This is the second article presenting evidence of the occurrence and timing of paleoearthquakes on the southern Hayward fault as interpreted from trenches excavated within a sag pond at the Tyson's Lagoon site in Fremont, California. We use the information to estimate the mean value and aperiodicity of the fault's recurrence interval (RI): two fundamental parameters for estimation of regional seismic hazard. An earlier article documented the four most recent earthquakes, including the historic 1868 earthquake. In this article we present evidence for at least seven earlier paleoruptures since about A.D. 170. We document these events with evidence for ground rupture, such as the presence of blocky colluvium at the base of the main trace fault scarp, and by corroborating evidence such as simultaneous liquefaction or an increase in deformation immediately below event horizons. The mean RI is 170 ?? 82 yr (1??, standard deviation of the sample), aperiodicity is 0.48, and individual intervals may be expected to range from 30 to 370 yr (95.4% confidence). The mean RI is consistent with the recurrence model of the Working Group on California Earthquake Probabilities (2003) (mean, 161 yr; range, 99 yr [2.5%]; 283 yr [97.5%]). We note that the mean RI for the five most recent events may have been only 138 ?? 58 yr (1??). Hypothesis tests for the shorter RI do not demonstrate that any recent acceleration has occurred compared to the earlier period or the entire 1800-yr record, principally because of inherent uncertainties of the event ages.