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Polynomial-based Video-Oculography (VOG) systems are one of the most attractive gaze estimation methods thanks to their simplicity and ease of implementation. Although the functionality of these systems is generally acceptable, there has been no thorough comparative study to date of how the mapping equations affect the final system response. After developing a taxonomic classification of calibration functions, we examined over 400,000 models and evaluated the validity of several conventional assumptions. Our rigorous experimental procedure enabled us to optimize the calibration process for a real VOG gaze-tracking system and halve the calibration time while avoiding a detrimental effect on the accuracy or tolerance to head movement. Finally, a geometry-based method is implemented and tested. 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