Ali was the greatest sports entertainer ever, easy. Greatest sportsman, more debatable.
What do we mean when we say the greatest sportsman?
They have to dominate their sport, and be the unquestioned greatest in their own sport. Otherwise they're not even in the conversation.
Do they have to extend in public perception beyond their sport? I don't see why - that's about sports entertainment, not sport.
So, among the handful who can legitimately claim to be the undisputed greatest at their sport, how do we distinguish? I'd say by level of competition and degree of dominance.
My view on Ali is that Louis, Johnson and Marciano are all in the argument as best heavyweight ever - and there are others if we put "pound for pound" into the question. If he's not the undisputed best boxer ever, how can he possibly be the best sportsman?
The most obvious list has Pele, Don Bradman and Babe Ruth. Every one is in a mbutt-participation sport. Bradman has the greatest degree of dominance, but in the smallest sport, since he played before the Indian cricket boom. Pele is at the opposite end - he's not as dominant, but he's in the biggest sport of them all. Ruth, of course, drops in the middle. I can't split these three, but they are #1-#3
The only other person I'd argue into the equation is Rod Laver, but I don't think that tennis in the 1960s has the level of competition it does now. Now, if he'd played the slams in 1963-8 and won 20+ slams and four or five Slams in the eight years, then he would get into the question - and he was *that* good. With the actual career: #4
Dismissing some of the other obvious names (these form the next tier down)
Nicklaus - is he really the best golfer ever? (Woods, Bobby Jones)
Gretsky - undeniably the best ice hockey player ever. I was going to dismiss him for the sport being too small, but he played in a sport that was a lot bigger than it was ten years earlier. However, there isn't the historical depth that soccer, baseball, cricket and tennis have. I think he's my #5.
Montana - not the best by enough, not enough depth in his sport, nor in his position.
Jordan - You're quite sure that Bird and Johnson weren't better? Really? And isn't this before the international breakthrough into the NBA, in which case the competition base is pretty narrow.
People who dominated smaller sports, like Sergei Bubka (pole vault), Paavo Nurmi (distance running), Michael Schumacher (motorsport)*, Mark Spitz (swimming), Steven Redgrave (rowing) just never faced the breadth of competition that the best in the bigger sports faced.
Oh, and finally: Anyone want to make a case against Martina Navratilova as the greatest sportswoman? Total dominance of a sport that has more depth of female competition than just about any other.
* Motorsport is something of an exception here - the problem here is more that to reach a high competitive level, the driver has to shell out a lot of money, and many young talented drivers never get the opportunity to prove themselves because they can't afford to. The consensus view is that there are probably loads of brilliant cart drivers who never get a sponsor and can't buy themselves into formula racing, so the problem is that the pool of potential competition is restricted by wealth, rather than by lack of interest.
-- Richard Gadsden "I disagree with what you say, but I will defend to the rest your right to say it" - Attributed to Voltaire