The graduate admissions process is crucial for controlling the quality of higher education, yet, rules-of-thumb and domain-specific experiences often dominate evidence-based approaches. The goal of the present study is to dissect the predictive power of undergraduate performance indicators and their aggregates. We analyze 81 variables in 171 student records from a Bachelor's and a Master's program in Computer Science and employ state-of-the-art methods suitable for high-dimensional data-settings. We consider regression models in combination with variable selection and variable aggregation embedded in a double-layered cross-validation loop. Moreover, bootstrapping is employed to identify the importance of explanatory variables. Critically, the data is not confounded by an admission-induced selection bias, which allows us to obtain an unbiased estimate of the predictive value of undergraduate-level indicators for subsequent performance at the graduate level. Our results show that undergraduate-level performance can explain 54% of the variance in graduate-level performance. Significantly, we unexpectedly identified the third-year grade point average as the most significant explanatory variable, whose influence exceeds the one of grades earned in challenging first-year courses. Analyzing the structure of the undergraduate program shows that it primarily assesses a single set of student abilities. Finally, our results provide a methodological basis for deriving principled guidelines for admissions committees.