Over time, the statistical results of multiple events should lead to averages for matchup results. Those averages should reveal what strategies are dominant and what players are dominant. A perfect tournament system would replicate this data set every time in order to reinforce theoretical tier lists or see how, over time, things are changing. Unfortunately, this type of tournament system is too lengthy to be practical, as will be explained below.
With 25 characters (as of now) there are 25 potential matchups per character when including the mirror matchup. So we have 625 different matchups, but in Injustice the stages are important as well, so the actual number of different matchups by a multiple of the number of unique levels, which is 25 (Joker's Asylum and Wayne Manor Night are functional duplicates of Arkham Asylum and Wayne Manor Day, so do not count as unique). So for all 625 character matchups there are 25 different levels that those character matchups can be played on, resulting in 15,625 matchups in the game's statistical layout. To determine the dominant player, a round robin would have to occur where every player plays every matchup against every other player; it would just take too long.
The math is obvious but merits inclusion here because the goal of practical, time limited tournaments should be representing, as accurately as possible, the data spread of those 15,625 matchups. This data spread will be referred to as the perfect matchup data spread.
Over time, random stage select on all matches will more accurately represent that data spread than using the 50/50 or direct counterpicking of the stage by the loser. Both of those options limit the representative data sample from a single tournament. Player choice will naturally impose arbitrary restrictions on what stages are potentially included in the representative sample.
The argument could be made, however, that if stage select is randomized, then it would also be more accurate to impose random character select to better reflect the perfect matchup data spread. I agree, but the inability to do this is a product of community norms. Players would not accept the validity of random character select, but random select for stage violates no norms. We would get tournament results closer to the perfect matchup data spread.
In regards to the argument that not using the 50/50 is removing a game feature for no reason, I would say the reason I laid out above is good enough. Also, by using the 50/50 you would be forgoing another game feature: the normal random select. I argue that using random select on its own is a more accurate method for achieving a representative sample of the perfect matchup data spread.
In regards to the argument that stages are akin to characters and thus Deathstroke - Ferris Aircraft should be considered a single entity, I feel it overlooks the fact that stages cannot be pitted against each other in a matchup. You cannot play your Deathstroke - Ferris Aircraft against your friend's Bane - Fortress of Solitude. You can each choose a character but must share one stage. Therefore I do not feel that stages in Injustice are akin to characters. The two are indeed separable from one another.
Consider, hypothetically, that Deathstroke is statistically proven to be the dominant character on Ferris Aircraft. He is thus dominant in 24 matchups out of the 15,625 possible; one for each character matchup, excluding the mirror, on the Ferris Aircraft stage. Just because Deathstroke is dominant on Ferris Aircraft does not mean that in the perfect matchup data spread Deathstroke will always be the dominant character. This further demonstrates that stage and character are, and should be, separate considerations.
And that's all from me. Thanks for reading and again I do not claim to have perfect logical reasoning. I'm only doing the best I can and am completely open to critique as long as there is some attempt at providing evidence, logical or experimental. I will continue to advocate for random stage select in all matches but also pledge to support the eventual community standard if it happens to differ from my opinion.[\spoiler]
