Fraction of pairs of photometric analogs differing by more than the amount along the abscissa in Δlog  R′ _HK. Although 26% have identical log  R′ _HK values within the typical scatter of 0.08 dex, 26% differ by more than 0.3 dex, and 16% differ by more than 0.4 dex. Because such large differences in log  R′ _HK are so common among photometrically indistinguishable stars, any attempt to predict log  R′ _HK from photometry alone will show large residuals, no matter what algorithm is used to make the predictions.