So many people going for none of the above. Given the criteria in the OP, give me a name that’s better than Ali.
Depends on criteria, really. Ali's greatness isn't down to his performance. There are athletes who were better at their sport than Ali was at boxing. His greatness came down to his impact outside of the boxing ring. I've chosen to base my vote on sporting performance only.
My vote is for Eddy Merckx. I don't think any other athlete comes close him in terms of dominating every area of his sport. Athletes like Karelin dominated Greco-Roman wrestling, but that's a fairly straight-forward sport. In cycling there are specialists for different races, and Merckx routinely kicked the ass of everyone in every type of race.
To put it into perspective:
- He won 11 Grand Tours (three week stage races) in total. 5x Giro d'Italia, 5x Tour de France and 1x Vuelta a España (which he only entered once). That's an all-time record for total Grand Tour wins, Giro wins and Tour wins. Only seven riders in history have all three Grand Tours. Merckx is one of three to win all three consecutively. Those numbers could go down to six and two if Froome is eventually banned for the dodgy test last year.
- He has more stage wins in Grand Tours than any other rider, and still holds the record for total amount of Tour de France stage wins.
- He won all three classifications (overall standing, points and mountains) during a single Tour de France and a single Giro d'Italia. He is the only rider ever to have done this in either race.
- Merckx won all five of the Monuments of cycling (the biggest one day races) at least twice. Only two other riders have won all five throughout history. He also has a total of 19 Monument wins, which is an all-time record. The guy behind him has 11 total wins. He also holds the record for most total wins in two of the Monuments (Milano-Sanremo and Liege-Bastogne-Liege).
- He won the World Championships three times. This is also a record.
- Merckx won a total of 525 races during his career. This is roughly 150 races more than any other rider.
- In 1972 he set an hour record that has only ever been beaten with more aerodynamic equipment or use of blood doping methods that weren't available in Mercxk' day.
He also did most of this after suffering a serious back injury in a crash with a motorbike that he never fully recovered from.
He's so far ahead of anyone else in the sport that it's hard to comprehend. When a rider matches just one of the exploits mentioned in the bullet points above he goes down as a cycling legend and all-time great. No single rider has ever matched two.
He was pretty much the best at every type of race in an era that includes several others of the best riders of all time, like Roger de Vlaeminck, Felice Gimondi and Jan Janssen. In terms of leaving a legacy filled with near unbreakable records, I think only Gretzky gets close to him.