In various embodiments, the gaming system, gaming device, and gaming method disclosed herein includes an accumulation sequence and a competition sequence. In one embodiment, the gaming system includes competitor points which determine (i) a competitor's eligibility to participate in the competition sequence and (ii) the competitor's relative probability of success in the competition sequence. In this embodiment, a competitor (which is either representative of an actual player or a virtual, gaming system controlled player) accumulates competitor points during one or more point accumulation sequences which occur in association with designated events. For a subsequent competition sequence, the gaming system determines if a competitor will participate in the triggered competition sequence based on the competitor's accumulated competitor points. For the subsequent competition sequence, the gaming system further determines the competitor's relative probability of success in the competition sequence based on the competitor's accumulated competitor points.