A natural way to think of player movement in arbitrary games is the path they take between different game states. A play trace is then a path that a player takes in this high-dimensional game state space. In order to visualize these paths, we use Classical Multidimensional Scaling (CMDS) [3, 17] to represent observed game states in two dimensions. CMDS takes an input matrix that specifies the distance between every pair of states and outputs a set of points, which are positioned to minimize a loss function on all inter point distances. Therefore, the transformation will place states that are similar close together and states that are dissimilar far apart, making it easy to see the similarity of states that are visited by many players. We used the MDSJ library for Java [18].
Different metrics for calculating distances between states will result in different configurations of points after CMDS is applied. In general, the distance metric should be different depending on the type of game. Additionally, the distance metric can be adjusted depending on what features of the game the designer wishes to analyze or what features he or she wants the state graph to have. For example, if the distance metric has a component that compares how many steps it takes to reach a goal state, then it will naturally cause goal states to cluster together. States from which it is difficult to reach a goal state will appear far away. This allows the designer to identify players who are not making progress and investigate why they are having trouble. An example of Play tracer's output can be seen in Figure 1, which shows the state space for one level of an educational game we have been developing. Playtracer takes in a list of all of the states that the player visited and a distance metric that calculates the distance between states, and creates a graph where the states are vertices and player movements are directed edges. Here, the yellow state is the start state and the green state is the goal state. To identify which states are most commonly visited, the size of a state is proportional to how many players reach that state.