The stress drops of small earthquakes often exhibit spatial patterns of variability. If moderate and large earthquakes follow the same spatial patterns, the stress drops of possible future damaging earthquakes could be better predicted by considering the stress drops of nearby small events. Better stress drop predictability could reduce ground-motion uncertainty in Probabilistic Seismic Hazard Assessment (PSHA) and Earthquake Early Warning (EEW). I find that for an internally consistent stress drop catalog of M1.8-3.1 events in southern California, the stress drops of the bigger earthquakes are predictable from the nearby smaller events. However, this catalog only weakly spatially correlates with another catalog of M3.0-5.8 earthquakes, and is spatially uncorrelated with five other stress drop catalogs of M≥3.4 earthquakes. For southern California events M5.5-7.5, stress drops compiled from the literature are weakly spatially correlated with the stress drops of the M1.8-3.1 events, although the correlations are not statistically significant. The lack of strong spatial correlation may be due to actual differences in the controlling factors of stress drop, for example dynamic weakening in moderate-to-large earthquakes. Alternatively, a stronger spatial correlation may exist that is obscured by methodological heterogeneity and large errors in the stress drop estimates. Either way, the stress drops of small earthquakes do not appear to be good predictors of the stress drops of nearby moderate-to-large earthquakes, at least for current techniques of stress drop estimation. If these results are representative, small-earthquake stress drops are not currently useful for substantially reducing uncertainty in PSHA and EEW.