Scholars have used mathematical models to estimate the missing length of deteriorated scrolls from ancient Egypt, Qumran, Herculaneum, and elsewhere. Based on such estimations, the content of ancient literature as well as the process of its composition is deduced. Though theoretically reasonable, many practical problems interfere with the method. In the current study, the empirical validity of these mathematical models is examined, showing that highly significant errors are quite frequent. When applied to comparatively intact scrolls, the largest contribution to errors is the subjectivity inherent in measuring patterns of damaged areas. In less well preserved scrolls, deterioration and deformation are more central causes of errors. Another factor is the quality of imaging. Hence, even after maximal reduction of interfering factors, one should only use these estimation methods in conjunction with other supporting considerations. Accordingly, past uses of this approach should be reevaluated, which may have substantial implications for the study of antiquity.