The Math of Tier Lists
In many competitive video games and trading card games, members of the community come together to create a tier list. Tier lists are a ranking of some part of the game, whether it be characters, decks, customizable abilities, or other variable facets of the game. Tier lists contain groups, or tiers, of characters, grouping them according to how good or powerful they’re perceived to be Many communities have some form of “official” tier list which is made by a committee of respected community figures, and when players discuss how good a character is they use this list as a reference. This definition raises a question–how are tier lists formed, and what do the relative positions of the characters mean?
All tier lists are not created using the same methodology. Some are based purely on opinion, while others factor in tournament results. The two in the linked articles contain tier lists for two games in the Super Smash Bros series, Melee and Project M. Both of these are opinion based, as many people believe that tournament results don’t accurately represent how good some characters are. Results are often skewed by the skill of one or two exceptionally good players as well as the popularity of certain characters. It also takes a lot more effort for people to study and analyze results than to base their lists off of personal experience. This comes mainly in the form of matchups, which are head to head comparisons of two characters. Matchups can either be even or in one character’s favor, and tend to be represented numerically. A 50-50 matchup is even, a 55-45 matchup is slightly in one side’s favor, an 80-20 matchup is heavily in one side’s favor and approaches being unwinnable for one side, and so on.
One interesting way to think of all of the matchups in a particular game is as a giant payoff matrix. The analogy doesn’t quite hold, as player skill often causes matchups to go in the opposite direction, but under ideal situations matchups should go according to their numbers. Therefore, there will likely be a few characters who end up being dominant, and several characters who are never dominant due to their bad matchups. For example, if conventional wisdom on what various matchups are is to be believed, the nash equilbrium in melee consists of between two and four characters, and everyone else should never be played. However, people play every character in the game, even when trying to compete. These players always know that what they’re doing is not strictly the best option for competition, yet they proceed regardless. This tends to be true for all games; for various reasons, people will willingly pick options that they know are bad. This ultimately links back to the purpose of playing games in the first place: fun. Even if many of the games we study for learning game theory aren’t deep or complicated, the main motivator for playing them would be fun. While math may be helpful for understanding these games, it doesn’t have the final say in how the game is played.
https://esports.htc.com/articles/esports-tier-list
https://smashboards.com/threads/the-project-m-backroom-releases-new-pm-3-6-tier-list.450025/