We present a complete information game-theoretic model for crowdsourcing contests. We observe that in design contests, coding contests and other domains, separating low quality submissions from high quality ones is often easy. However, pinning down the best submission is more challenging since there is no objective measure. We model this situation by assuming that each contestant has an ability, which we interpret as its probability of submitting a high-quality submission. After the contestants decide whether or not they want to participate, the organizer of the contest needs to break ties between the high quality submissions. A common assumption in the literature is that the exact tie-breaking rule does not matter as long as ties are broken consistently. However, we show that the choice of the tie-breaking rule may have significant implications on the efficiency of the contest. Our results highlight both qualitative and quantitative differences between various deterministic tie-breaking rules. Perhaps counterintuitively, we show that in many scenarios, the utility of the organizer is maximized when ties are broken in favor of successful players with lower ability. Nevertheless, we show that the natural rule of choosing the submission of the successful player with the highest ability guarantees the organizer at least 1/3 of its utility under any tie-breaking rule. To complement these results, we provide an upper bound of Hn ~ \ln(n) on the price of anarchy (the ratio between the social welfare of the optimal solution and the social welfare of the Nash equilibrium). We show that this ratio is tight when ties are broken in favor of players with higher abilities.