In the LATER model, randomness of saccadic latency arises through random variation in the rate of rise of the decision signal. But does it vary independently at different locations? If so, when pairs of targets are presented asynchronously, and the participant makes a saccade to the more salient one, the choice of target should be stochastic. Further, it should be possible to predict the probabilities at different asynchronies from the latency distributions for each target on its own. This study verifies the prediction in human subjects. In the real world, independent random variation of latency at different locations will give rise to randomness of choice of target.