The thermodynamic theory for the physics of a mature tropical cyclone (TC) tells us that the cyclone's intensity cannot exceed an upper bound, the potential intensity (PI). This combined with an empirical result due to Emanuel leads to a prediction of average TC intensity change, given the change in PI. The slope of the predicted relationship between percentagewise variations in PI and those in intensity can vary between 0.5 and 1, depending on the mean PI and on what threshold is applied to the intensity data. For the Atlantic and Pacific, typical values are around 0.65 when tropical storms are excluded and 0.8 when they are included. The authors use best track data for the North Atlantic and western North Pacific, combined with PI computed from reanalysis data sets, to test these predictions. The results show that observed interannual variations of maximum TC intensity are consistent with the predictions of PI theory. Modest fractions of the variance in actual intensity are explained by PI variations. Much of the interannual variation in PI experienced by the storms comes from variation in TC tracks, so that the storms in different years are more or less likely to sample regions of high PI, rather than from variations in PI at a fixed location.