A new ocean evaluation metric, the crossover time, is defined as the time it takes for a numerical model to equal the performance of persistence. As an example, the average crossover time calculated using the Lagrangian separation distance (the distance between simulated trajectories and observed drifters) for the global MERCATOR ocean model analysis is found to be about six days. Conversely, the model forecast has an average crossover time longer than six days, suggesting limited skill in Lagrangian predictability by the current generation of global ocean models. The crossover time of the velocity error is less than three days, which is similar to the average decorrelation time of the observed drifters. The crossover time is a useful measure to quantify future ocean model improvements.