The impact of metallicity on the mass-loss rate from red giant branch ( RGB ) stars is studied through its effect on the parameters of horizontal branch ( HB ) stars . The scaling factors from Reimers ( 1975 ) and Schröder & Cuntz ( 2005 ) are used to measure the efficiency of RGB mass loss for typical stars in 56 well-studied Galactic globular clusters ( GCs ) . The median values among clusters are , respectively , \eta _ { R } = 0.477 \pm 0.070 ^ { +0.050 } _ { -0.062 } and \eta _ { SC } = 0.172 \pm 0.024 ^ { +0.018 } _ { -0.023 } ( standard deviation and systematic uncertainties , respectively ) . Over a factor of 200 in iron abundance , \eta varies by < \sim 30 per cent , thus mass-loss mechanisms on the RGB have very little metallicity dependence . Any remaining dependence is within the current systematic uncertainties on cluster ages and evolution models . The low standard deviation of \eta among clusters ( \approx 14 per cent ) contrasts with the variety of HB morphologies . Since \eta incorporates cluster age , this suggests that age accounts for the majority of the “ second parameter problem ” , and that a Reimers-like law provides a good mass-loss model . The remaining spread in \eta correlates with cluster mass and density , suggesting helium enrichment provides the third parameter explaining HB morphology of GCs . We close by discussing asymptotic giant branch ( AGB ) mass loss , finding the AGB tip luminosity is better reproduced and \eta has less metallicity dependence if globular clusters are more co-eval than generally thought .