The Game Theory of Drafting Heroes in Dota 2
Dota 2 is a competitive, e-Sport game which has been updated and played by millions since 2011. Every year, the community comes together for ‘The International’, a community funded tournament where the stakes are extremely high- the winner in 2019 won over fifteen million dollars. Dota 2 is an extremely complex game, as there are 10 players in each game playing simultaneously, reacting to each other’s moves. It is hard to analyze the live action gameplay of Dota 2 in the language of game theory, but we can discuss another part of the game which is just as important- the drafting phase. Like I said, Dota 2 is a 10-player game, with 5 people on each team. In professional Dota, each team has a captain, a player who picks and bans heroes (heroes are the Dota’s characters, of which there are about 110 of them). Two teams cannot pick the same hero, so every draft is unique and an integral part in winning the game. The article I’ve linked below shows how OG, the previous International winners, used drafting to lead themselves to victory and defeat their competition. It largely details what heroes they picked and why (analogous to rating payoffs of specific heroes or certain playstyles). The drafting stage is extremely complex, as it is based on a variety of factors like the game’s current meta (what is popular/strong), what heroes specific teams like to play, nerves, and surprise strategies. We will simplify the drafting stage to help us understand some of the principles that still hold true in the real, complex world of drafting.
An example of an actual Dota 2 Draft- each team picks 5 heroes and bans 6 heroes.
Let’s consider a drafting stage where there are two heroes, hero Strong and hero Weak. Like their names suggest, Strong is preferable (better than Weak) and is not preferable. For simplicity, let’s say Player 1, Tim, is the banner: his two strategies are to either ban Strong or ban Weak. Player 2, Kevin, is the picker, he can either pick Strong or pick Weak. In a set-up like this, Tim has a clear dominant strategy– he should always ban Strong, as the payoff will always be higher compared to banning Weak. Kevin, in response, realizes that Tim will always ban Strong—this could push Kevin and his team to practice Weak, so that if they are forced to pick Weak, they can at least stand a better chance since they have practiced with it. This increases the payoff for Kevin to pick Weak, and over time, this can shift the dominant strategy of Tim.
As we can see, the Game Theory behind drafting is complex- mostly because the payoffs are extremely fluid and always changing. In the case above, Kevin responds to Tim’s dominant strategy by attempting to change the payoff of picking Weak. Scenarios like these are very real and teams often practice (in secret) ‘weak’ heroes before a tournament so that they can pick it (it would be strong for them) without fear of the enemy team banning it. Once we expand the draft to 10 heroes total, the situation becomes even more complicated, since heroes can either work well with each other or counter a hero on the enemy team. The payoff of any hero is changed when a new hero is picked or banned- which makes it almost impossible to quantitatively evaluate Dota drafting. Assistants developed using ML/AI are avaliable which provide hero suggestions based on the current draft, but these are far from perfect. When OpenAI, a startup AI company attempted to create an AI to play Dota 2 against humans, they were very successful in making the AI play the actual game, but they had to put a lot of restrictions on the drafting stage so that the AI could draft effectively, like reducing the hero pool. This showcases how tough of a problem drafting is in Dota, and how we can use Game Theory to understand the nuances of picking and banning.