Above is a video of Leo Manzano, bronze medalist at 1500m doing a prerace ritual of licking his fingers and making the sign of the cross on different parts of his body. I watched him do this before every round. Call it what you will, but what it most definitely is, is a way to calm down before his races. A couple other interesting calming techniques I saw during the Olympics were a Czech sprinter pulling on her ears in different directions and a US high jumper aggressively rubbing his head. If you doubt that they work, give them a try, it is almost hard to worry about anything when you do either of them.
In college part of my degree was a basic class called "Psychological and Sociological Aspects of Sport." In which we learned about many different theories pertaining to anxiety and arousal before a competition. The one that stands out is the "individual zones of optimal functioning", meaning everyone has their own zone of anxiety that will lead to their best performances. With that said both extremes are always going to be bad. You don't want to be on the line in complete boredom, and you don't want to be on the line with clammy hands and your heart racing. What Leo, the Czech sprinter and the US high jumper are doing is getting themselves to tap into their optimal zone that they have discovered over years of racing experience so they do not waste valuable energy. One of the most frustrating things I see as a coach are athlete's doing tons of sprints before a race, or doing crazy mobility, form and flexibility drills before a race that they don't do in practice. This is a recipe for disaster. Contain your anxiety, follow a script, and success will follow.
Again, what you do in the short period of time leading into the competition can be an important factor in what the result will be. When in doubt, have fun and do what you know, fun and routine is never a bad thing.