Explaining trait differences between individuals is a core but challenging aim of life sciences. Here, we introduce a powerful framework for complete decomposition of trait variation into its underlying genetic causes in diploid model organisms. We intercross two natural genomes over many sexual generations, sequence and systematically pair the recombinant gametes into a large array of diploid hybrids with fully assembled and phased genomes, termed Phased Outbred Lines (POLs). We demonstrate the capacity of the framework by partitioning fitness traits of 7310 yeast POLs across many environments, achieving near complete trait heritability (mean H2 = 91%) and precisely estimating additive (74%), dominance (8%), second (9%) and third (1.8%) order epistasis components. We found nonadditive quantitative trait loci (QTLs) to outnumber (3:1) but to be weaker than additive loci; dominant contributions to heterosis to outnumber overdominant (3:1); and pleiotropy to be the rule rather than the exception. The POL approach presented here offers the most complete decomposition of diploid traits to date and can be adapted to most model organisms.