Today I'm going to dissect the matter and try to point out some common misconceptions that are often made when talking about the subject. I'll also attempt to summarize what I believe to be the real underlying criticism that is posed by advocates of the "luck opposite to skill" philosophy.
My Definition of Sport
My definition sport is: "A game wherein the rules are designed in such a way to minimize random factors as much as possible".
So why is this relevant? On many occasions the Luck vs Skill proponents have in mind that a true test of skill measuring should aim to be a sport (according to my definition) and that the use of random factors will undermine the true measurement of the player's skill levels.
Honestly, part of the rationale employed on that argument is true. When used improperly randomness (and, by extension, luck) can occasionally be detrimental by handing the victory to the luckiest player rather than the most skillful. But, on the flip side, randomness can also be used to enhance the underlying competition of the game (as well as a myriad of other benefits that I will have to reserve for a post of its own).
For a long time I have been thinking about this topic, so much so that I have devised a phrase that has now become one of my truisms: "There's just as much luck in skill as there is skill in luck". So, if you'll indulge me for a while, let me dissect what I mean by it.
Luck in Skill
This aspect of the phrase is the one most readily recognizable but sometimes also forgotten by many. What this means is that, even at absolute competitions with no overt randomness whatsoever, there are still unaccountable factors that most certainly will affect the outcome.
We normally view this as the "human-factor" or the "external-factor" of a game. When a competitor under-performs seemingly at random because it "wasn't their day" or when teams demonstrably attain better results when playing at their home stadiums in contrast to unfamiliar ones.
We understand that these factors are just a natural part of reality and that no amount of checks, rules and boundaries can ever completely get rid of them. We embrace the competitive spirit of the game and recognize that these factors, while undeniably existent, are generally disregarded in the light of the objective and concrete skills the game demands.
Skill in Luck
Perhaps less obvious than the former is the notion that there is also plenty of skill in dealing with random factors. The most obvious of which is the skill of dealing with unforeseen outcomes. In a game like poker, a lot of the strategy lies on devising your game plan based on the initial hand you're given, and many recognize professional poker play as one of the most skill intensive games there are.
Sure, on any given hand, a beginner may even beat a pro, but given enough rounds, the more experienced player will incrementally tend to win, based on their ability to deal with the adverse random nature of the starting positions.
Another frequently ignored part of randomness is that, often, games offer possibilities for players to diminish or augment random factors. This means that the veteran player who is more skilled at the game will know at what times to press their luck or to fall back onto more reliable strategies.
The Proper Relation between Both
So if Skill and Luck are not the opposites of each other, what is the relation between them? Well, on my opinion, they can be interpreted as two different axis on a graph.
A Final Thought Experiment
As a thought experiment; how much luck is too much? In other words, when analyzing the factors that contribute to a player's victory, what percentage can be attributed to random factors and events such that it would significantly impact the outcome?
While there's no clear answer to this question (and it is likely there never will be given the volatile nature of human taste), I have come to believe that the rule of thirds seem to apply reasonably well in this situation too. That is, if on a given game at least 33% of the factors that led a player to win were purely random, that game will generally be perceived as being too luck based, especially by those who tirelessly claim that luck and skill are opposites.