We hypothesize that highly stressed asperities may be defined by mapping anomalously low b values. Along the San Andreas fault near Parkfield the asperity under Middle Mountain, with its b=0.46, can be distinguished from all other parts of the fault surface. Likewise, along the Calaveras fault the northern asperity of the Morgan Hill 1984 (M6.2) rupture can be identified by its low b of 0.5 as a high stress patch along the fault. We add further evidence to the observations that the b value of the frequency-magnitude relationship of earthquakes is inversely proportional to stress by showing that it decreases with depth in the Parkfield segment of the San Andreas and along the Calaveras fault. In both of these areas, b values above and below 5 km depth are ~1.2 and 0.8, respectively. We propose that probabilistic recurrence times Tr, based on the seismicity parameters a and b, should be calculated from their values within asperities only, instead of from the values of the entire rupture area of the maximum expected earthquake. The strong patches on faults control the time of rupture because they are capable of accumulating larger stresses than the rest of the fault zone, which slips along passively when an asperity breaks. Therefore no information on Tr is contained in the passive fault segments, only in the asperities. At Parkfield the probabilistic estimates of Tr derived from the data in the whole rupture and in the asperity only are 72 (-18/+24) and 23 (-12/+18) years, respectively, compared to the historically observed repeat time of 22 years. At Morgan Hill the Tr estimates are 122 (-46/+76) and 78 (-47/+110) years, respectively, compared to the observed repeat time of 72 years.¿ 1997 American Geophysical Union