You might want to read what John Benson has to say about the value of math contests. There’s a level of thinking and problem-solving in these contests that is extremely valuable beyond mere rankings, accolades, or recognition.
The contest itself is the carrot, but by no means is it why we spend so much time doing this. Out hope is that some of our mathletes will find that math is not about grades, nor is it about winning. It is about working on interesting problems with others who also think it is fun to work on interesting problems.
Go to the link and read it all.