Marcus Allen, who went into the Hall of Fame as a Kansas City Chief, repudiating his time with the Raiders, was the epitome of competitiveness tempered with humility. Allen would make the most exhilarating of runs from 20, 25 yards out, breaking tackles, spinning, hanging a tempting leg out for a linebacker to grab only to snatch it away just as the defensive player reached for it, juking and hopping around tacklers and ending up in the end zone, whereby he would simply look for the nearest official, hand him the football, and jog to the sidelines. No one was more competitive, to my knowledge, than Marcus, but no one was more humble, either.
He used to tell the young Chiefs' running backs and wide receivers, "When you get in the end zone, act like you've been there before." The only time I saw him refuse to hand over the football was when he broke the all-time career touchdown record (I've gotta rub this in, guys, sorry: It was against Denver). He floated over the defensive line with a tremendous leap from three yards out and came down fully a yard and half inside the end zone. As he came to his knees, the umpire was standing there holding out his hands for the ball. If you've ever seen the film clip, it is classic Marcus. You can see him clearly mouth the words, "Sir, if you don't mind, I'm keeping this one."
If you can play any game with the attitude that Marcus Allen played football, you have nothing to worry about from your competitive spirit.