The recurrence of substorms in the terrestrial magnetosphere depends on many factors. Chief among these are (1) the mechanism(s) by which the magnetosphere stores and rids itself of excess magnetic flux accumulated in the tail (loading‐unloading behavior) and (2) the way in which the power input from the solar wind to the magnetosphere (the coupling) varies with time. In this paper we explore the possible effects of the variability of the interplanetary medium on the statistical temporal distribution of substorms, using a simple substorm model. In this model, substorms recur at fixed time intervals in response to a steady solar wind power input, regardless of its level. In our simulations the power input into the magnetosphere is measured by the rectified north‐south component, Bs, of the interplanetary magnetic field (IMF). We use IMF data at 15‐s resolution from long‐term surveys to construct three statistical model inputs: (1) the random Bs model, (2) the shortwave Bs model, and (3) the longwave Bs model. We find that all the resultant distributions of intersubstorm intervals are skewed with respect to a clear modal peak and cover a wide range of intersubstorm intervals. We also find that the temporal succession of substorm onsets is sensitive to the ratio of the timescale of IMF variation to the assumed intrinsic intersubstorm period. For small values of this ratio the mode of the distribution can be greater than the intrinsic intersubstorm interval by a factor of 2 or more. For large values of this ratio the modal substorm recurrence rate approaches the intrinsic value. We also assess the effect on the temporal distribution of substorm onsets of random (failure to identify a substorm onset) and quasi‐random (incomplete coverage) errors. We use our findings to interpret the results of a large‐scale survey of substorm recurrence rates in the terrestial magnetosphere under nonstorm conditions recently undertaken [Borovsky et al., 1993]. Both shortwave and longwave Bs models could provide an interpretation for this empirical distribution but with certain provisos, which are different for the two alternatives. In the shortwave Bs model, allowance would have to be made for about a 45% failure rate in the identification of substorms. In the longwave Bs model the solar wind power input over the >8‐month duration of the survey would have to be dominated by intervals, each longer than about 3 hours, when the power input was continuously on or off. Reasons are given for preferring the first of these alternatives. Thus, once the contribution of the variability of the solar wind power input on the substorm recurrence rate has been separated out, this would then show that the empirical distribution is not at variance with the notion that under constant solar wind power input, substorms recur periodically.