Even if only 10% of olympic sports were team sports - but those teams were things like basketball/soccer/volleyball that have 15+ players per team - that would mean the majority of medals given out are to people who were on a team.
Teams are hardly as large as 15+. Of course the athletes that don't compete are not given medals. Even if you more then double the amount I calculated let's say 1%. That's still a reasonable price pool.
