The competitor may only rely on the facilities of his own person. His logic, awareness, strength and endurance will often come into play. This excludes auto racing and horse racing, most immediately, but also present problems in light of more "developed" competitions where equipment become an important factor. Speed skating, cycling, hockey, football and golf are all called into question by this criterion because equipment is never standardised, or even encouraged to vary.
So you have eliminated just about all modern "sports" . Under your criteria only track and wrestling or boxing seem to come under the heading of sports.We went through all this on my thread are race car drivers atheltes