Nash Equilibrium and Game Theory in Fantasy Football (Fpl)
Fantasy Premier League is a game that casts you in the role of a fantasy manager of Premier League players. Each manager has his own team and competes against other managers. The goal of the game is to score as many points as possible, the player with the most points at the end of the season wins.
Nash equilibrium is a game theory concept that describes a situation in which no player has any incentive to change his strategy, given that the other players maintain their strategies. In other words, it is a state of equilibrium in which no player can improve his outcome by changing his action while the other players maintain their actions.
Nash equilibrium was named after the American mathematician (Nobel Prize winner and who also inspired the movie A Brilliant Mind) John Nash, who described it in his 1950 paper "Equilibrium in Non-cooperative Games".
An example of the Nash equilibrium in FPL would be the template team phenomenon. When there is a certain group of players that have a good performance and most managers have them in their team a base team or template is formed. If most of the managers have the same players then the score of their teams will be very similar, with small differences marked by a few differential players.
When this situation happens it’s hard to climb in the overall rank or in the mini-leagues, remember that FPL is a non-collaborative game, how can I beat my rival if my team gets the same points? In this situation a Nash equilibrium is formed, nobody changes players because they are scoring a good amount of points, and as most managers have the same team they score the same (or very similar) and nobody takes advantage of the strategy.
Another situation where we see Nash equilibrium in FPL is in the captaincy election.
The captaincy has been a part of FPL from the beginning. FPL's first season was in 2002/03, and captains have been part of the game ever since. The captaincy is one of the most important decisions FPL managers make each week. Captain's points are doubled, so a good captaincy can make a big difference to your overall rank.
When a player performs exceptionally he becomes the best choice for captain. In the 2021/22 season Mohamed Salah had a very strong start to the season, because of this he was the most captained player by most managers for several weeks in a row.
This made moving up the ranks very hard. In January Salah joined the Egyptian national team to participate in the African Cup of Nations, in that moment Nash's balance (at least in the captaincy) was broken, causing managers to be forced to give the captain's armband to different players. The ranks varied and so did the teams.
A similar situation happened in the 2022/2023 season with Erling Haaland, who quickly became the permanent captain of the teams due to his performance. With Haaland we saw a situation that did not occur with Salah, the Norwegian broke the record for the most captained player by obtaining more than 90% of captainships in all teams overall.
In this scenario choosing another player as captain became almost mission impossible, because your captain had to score more points than Haaland in order to don’t see your overall rank affected. However if Haaland didn't score points your team was disadvantaged. There were players like Harry Kane scoring points almost every gameweek but as most players picked Haaland you had to pick him, or risk sinking in overall rank.
As we can see Nash's balance is not always an optimal result. In several gameweeks there were other players who scored more points than the Norwegian but the strategy used by the majority prevailed.
Nash equilibrium is a valuable tool for understanding how individuals make decisions in conflict situations. It can also be used to design strategies that help individuals achieve better outcomes. As the saying goes “You can’t make an omelette without breaking a few eggs” if we want to break the balance and move up in the rank we have to take a risk, although we must analyze well which is the best time to do it, undoubtedly the reward can be very high.
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