Performance can be saved by having multiple objects share the result of some calculation; of course, this only works if all of them generate the same result. Such situations are often easy to spot but can be tricky to refactor, and so exploiting this would be very implementation-dependent.
Some examples might include finding an object in a scene, reading data from a file, parsing data (such as XML or JSON), finding something in a big list or deep dictionary of information, calculating pathing for a group of Artificial Intelligence (AI) objects, complex mathematics-like trajectories, raycasting, and so on.
Think about each time an expensive operation is undertaken, and consider whether it is being called from multiple locations but always results in the same output. If this is the case, then it would be wise to restructure things so that the result is...
