Intuitively, extrapolating object trajectories should make visual tracking more accurate. This has proven to be true in many contexts that involve tracking a single item. But surprisingly, when tracking multiple identical items in what is known as "multiple object tracking," observers often appear to ignore direction of motion, relying instead on basic spatial memory. We investigated potential reasons for this behavior through probabilistic models that were endowed with perceptual limitations in the range of typical human observers, including noisy spatial perception. When we compared a model that weights its extrapolations relative to other sources of information about object position, and one that does not extrapolate at all, we found no reliable difference in performance, belying the intuition that extrapolation always benefits tracking. In follow-up experiments we found this to be true for a variety of models that weight observations and predictions in different ways; in some cases we even observed worse performance for models that use extrapolations compared to a model that does not at all. Ultimately, the best performing models either did not extrapolate, or extrapolated very conservatively, relying heavily on observations. These results illustrate the difficulty and attendant hazards of using noisy inputs to extrapolate the trajectories of multiple objects simultaneously in situations with targets and featurally confusable nontargets.