The field of visual object tracking is dominated by methods that combine simple tracking algorithms and ad hoc schemes. Probabilistic tracking algorithms, which are leading in other fields, are surprisingly absent from the leaderboards. We found that accounting for distance in target kinematics, exploiting detector confidence and modelling non-uniform clutter characteristics is critical for a probabilistic tracker to work in visual tracking. Previous probabilistic methods fail to address most or all these aspects, which we believe is why they fall so far behind current state-of-the-art (SOTA) methods (there are no probabilistic trackers in the MOT17 top 100). To rekindle progress among probabilistic approaches, we propose a set of pragmatic models addressing these challenges, and demonstrate how they can be incorporated into a probabilistic framework. We present BASE (Bayesian Approximation Single-hypothesis Estimator), a simple, performant and easily extendible visual tracker, achieving state-of-the-art (SOTA) on MOT17 and MOT20, without using Re-Id. Code will be made available at https://github.com/ffi-no

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