2 Association football
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Chapters 1
2
3
4
5
2-1 Some history
2-2 Double round-robin
2-3 Uncertainty
2-1 Some history
Some time ago, during the 3rd-2nd centuries BC, people played a game called Cuju in China. It started as a playful way for the military to maintain and improve their fitness. Over time it spread into society with families also playing the game.
"One Hundred Children in the Long Spring" A painting by Su Hanchen, active 1130-1160s AD. Cuju is an ancient form of football. See Wikipedia.
The Fédération International de Football Association ("FIFA") considers Cuju as the forerunner of football. Historic accounts of modern football usually refer to a meeting in 1848 between the representatives of five public school teams in Trinity College of Cambridge University. They met to agree on how they should play football against each other. This meeting resulted in a set of rules—the "Cambridge Rules"—that describe how to play the game.
Although not all school teams in England adopted these rules, it led eventually to a national association of football teams. Eleven teams founded the English Football Association ("FA") on 26 October 1863 and later that year, on 8 December, this association issued "Laws of Football". These laws evolved into the current Laws of the Game—rules that aim at ensuring that everybody can enjoy playing football in a safe way everywhere.
In 1888 the FA organised its first season of association football. The format in which they organised matches is called the double round-robin format. Most football associations still use this format, or a version thereof, for their national championships.
2-2 Double round-robin
In a tournament with a double round-robin format each team plays two matches against each other team — one "home match" in its own stadium and one "away match" in its opponent's stadium. The number of matches and the length of the season—the period during which teams play matches—depend on the number of competing teams. Seasons with around twenty competing teams last about eight or nine months.
Figure 2-1 shows an example of match results in a double round-robin tournament with 22 teams. Each team plays twice against each other team.
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Figure 2-1: Matches of the English 1971-1972 First Division.
During a season teams can earn points for each match—depending on how well they play. Teams win a match if they score more goals than their opponent. Teams lose a match if they score less goals than their opponent. They don't get points if they lose their match. Both teams earn one point if they score the same amount of goals. Teams earn more points if they win a match. They used to get two points for a victory but nowadays they get three points.
The team with the highest number of points at the end of the season wins the tournament, the team with the second-highest number of points finishes second, the team with the third-highest number of points finishes third, etc. Tie breaker rules exist to determine the ranks of teams that earn the same amount of points during a season. They include, for example, the number of goals that teams scored and the inter-team results of teams with the same amount of points.
A main reason for organising matches in this format is to identify the best team as the winner at the end of the season. It is considered to be more reliable than a tournament with elimination rounds like, for example, the World Cup for country teams.
Not all teams play a match against each of the other teams in tournaments with elimination rounds. Moreover, a lottery usually determines the matches in the first round in such tournaments. In a double round-robin format each of the teams plays two times against each of the other teams—removing the need of a lottery to determine which teams play against each other.
Match scheduling for this format includes two main parts. The first part consists of finding those matches that make sure every team plays against each other team on the match days envisaged to make up the season. A computer program may provide the first tentative schedule— including restrictions on the teams' calendars that are known in advance. The second part consists of checking and adapting the schedule until it fits with other tournaments and obligations of the competing teams.
This scheduling of matches takes more time than scheduling matches for a tournament with elimination rounds. For the latter you only need to know the participating teams and a lottery that determines the matches of the first round. The matches of other rounds follow automatically by the structure of the elimination rounds.
Identifying the strongest team as the winner is not the only reason for organising matches in a double-robin format. It also allows the participating teams to earn revenues throughout the season. This allowed the FA to get enough teams on board to launch its first domestic association football competition in 1888.
2-3 Uncertainty
Compared to a tournament with elimination rounds the double round-robin format reduces the role of chance in identifying the strongest team of a season. Chance, however, still affects the outcome of association football matches.
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For example, the Laws of the Game mentions various unpredictable events or factors which can affect a match.The International Football Association Board (IFAB) publishes the Laws of the Game—an annual publication which presents the rules of playing football to ensure it takes place in a safe way. They include the weather, a defective ball, a player who loses his shoe or shinguard, problems with the lights in the stadium, a spectator blowing a whistle similar to that of the referee, an extra ball at the field and a spectator, object or animal entering the field, respectively.
Unpredictable events can also be a direct consequence of how teams play. Examples include a striker that scores a goal after the ball hit the goal post or by accidentally giving a spin to the ball that nicely curves it into the goal nets.
These examples remind us that sometimes teams can lose a match even if they show better play than their opponent. The presence of chance means that we cannot say with certainty what will be the result of a match between two teams. To realistically describe goals in football matches requires a probability model because probability models describe phenomena which are subject to randomness—things that happen in an unpredictable way.