An analysis of 1955 physics graduate students from 19 Ph.D. programs shows that undergraduate grade point average predicts graduate grades and Ph.D. completion more effectively than GRE scores. Students' undergraduate GPA (UGPA) and GRE Physics (GRE-P) scores are small but statistically significant predictors of graduate course grades, while GRE quantitative and GRE verbal scores are not. We also find that males and females score equally well in their graduate coursework despite a statistically significant 18 percentile point gap in median GRE-P scores between genders. A counterfactual mediation analysis demonstrates that among admission metrics tested only UGPA is a significant predictor of overall Ph.D. completion, and that UGPA predicts Ph.D. completion indirectly through graduate grades. Thus UGPA measures traits linked to graduate course grades, which in turn predict graduate completion. Although GRE-P scores are not significantly associated with Ph.D. completion, our results suggest that any predictive effect they may have is also linked indirectly through graduate GPA. Overall our results indicate that among commonly used quantitative admissions metrics, UGPA offers the most insight into two important measures of graduate school success, while posing fewer concerns for equitable admissions practices.