God, this is truly not worth the time I'm spending on it, but on the off-chance you're just young and bright, let me restate:
Pulling numbers out of your ass looks bad. If nobody's run data. say that first. My question was rather or not you would expect a large online component to inform your estimate, not whether or not you would put up exact numbers for such a model. Apologies if that was unclear, but in context I think it was fairly stated. You clearly do not expect a significant online component and I disagree. I would suspect most people would disagree, again entirely anecdotally.
Randomness is not heteroscedacticity. It isn't. Randomness is not dispersion, period. Don't say one is the other or people who know what they're talking about will call you on it, trust me on this one. Additionally, either the distribution of estimates for probability of victory in offline or online play are homoscedastic or heteroscedastic, depending on whether their variance is significantly different. But the random factor of online play is not necessarily influential on the variance of the distribution of the probability estimates of the outcome even if it is highly influential on the outcomes themselves we make those estimates from. It's entirely possible that the online/offline victory probability estimate distributions are homoscedastic but not identical if their means are significantly different, and our argument is more about a mean shift, ultimately.
I refer to the online component as "random" since moment to moment the effect is largely unpredictable to the player and again, metaphorically, makes the game more akin to roulette rather than poker. In the aggregated data, though, one could have a model taking something like connection bars into account as a factor variable (say, a logistic model regressing p = logit(player_skill_1 + player_skill_2 + connection_quality)) and that could produce a worthwhile model of the influence of the three variables. The question is whether or not the connection quality variable would be significant. Again, I strongly suspect it would, and it would not influence that estimate in a direction that would tend to weight player skill more highly stratifying on worsening connection strengths. If the point of the game is to demonstrate which player has better skill then that outcome would strongly suggest offline isn't "meaningful" for determining that sort of thing. I strongly suspect even an online skill variable would be less influential than the connection quality if we split "offline" and "online" skill components out for each player. To go a little reductio ad absurdum, play anybody in the world on 1 bar and see how well you think that represents your skill level or theirs. This is all hypothetical, but the mechanics of the situation in terms of the effects of lag suggest that this is the case, to the extent that skill is dependent on the lack of variability in the frame data (and it is dependent on that, whether or not you in fact intellectually know the precise frame data or merely that one move beats another). Hence, online play seems less meaningful.
This is getting deep into the statistical weeds, but this is a sore spot with me. TL;DR: Precision in terminology does count, and if we're going to take victory as indicative of skill then online play is almost necessarily less meaningful as a test for such skill.