journeys. 

The lowest mean value (6.80, the most unbalanced case) is observed in Figure 2 (in which each victory is awarded 1 point, and each draw and defeat are awarded 0 points). This lowest value relates to the following combination of weights: 60% (Teams’ budgets), 10% (Home advantage), 15% (Tactical quality), 10% (Referees), 5% (Assistance), and 0% (Luck).

Figure 2. Competitive balance simulated for 20 seasons (win = 1 pt; draw = 0 pts)

Notes: 16 teams, round-robin, 30 journeys. 

As a further step, we intend to develop our template to consider the data for each match. We also intend to record as many (professional or youth) football leagues as possible to inform the user which league is closest (or most correlated) to the league generated by the simulations, accounting for the parameters chosen by the user.


As a synthesis, we concluded that the most balanced leagues are characterized by rewarding victory with 2 points and draws with 1 point and when the influence of the teams’ history or budget is minimized.

Authors’ note: This article presents some of the most important ideas from our recent paper “Changing the hidden rules – An Excel Template for discussing soccer’s competitive balance”, published as Teixeira et al (2014).