Yes, and we're talking about statistically measurable things. There is plenty of room to experiment with different reward systems in competitions. For example, in Finland, there is an alternative figure skating judging system for kids' competitions, and they have medals (1,2, and 3 place), but everyone else is the rest. Thus they send a positive competence signal to the winner and a relatively weak negative competence signal to others (i.e. no one is labeled "worst", plus everyone gets some prize reward).

Tennis' Play&Stay program for kids under 10 years old is also a good example – they use different tournament structures, so no one feels like they lost.