For competition, I believe that in life in general, it comes from a fear of scarcity: there is only a finite amount of resources in the world, so we have to compete to get a bigger slice of the pie. (Thankfully, that isn't true: the Universe is abundant, and can fulfil our every need if we believe this to be so).
In in terms of sports, those are competitive by nature, so it's a different kettle of fish. The people who excel in sports of any kind are the ones who really believe that they are talented, and TRULY GOOD ENOUGH. They believe this deep down, and as a result, this belief then creates the circumstances for them to excel in their sport. From the coaches who coach them, to the club's they belong to, to the team mates they okay alongside, to 'luck' in games and so on. Excellence in sport is the outcome of self-belief.
So if you really want to excel in sport, send out thoughts of being truly good enough. Not better than opponents, but being great in your own right.