I agree with stranger. The saddest kids we know are the ones whose mothers took great pride in their achievements and happily "enjoyed" maths together. Roll on a few years and if these children don't excel, and worse still are passed by the ordinary kids they used to consider less able, they can have a problem. Their identity can be very much tied around their status as the clever kid in the class, and as well as them then not knowing who they are, they are not confident their parents will accept them for being "average".
(My DC are at a very selective school where roughly 50% go on to Oxbridge and a further two dozen to top American Universities. Here "average" can mean not getting A*s or not getting into Oxbridge. It is a high bar. Curiously my neighbour said last night, he knew 4 people who had been to the school, and none of them had suceeded later in life, indeed a couple were long term unemployed. This might say more about my neighbour and his friends, but I think that there can be a danger at very selective schools and Universities of losing your grounding. There are lots of attributes beyond academics that cause people to become sucessful. And indeed what is success.)
When I said sport, drama or music, I was not really talking about elite sport or orchestra music, but simply widening interests, and mixing with people from different backgrounds or with different abilities.
(Sendsummer - in answer to your question, teenagers taking 20 minutes or more of aerobic exercise each day is proven to be important for long term bone and cardiovascular strength adn weight control, and is, apparently, the single best thing that can be done to improve teenage sleep. Our experience is also that it helps with focus, discipline, team playing and resiliance. It can be quite a shock for academic kids used to being the best at everything, to find that sport takes effort, and that talent is differently distributed.)