We propose a new model to explain the transport properties of AgI-based fast ion conducting glasses. The main factor affecting the ionic conductivity is the mobility of the Ag+ carriers, that is controlled by the Ag local environment. We model the ionic conductivity in terms of a percolation between a low-conducting phase (purely oxygen-coordinated sites), and a high-conducting one (iodine/oxygen, I/O, coordinated sites). The percolation takes place along pathways with fractal structure. The nature of the glass network, and namely its connectivity and dimensionality, plays a significant role only for low I/O values, originating the transport and thermal anomalies observed in borate and phosphate glasses.