Transmissible spongiform encephalopathies are believed to be caused by an infectious form of the prion protein, designated PrPSc. The concentration of PrPSc is often poorly correlated to the level of infectivity. Infectivity can be measured in two ways, namely endpoint titration and the incubation time assay, but patterns of infectivity vary depending on which method is used. These discrepancies can be explained by variation in the aggregation state of PrPSc. Both methods of measuring infectivity are modelled mathematically, and the theoretical results are in agreement with published data. It was found to be theoretically impossible to characterise prion infectivity by a multiple of a single quantity representing ‘one prion’, no matter how it is measured. Infectivity is instead characterised by both the number and sizes of the PrPSc aggregates. Apparent discrepancies arise when these complexities are reduced to a single number.