Most online poker sites offer the same game structure (up to slight differences in rake) at multiple stakes. Take, for example, the 6-max hyper SNGs on Pokerstars, which are offered at 11 different buy-ins ranging from a low of $1.50 to a high of $1000.
Now, comparing the level of play at the top end (as showcased on tonkaaaa's Twitch stream, for example) to that at the lowest levels, the quality of play is clearly better at the upper end. But differences in the skill levels of the player pools at adjacent "rungs on the ladder" are much harder to spot; indeed, there is frequently some degree of overlap between pools at one level and its neighbours.
Does the mean skill level of the associated player pool increase at a uniform rate as one moves up the ladder, or is the pattern more complicated? (e.g., does the skill level "saturate" somewhere below the highest stakes, with bankroll considerations, rather than skill edge, determining who plays at the very top?)
While I use the 6-max hypers as an example case, I would be interested in observations from other users on skill gradients across other tournament structures or cash games as well.
A commenter has raised a legitimate question -- how does one measure skill? For the sake of argument, let's use ROI as a proxy measure.
Consider the following thought experiment. Imagine a poker player with a short term memory problem -- the player immediately forgets the hand he/she has just played. (This way, there's no potential learning effect to worry about.)
Let's say we very carefully measure this player's ROI at the $1.50 level by having the player play 1,000,000 tournaments against randomly selected opponents. We repeat the experiment at the $3.50 level, the $7.00 level, and so on.
Our player's ROI is now effectively functioning as our "skill-o-meter" for the average player at each of the rungs on the ladder between the top and bottom of the ecosystem. Naively, we would expect this to show some form of decreasing trend (although the corresponding decrease in rake at the higher levels will likely contaminate our signal in practice).
What I'm wondering about is the form of this decrease. Is the pattern going to be something straightforward like, say, a 2% decrease in ROI with each step up the ladder? Is there a "wall" at some level, at which the ROI starts to drop off far more rapidly? Or will we see the ROI remain the same from, say $100 to $1000, suggesting that the play is (on average) the same at each of these levels, with the distribution of players determined more by bankroll than by pure issues of skill?