What could you learn from studying player movement and behaviour on online FPS games? Just thinking of Counter Strike as a canonical example, if you have a coordinate representation of the map and for every player you have a complete history of everything you might need for every moment of time, say every 10 miliseconds or something and you just recorded where the players went around the map, and what they did. So maybe, for example, at each time t you had v(t) a vector function whose components are (location(t), velocity(t), rotationVector(t), rotationVelocity(t), isFiring(t), ammoCount(t), health(t), isEnemyVisible(t), isTeamMateVisible(t)) or whatever other measurements you think would be useful for the state space.

If you collected a bunch of data like this what sort of hypotheses or models would you consider testing? Would it be possible to construct a probabilistic model to classify histories and possibly predict outcomes of player-enemy encounters? Could you train AI bots on this data?
File each given vector function with the win/loss of the game and the team each vector was on. 
Applications of this data: To gauge map balance and provide the least advantage to any one particular team. 

Determine how particular elements of the map effect balance.

Make bots more effective by determining common strategies employed against bots, and the manner in which players address situations (going with the counter strike example: We're down players lets group up on the objective). 

It would be interesting to see which would provide better balance or more effective bots, conventional testing or this in-depth vector analysis.