Geomagnetic indices are routinely used to characterize space weather event intensity. The DST index is well resolved, but is only available over 5 solar cycles. The aa index extends over 14 cycles but is highly discretized with poorly resolved extremes. We parameterize extreme aa activity by the annual averaged top few % of observed values, show these are exponentially distributed and they track annual DST index minima. This gives a 14 cycle average of ~ 4% chance of at least one great (DST<‐500nT) storm and ~ 28% chance of at least one severe (DST<‐250nT) storm per year. At least one DST=‐809 [‐663,‐955]nT event in a given year would be a 1:151 year event. Carrington event estimate DST~ ‐850nT is within the same distribution as other extreme activity seen in aa since 1868 so that its likelihood can be deduced from that of more moderate events. Events with DST ≲ ‐1000 nT are in a distinct class, requiring special conditions.