One of the issues with trying to rank and evaluate individual players is the distance between ability/potential and performance. And further, since this is entirely a team sport, there's also the matter of team improvement/performance, which I suppose ultimately is all-important but is also distinguishable (at least in theory) from individual accomplishments.
While I do consider all the members of "The Big 4" to belong and to be entirely legit as such, I see Mario as a clear #4 because of my first point, above -- i.e., the distance between ability/potential and performance. No one in their right mind would deny Lemieux admittance to the "The Big 4" based on ability/potential. In fact, many of us, myself included, consider him the quintessential "hockey human" and perhaps the single most physically talented hockey player in the history of humanity. But in the area of performance, one could make the argument that Lemieux -- for all his obvious peaks and incredible displays -- didn't do anything that Gretzky didn't already do, better and more frequently, and much more consistently, for a longer period, and with more team success, just a few short years before Lemieux did them (even concurrently). That is why I'd have difficulty seeing his ranking higher than #4.
I'd have no particular argument with anyone placing Howe, Orr, or Gretzky at #1. Even if Orr lacked longevity, all three of those guys were the undisputed best player of their eras. I suppose Howe, like Lemieux in his younger years, was occasionally overshadowed here and there by a peak season (Beliveau, Hull) of a rival player, but then Howe has 20 or 22 seasons in a row of elite performance, plus one of the five or six greatest peaks.
So, in conclusion, I do think "The Big 4" is a legit and justifiable thing.
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Another example of what I'm talking about in terms of a difference between ability/potential and performance: Consider, as a random comparison, Doug Harvey and, say, Chris Pronger. Obviously, I never saw Harvey play at all, so I'm not going to attempt to describe or evaluate his play. But, my question would be: Was there really an appreciable difference (in comparison to peers, in ability to control a game) between Doug Harvey and peak Chris Pronger? I don't know, but I suspect there isn't much of a difference. (Pronger in fact won the Hart trophy, which Harvey didn't.) I suspect that peak Harvey from around 1956 or whenever, and Pronger in one of his few peak seasons, are very even. The difference is not in ability/potential but in overall performance. Harvey had a much more consistent career, over several seasons in a row, of course.
So, then, the matter of dispute when we sometimes try to evaluate players' is the classic peak/prime/career assessment problem. Another way to put it is: How many elite seasons does a player need to have so that (a) longevity and (b) lack-of-sustained prime are not issues of criticism? Those are important questions in trying to compare two or more elite players. On top of those questions, for me another highly important matter of consideration is consistency, the ability to bring it at elite level every night, every season, for a sustained prime.
In the end, there's too much subjectivity in how each of us considers those points to arrive at any reasonable conclusions, but I do generally agree with "The Big 4" at least. And personally I don't see anybody at #5 being close to #4.