Success, like happiness, is an objective standard, not a relative one.
If you make more money than your competitor, this says little about your success. Your success is defined by the relationship among: the use of your mind, your efforts in practice and the skill with which you accomplish the realization of a goal. These are things you know, and are objectively verifiable to anyone interested, whether you win any particular competition or not. If you focus primarily on how well you do in relation to others, you’ll lower your esteem in regard to yourself–and you need that esteem in order to succeed. If you focus on how well you do in relation to others, and then you beat most others, you’re still not going to feel very good, because the respect for yourself was never there.