What could you learn from studying player movement and behaviour on online FPS games?
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.