Here is a critical topic for anyone who plays FPS games. Predicting movements can be a tough topic to master, but it is so crucial in giving you the upper hand. It builds upon the map understanding you gain from the previous FPS post.
In predicting the movement of another player, you need to get an idea of what most people will do in a given situation. For example, you see someone running behind a building or box, we can safely assume that as long as they know that no one is tracking them, they will continue to run out from the other side of the building (or box). However, if you shoot at them and they know you are tracking them, then you can't be sure what side of the building they will come out from, thus your element of surprise is lost. We'll discuss this more in a post on patience.
The general thought that you have to ponder is what would you do in a given situation. For instance, if you are approaching a camped defender, you probably wouldn't go charging at his fortified position, but try to find another way around to get a cleaner shot on him. So when you are the camped defender, think about how your team could really surprise and ambush someone who is trying to circumvent the set defenses.
The final point I'll make on this topic is predicting movements when you are locked in a fight. Generally most people will try to avoid fire however possible, by jumping, ducking, or strafing. If you are both doing the same things, then it comes down more to luck on who will come out alive. So think about the possibility of stepping out of the battle to entice your enemey to follow, then you have set a trap for him and you now have the upper hand again. We'll also discuss this more in a later post on turning the tables.