Based on accomplishments. I do not take H2H into consideration because styles make fights and athletes from different eras cannot be compared, however i do consider dominance over the contemporary competition. I dont consider losses when the fighter is not at his best, but i do consider wins after the boxers prime because it represents overcoming adversity. 1.Ali(3 time lineal champion, regaining title 10 years after first time after 3 years exile, avenged loss to frazier, beat George Foreman, Ken Norton, Patterson and Liston among many many others), 2. Joe Louis(Extremely long reign, 20 title defenses, exciting fighter, came back from a loss to schmeling to get a first round KO.), 3. Larry Holmes(7.5 year reign ended only by Spinks Robbery, wins over ****ey, williams etc), 4. Evander Holyfield(Top wins vs Tyson, Bowe, Foreman, Holmes, moorer 2x, mercer, Douglas, Dokes, Ruiz, stewart. Came back from adversity several times, longevity, came from LHW, exciting action fighter who ogave fans countless wars, written off as finished countless times, robbed of 5th world HW title against Valuev 20 years after going up to HW ) 5. Jack Dempsey(7 year reign, exciting action fighter, knocked the **** out of bigger fghters), 6. Mike Tyson(Youngest HW champ ever, unified the title by beating all 3 champions, came back to win 2 titles after 4 years inactivity, exciting action fighter, Wins over Berbick, Smith, Tucker, Holmes, Thomas, Biggs, Spinks, Bruno 2x, Williams, Stewart, Ruddock 2x, Seldon(LOL), Botha, Golota) 7. George Foreman(destruction of Joe Frazier, Ken Norton came back from reitrement after 10(!) years to destroy Gerry ****ey, Cooper, Rodriguez. Valiant effort against evander holyfield, knocked out Coetzer, beat Stewart, won HW champonship again after 20 years against MM by knockout, robbed in 1997) 8. Rocky Marciano(retired undefeated, showed grante chin and huge heart several times, knocked out walcott, behind on the scorecards with one punch in the 13th round) 9. Lennox Lewis(3 time world champion, undesputed champion, wins over Bruno, Ruddock, Morrison, Mercer, Tua, Rahman, McCall, Holyfield, Tyson, V. Klitschko) 10. Joe Frazier(wins over ellis, quarry, bonavena and ali) 11. W. Klitschko, 12. Sonny Liston, 13. Floyd Patterson, 14 V. Klitschko 15. Rid**** Bowe