In gamma-ray burst research, it is quite common to fit the afterglow light curves with a broken power law to interpret the data. We apply this method to a computer-simulated population of afterglows and find systematic differences between the known model parameters of the population and the ones derived from the power-law fits. In general, the slope of the electron energy distribution is overestimated from the prebreak light curve slope while being underestimated from the postbreak slope. We also find that the jet opening angle derived from the fits is overestimated in narrow jets and underestimated in wider ones. Results from fitting afterglow light curves with broken power laws must therefore be interpreted with caution since the uncertainties in the derived parameters might be larger than estimated from the fit. This may have implications for Hubble diagrams constructed using gamma-ray burst data.