Inferring and Comparing Game Difficulty Curves using Player-vs-Level Match Data

Prior work has focused on formalizing difficulty curves by using function composition to give precise definitions to curves and their transformations. However, the proposed framework was demonstrated using a single game, and the curves and transformations were defined with respect to the game's ratings-based dynamic difficulty system. In this work, we infer difficulty curves from gameplay data using a method that is based on the aforementioned difficulty system but that can also be generalized to other games for which information on player-vs-level win/loss outcomes is available. Moreover, since this method uses the same difficulty mechanism as past work, it lets us similarly leverage function composition to compare difficulty curves across games, having either a fixed or dynamic level ordering, using a clearly defined vocabulary. We use four different games to demonstrate our method, which relies on an adjustment to traditional playback of ratings-based match data, which we also present in this work.