We study the manipulability of stable matching mechanisms. To quantify incentives to manipulate stable mechanisms, we consider markets with random cardinal utilities, which induce ordinal preferences over match partners. We show that most agents in large matching markets are close to being indifferent overall stable matchings. In one- to-one matching, the utility gain by manipulating a stable mechanism does not exceed the gap between utilities from the best and worst stable partners. Thus, most agents in a large market would not have significant incentives to manipulate stable mechanisms. The incentive compatibility extends to many-to-one matching when agents employ truncation strategies and capacity manipulations in a Gale-Shapley mechanism.