Distance-bounding (DB) protocols protect against relay attacks on proximity-based access control systems. In a DB protocol, the verifier computes an upper bound on the distance to the prover by measuring the time-of-flight of exchanged messages. DB protocols are, however, vulnerable to distance fraud, in which a dishonest prover is able to manipulate the distance bound computed by an honest verifier. Despite their conceptual simplicity, devising a formal characterization of DB protocols and distance fraud attacks that is amenable to automated formal analysis is non-trivial, primarily because of their real-time and probabilistic nature. In this work, we introduce a generic, computational model, based on Rewriting Logic, for formally analyzing various forms of distance fraud, including recently identified timing attacks, on the Hancke-Kuhn family of DB protocols through statistical model checking. While providing an insightful formal characterization on its own, the model enables a practical formal analysis method that can help system designers bridge the gap between conceptual descriptions and low-level designs. In addition to accurately confirming known results, we use the model to define new attack strategies and quantitatively evaluate their effectiveness under realistic assumptions that would otherwise be difficult to reason about manually.