Explaining trait differences between individuals is a core and 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 sequence and systematically pair the recombinant gametes of two intercrossed natural genomes into an array of diploid hybrids with fully assembled and phased genomes, termed Phased Outbred Lines (POLs). We demonstrate the capacity of this approach by partitioning fitness traits of 6,642 Saccharomyces cerevisiae POLs across many environments, achieving near complete trait heritability and precisely estimating additive (73%), dominance (10%), second (7%) and third (1.7%) order epistasis components. We map quantitative trait loci (QTLs) and find nonadditive QTLs to outnumber (3:1) additive loci, dominant contributions to heterosis to outnumber overdominant, and extensive pleiotropy. The POL framework offers the most complete decomposition of diploid traits to date and can be adapted to most model organisms.