I thought I'd pick a fight
Here's the criteria
1. Great fighters beaten when they were great fighters
2. Division wrecking
3. Ranked fighters beaten
3. Taking on everyone or nearly so
4. Occasional losses top great fighters don't have large impact
5. Losses to less than great fighters when in one's extended prime have a significant impact
6. Judgement is made over one's "extended prime." The longer the prime the better
7. Guesses over "who could beat who" have zero import. Why? Easy, because they are just guesses.
8. Social impact has no bearing. This an in the ring approach.
9. It is only what they did as heavies that counts.
I think too often fighters are simply too close to really rank them. Instead what I am going to do is put them in broad groups and within those groups rank them however you want and I won't argue very often.
Those having an argument for the top spot
Only two men defeated over 30 ranked fighters, were champions across a decade had dominant records against HOFers and had over fifteen defenses as undisputed champion. Joe Louis and Muhammad Ali.
Jack Johnson. Li'l Arthur was simply dominant after his loss to Joe Choyinski. In the month they spent jailed together Choyinski taught Johnson the sweet science and Johnson never looked back. The best of the four black HOF heavies of the time he retired with a 13-3-3 record against HOFers and eight defenses as champion. Clearly the best heavy in the decade from 1906-1915.
These are the division wreckers. Jack Dempsey who once he came under Doc Kearns and really got rolling was simply a revolution in the heavyweight division. He defeated 11 HOFers against only two losses. Though criticized today for not fighting any blacks as champion, the fact is there was only one guy Harry Wills, who remotely deserved a shot. Nevertheless Dempsey loses some position for not fighting Wills in my view. In ony 23 fights Jim Jeffries fought HOFers nine times. Jeffries went 7-1-1 with his loss coming to Johnson after a six year layoff. An athlete so far ahead of his time it asn't funny. Jeffries also didn't fight a black fighter as champion. In his case though i is hard to come up with who the logical guy would have been prior to his initial retirement. Had he stuck around another 2-3 years? The four black heavies noted above would have been severe challenges. While there is a variety of opinion on Larry Holmes' reign? I take the view there were few fighters he should have fought that he didn't. His 2-4 record against HOFers is mitigated somewhat by his twenty title defenses and defeating nineteen ranked fighters. The test of Rocky Marciano's greatness is not that he never lost. It is that he left the division so bereft of challengers it took the sport over a year to make a credible match for the vacant crown and one of the participants had already lost to the Rock. Marciano went 6-0 against HOFers and had six title defenses.
George Foreman gets here really on his singular achievement of winning the undisputed crown twenty years apart. It is a staggering achievement. He went 4-2 against HOFers but only knocked off seven ranked fighters. Sam Langford was not at his best as a heavy but he was still special. Before his eyesight went he was 14-9-8 against HOF heavies. Sam isn't higher because as a heavy he got lazy and he occasionally lost to men he shouldn't have.
Smoking Joe Frazier fought in an in-arguably tougher era than Marciano and may well also have wrecked that division. It is what it is. 1-4 against HOF heavies and defeated eight ranked heavyweights. One of the five most prestigious wins in boxing history makes a big impact here. Sonny Liston was as intimidating as they come. 2-2 against HOF heavies, seven ranked heavies beaten, undisputed heavyweight champ. Evander Holyfield was at his best below heavy, but with the big boys he went 4-1-1 against HOF heavies and defeated ten ranked men and was a two time lineal champion. Ezzard Charles another guy at his best below heavy. But he went 4-4 against HOF heavies, was undisputed champ with seven defenses and defeated 15 ranked heavies. Why isn't he higher? He lost to some heavies he had no business losing to.
One can make a pretty good argument these guys are indistinguishable from the above group, though I disagree. Lennox Lewis went 3-0-1 against HOFers but really met only Vitali in what could be called his prime. He defeated 13 ranked heavies. So why isn't he higher? Two bad KO losses just can't be ignored. Mike Tyson really only beat one HOF heavyweight and that was Holmes. His overall record against HOF heavies? 1-3. He defeated 12 ranked fighters and had two defenses as undisputed champion.
Jersey Joe Walcott went 3-6 against HOF heavies with almost all those fights after he was 35. He defeated eight ranked heavies but was hardly unbeatable. Floyd Patterson is a guy I think gets short shrift. Yup he got destroyed by Sonny Liston, twice. Six of his eight losses came to HOFers and the only HOFer he defeated was Ingo. But he also defeated eleven ranked guys over 15 years. Not bad. Harry Wills came along too late to face the four great black heavies pre WWI, bu in their decline he owned them. He went 15-5-6 against HOFers but all those fights were a good five years after Langford, McVea and Jeanette were past it. He should have gotten a shot against Dempsey. Max Schmeling has one of the five most prestigious wins in the history of the division. The only man to handle Louis in his prime. Six wins over ranked fighters and three wins over HOF heavies. Max Baer punched his way through nine ranked fighters and went 2-2 against HOFers.
Now one might ask where Gene Tunney and Bob Fitzsimmons are. In my view neither did enough at heavyweight to make this list. Ona p4p basis? Those two would both belong inside the top ten here. But that's not what I'm trying to do. The other guy it kills me to leave off is the great Peter Jackson. An Australian Aborigine who went 61 rounds to a draw with Jim Corbett was viewed in his own time as a legend but I just haven't gotten my hands around his career.
This leaves us with the open question of the Brothers Klitschko. I did not leave them off because they are still active, I left them off because though they have beaten a cauldron of ranked guys, between them they have faced only one clear HOFer to this point. Not their fault, but again, it is what it is. I also don't know how to deal with them not facing one another and what that means (if anything).
That's my list. Have at it!