The presence of extra centrioles, termed centrosome amplification, is a hallmark of cancer. The distribution of centriole numbers within a cancer cell population appears to be at an equilibrium maintained by centriole overproduction and selection, reminiscent of mutation-selection balance. It is unknown to date if the interaction between centriole overproduction and selection can quantitatively explain the intra- and inter-population heterogeneity in centriole numbers. Here, we define mutation-selection-like models and employ a model selection approach to infer patterns of centriole overproduction and selection in a diverse panel of human cell lines. Surprisingly, we infer strong and uniform selection against any number of extra centrioles in most cell lines. Finally we assess the accuracy and precision of our inference method and find that it increases non-linearly as a function of the number of sampled cells. We discuss the biological implications of our results and how our methodology can inform future experiments.