Genome editing is almost completely reliant on viral delivery to achieve therapeutic goals, hindering widespread clinical adoption. Chemically defined delivery vehicles such as cationic polymers are versatile alternatives to engineered viruses, but their clinical translation hinges on rapidly exploring vast chemical design spaces and deriving structure-function relationships governing delivery performance. Here, we discovered a polymer for efficient ribonucleoprotein (RNP) delivery through combinatorial polymer design and parallelized experimental workflows. A chemically diverse library of 43 statistical copolymers was synthesized via combinatorial RAFT polymerization, realizing systematic variations in physicochemical properties. We selected cationic monomers that varied in their pK<sub>a</sub> values (8.1 to 9.2) as well as in the steric bulk and lipophilicity of their alkyl substituents. We also incorporated co-monomers of varying hydrophilicity and elucidated the roles of protonation equilibria and hydrophobic-hydrophilic balance. We screened our multiparametric vector library through image cytometry and rapidly uncovered a hit polymer (P38), which outperforms state-of-the-art commercial transfection reagents, achieving nearly 60\% editing efficiency via non-homologous end-joining. Structure-function correlations underlying editing efficiency, cellular toxicity, and RNP uptake were probed through unbiased statistical learning approaches to uncover the physicochemical basis of P38's performance. Although cellular toxicity and RNP uptake were solely determined by polyplex size distribution and protonation degree respectively, these two polyplex design parameters were found to be inconsequential during RNP delivery. Instead, polymer hydrophobicity and the Hill coefficient, a parameter describing cooperativity-enhanced polymer deprotonation, were identified as the critical determinants of RNP delivery. Our unconventional approach not only discovered a novel polymeric vehicle that may have remained inaccessible to chemical intuition, but also yielded statistically derived design rules to guide the synthesis of future polymer libraries.