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Game Theory and League of Legends

League of Legends by Riot Games is currently the biggest game in the world with 67 million players who enjoy the game monthly, compared to Candy Crush which sits at 46 million monthly players ( This game falls under the category of MOBAs, in which two teams of five players battle each other with the goal of destroying the opposing team’s nexus in real time. I personally have been playing this game since its first season in 2011 and I believe I understand the game well enough to discuss direction targeted spells (“skill shots”), which is a mechanic of the game that can be related to game theory and penalty kicks in soccer.

Certain playable characters in the game have direction targeted spells, which function as the name suggests. The player activates the spell, chooses a direction with the mouse, and left clicks to fire a linear projectile with the intention of hitting an opponent’s character. In a given scenario, veterans of the game will know that in order for the projectile to land the user has to predict the enemy’s movements, just like a gunman must lead his target. Typically, the user of the spell has two choices to lead his target: either aim slightly above where the enemy currently is, or aim below. Similarly, the enemy player has two options for dodging the spell: run downwards, or upwards. With these two strategies and assuming both players play perfectly, we can make a payoff matrix in which both players A (the user of the spell) and B (the target of the spell) have two strategies each, to either head in an upwards direction or head in a downwards direction. This situation is similar to that of goalies blocking penalty kicks, where the goalie must decide as the kicker shoots whether to block left or block right and the kicker has to decide to shoot left or shoot right. Payoffs can be distributed as 1 for a hit for player A, and 1 for a dodge for player B and 0’s for the opposite case for each. Thus, the payoffs in this matrix will be always (1,0) or (0,1) since one player must be in a losing situation. Although there are certain game elements that I have decided to ignore (such as the summoner spell Flash, or the terrain in the game), for simplicity and for understanding the essence of direction targeted spells I believe that the information presented is sufficient. Something interesting to note is that although technically the probabilities for either strategy should be 0.5, it has been noted that because of camera angles in the game and right handedness of players, most players in fact dodge upwards a disproportionate number of times.

Good luck on the fields!


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