The concept of quantitative performance has been used increasingly outside work management, its main field of origin, since the advent of the industrial era, pervading not just experimental psychology and many domains of science and engineering, but virtually all sectors of social life. Surprisingly, the key defining characteristic of performance measures seems to have systematically escaped notice: a performance is a numerical score subject to a deliberate extremization (i.e., minimization or maximization) effort exerted by a human agent against the resistance of a limit. Because of this characteristic performances must be recognized to constitute measures of a very special kind, where the numerical is marked axiologically. The paper contrasts the extremized scores of performance measurement with the optimized measures of feedback-controlled, regulated systems. In performance measurement the best numerical values are extrema, rather than optima, and the function that links the axiological value to the numerical value is strictly convex, rather than strictly concave. One-dimensional performance measurement is analyzed in the extremely simple case of spirometry testing, where forced vital capacity, a measure of respiratory performance, is shown to be determined by the interplay of two variables, neither of which can be directly measured: the maximization effort, which varies haphazardly from trial to trial, and the patient’s total lungs capacity, a personal upper bound, whose inductive estimation is the goal of spirometry testing. The paper shows that the magnitude of the estimation error decreases linearly with the magnitude of the patient’s effort, explaining why respirologists so strongly urge their patients to blow as hard as they can into the spirometer. The paper then turns to two-dimensional performance, analyzing distributional data from a psychology experiment on speeded aimed-movement. The variation of the speed/accuracy balance is shown to entail systematic changes in the markedly asymmetrical shapes of movement time and error distributions: The stronger the directional compression effect observable on one performance measure, the weaker this effect on the other. These observations are hard to reconcile with the traditional view that performance measures are random variables and raise doubts on the suitability of the classic descriptive tools of statistics, whether parametric or nonparametric, when it comes to the decidedly special case of performance data. One possible direction for a more appropriate statistical approach to performance data is tentatively outlined.