To win in New York hip-hop, you gotta embody brash triumph against stacked odds; scrappy runners-up only earn affectionate shrugs. Burly Brooklyn ex-con Saigon once thought that he could win like Biggie or Jay-Z (or at least Jadakiss); but his label, Atlantic, balked, and tied up his 2007 debut album. Now freed, and executive produced by Just Blaze, Greatest Story pounds and sways with teary defiance, testifying for lives proscribed by broken homes, petty crime, and prison. It also boasts one of the aughts’ fiercest nonhit singles, “Come on Baby” (which samples J. Geils and features Jay-Z). Saigon deserves more than a shrug.