THE ENGLISH PREMIER LEAGUE
This blog is an analysis of the English Soccer/Football League along the concepts of modern networks and game theory.
Data and information is directly referenced from the league’s official website:http://www.premierleague.com/page/Home/0,,12306,00.html
The English Premier League is the most popular football/soccer league in the world. It runs for an annual season in which case twenty teams(nodes) play head to head games with each other in such a way that TEAM A plays with TEAM B in TEAM B’s stadium and again in TEAM A’s stadium. These two games are referred to as “away” and “home” matches respectively. This kind of an organization creates a directed graph whereby two nodes interact both ways creating a strong edge. Throughout the season the league standings are updated to reflect the position occupied by each of the teams in relation to the others.
The strength of a link between two teams is heavily influenced by the amount of skill accumulated in each team. Very strong teams are strongly linked with other strong teams than with weak teams. This strength is explainable in a number of ways. Given a strong Team A and a strong Team B, there is a higher tendency to link up more often in bid to give one team an advantage over another. This connection is seen in how much of TEAM A’s activity is influenced by TEAM B. For instance, TEAM A will always have its representatives every time TEAM B is playing against another TEAM, this keeps it always updated about their new tactics, styles of play and nature of players they have, similarly TEAM B will do the same. This mutual interaction results in a strong edge. During the transfer period, a duration where TEAMS can buy and sell players from and to other teams. TEAM A and TEAM B keep their tabs on all the news outlets to determine what kind of businesses their opponents are involved in often coming up with ways of dealing with them. Important to note is that teams that are considered relatively weaker do not receive this huge attention from strong TEAMS justifying the notion of a weak link between a strong team and a weak team. Assuming TEAM A is first on the table, it maintains a strong edge with the TEAM B which is next on the table but maintains a relatively weaker link with TEAM C third on the table. As a result Strong Triadic Closure is never violated.
A second interesting concept happens towards the end of the season. If for some reason TEAM A and TEAM B are level on points with only one game to go before the season elapses then the management has to come up with a way of ensuring an outright winner. This follows the ideas covered in game theory. A typical way tactic is to have the two teams play at the same time and in two different places, to ensure players in one team are not influenced by the other team. Given this situation, two strategies arise, play defensively or offensively. The matrix of the outcomes is as shown below:
TEAM B
Offensive Defensive
| G,G | G,NG |
| NG,G | NG, NG |
TEAM A Offensive play
Defensiveplay
G-GOALS, NG-NO GOALS
In the case above, either of the team must win to claim the trophy. The only way to win is to score a goal and not concede. That is the best pairs of strategies will be (G,NG) in which case A wins or (NG, G) in which case B wins. Each team has to make a choice basing on what they assume the other team will. If they choose to defend, there is a chance they will not score and the other team will, if they choose to attack, there is a chance they can win or not. In this case (G, NG) and (NG, G) come out as the only dominant strategies since each of them happens to be the best response to the other.