Transforming Game Difficulty Curves using Function Composition

Player engagement within a game is often influenced by its difficulty curve: the pace at which in-game challenges become harder. Thus, finding an optimal difficulty curve is important. In this paper, we present a flexible and formal approach to transforming game difficulty curves by leveraging function composition. This allows us to describe changes to difficulty curves, such as making them "smoother", in a more precise way. In an experiment with 400 players, we used function composition to modify the existing difficulty curve of the puzzle game Paradox to generate new curves. We found that transforming difficulty curves in this way impacted player engagement, including the number of levels completed and the estimated skill needed to complete those levels, as well as perceived competence. Further, we found some transformed curves dominated others with respect to engagement, indicating that different design goals can be traded-off by considering a subset of curves.