There are three levels of sports:
The classic olympic sports, which test strength and form. Speed, lifting weights, throwing spears, etc. Most of them are just barely group activities:
The Olympics does have another aspect of "graceful" sports such as figure skating, acrobatics, etc. which I am not talking about. Since the things the Olympics rewards are so primitive, the rarity of olympic athletes is mostly being 1 in a million genetically + goal-driven and able to work hard.
This type of sport is left over from primitive times when we considered health to be a sign of virtue. There was little enough health, height, power and strength in the world then that it made sense to just honor people who had it. But today these sports are pretty boring! When the Olympics were started, it must have been amazing just to see so many people without any deformities, diseases, malnutrition - so many tall, well-formed people were rare back then. But today nobody thinks that someone who has all 10 good gene variants for leg strength is any better than someone who has only 5 of them. We've moved on and are no longer struggling with basic health matters.
Of course, seeing a gigantic monster lift 1000 kg is still pretty interesting - being one of those people must be an interesting experience, today. But essentially it's arbitrary; if we had preserved a bit more neandertal DNA that 1000kg would be normal, and 2000kg would seem like a big deal, and if we'd never adapted any of it, we'd all be a little bit weaker than we are now. It's just nominal, people could be any size, and have any amount of strength, and the human condition would still be the same. No matter our history there'd always be a distribution.
Within olympic sports, there are divisions - pure, arbitrary power, vs form. Most activities involve both, of course, but in different combinations. In general, though, they focus on power - most of them are about maximizing speed, distance, or weight. Not many involve accuracy.
These are team sports games that have evolving strategy, coordination, and real-time adjustment involved. Baseball, american football, soccer, etc. To be a pro for most positions, you still have to be pretty physically gifted, but not as much as an Olympian. Originally the players had to think on their feet, and strategy mattered - but lately the thinking has moved to the coach, who does a lot of preparation and analysis of trends. There is no longer one "perfect" way to play the game - situational stuff matters.
The rules and regulations about movement within these sports are simulations of the restrictions of movement within a bureaucratic society. This ranges from sports which are extremely controlling of physical motion, like baseball & american football, to ones which are pretty free, like soccer.
Modern sports contain an element that is completely irrelevant to older ones: Information. Now, reputations, patterns, and tendencies matter. This is the next level of competition, and of the theoretical reality of what sports actually are - limited information games. Within this world we don't know what perfect play really looks like.
Pure games of this type are poker, bargaining, and prisoner's dilemma - these games are set up explicitly to remove the physical parts of the game, and directly attack the difficulty of deciding what to do with imperfect information. Olympic sports, which don't have this aspect at all, are totally left behind, and are being demolished by physical advances. It now seems almost immoral to honor an Olympic athlete for his raw power, when he has done nothing to deserve it.
I would advocate changing traditional sports even more to emphasize their modern side - I would support heigh-limit basketball and football (a team can only have players totalling a certain heigh, with an average of 6 feet). By removing the 1 in a 10,000 requirement for height from players, the number of people who could play would be hundreds of times larger. So the ones who made it would be better than a much larger field - and therefore would be much more rare. Imagine how fast, accurate, and smart players would be!