I would expect that PG/EG participants in math competitions find themselves up against other PG/EG participants in short order, at which point the number hours of study and practice become a significant determining factor in success. Once "Who wants it more?" is a major part of the activity, it becomes very easy for someone to say, "Not me," or, "Eh... I want it, but not that badly."
I would have expected this too, and I still expect that this effect kicks in eventually, but I've been surprised not to see it so far (and "so far" includes everything in the UK below the "top 1000 under-19s" competitions). I think what's going on is that presenting as "PG in maths" goes along with enjoying doing for fun the kinds of things you need to do to prepare, at the levels DS has met so far. If I think about it, he spends a fairly large amount of time doing maths, and a fair chunk of that is spent being stretched to the point of frustration, but he nevertheless doesn't think of himself as working particularly hard at it, and hence neither do I. It hasn't so far been necessary for him to work with doing well in competition as a goal: doing well in competition has been a side-effect of things he was doing anyway, for a mixture of ordinary school work and amusement. I am going to be interested to see how far that continues, and what happens when DS does have to choose, or not, to do something specifically in order to do well in competition.
Competitions can be fun and healthy, but striving for the very highest levels is often unhealthy. Training at any one thing comes with real opportunity costs as it crowds out other healthy activities, and the individual has to be willing to pay those costs.
I strongly agree.
