Recently, in #general-conc a discussion was started relating to the tiering of maps which brought up some interesting questions involving how we rate maps in general across all game modes.
Primarily, these questions involve the zero point and t1 cutoff point of the tiering system, and secondarily how the absolute difficulty of each tier lines up/varies across game modes.
For clarity of discussion, here are some terms I will be using and how I am defining them:
Zero Point - Assuming a continuous tiering function (that is, one with decimal points and infinite precision), the point on the Absolute Difficulty scale where you pin zero, or the point at which a map stops being too easy to matter and starts being Tier 1
Minimum Valid Challenge - A similar idea to the previous, but generalized. The point on the absolute difficulty scale at which any challenge is considered non-trivial. The major difference is that the MVC point varies depending on what you are measuring, a single jump on a jump map is measured differently to a single surf bonus, or a whole map.
Skill Floor - A generic Difficulty Theory concept, the required amount of skill to be effective. This is sometimes easy to define, sometimes very hard. For example, the skill floor in juggling is agreed to be qualifying 3 ball cascade.
Skill Ceiling - The inverse of the previous, the theoretical maximum amount of skill possible. Usually not a real point, but often functionally defined as the point at which extra skill results in diminishing returns against the hardest challenge possible.
Absolute Difficulty - A theoretical linear difficulty scale, calibrated from "zero skill", so something ranked 2 takes exactly twice(2x) the effort of something ranked 1 for someone starting at zero
Relative Difficulty - A theoretical logarithmic difficulty scale, used as the basis of most real difficulty scales, where each new rank takes twice as much total absolute difficulty as the last step, following ex. This happens to be extremely useful because of our perception of difficulty and previous effort compounds to be roughly logarithmic, meaning the the amount of perceived effort required to move up in ranks grows linearly.
Cutoff Point - The point at which you stop considering something to be of one rank and start considering it of the next rank.
So the problem is this, because momentum is bringing together many different game modes and showing a difficulty rank for different game modes next to each other, players will assume that one tier in one mode is the same relative difficulty as the same tire in another mode, and will primarily base that off of their experience in the modes they already know.
On the face of it, this isn't an issue, except for the fact that that currently different modes have the MVC sitting at different cutoffs, for example surf generally considers the MVC to sit at the cutoff between trivial and T1, while RJ/SJ consider T2 to be the point at which the MVC sits.
Adding complication to this is because the skill floor varies between modes, the MVC isn't necessarily at the same point above zero, which in turn effects how large the cutoff point between the MVC and the next tier is, which has a knock-on effect pushing the harder tier further out of alignment.
The harder tiers are not simple either, as you can't assume that the difficulty of a max tier map in one mode is similar at all to the difficulty of a max tier map in another mode, both because of game mode maturity, and also because of the possibility of skill ceilings locking out higher tiers on the momentum universal scale.
This ranking challenge also gets worse for less mature modes, such as ahop. Currently, ahop_reptile is ranked t6(old system), a ranking generally agreed upon by players good enough to beat it, but without a good amount of t3/4/5 maps that ranking is hard to verify. The mode could be capped at t5 and its a tier too high, or it could be accurate but t7 and t8 are also reasonable tiers to assign to even harder maps than it.
All this does bring us back to our first question, of tier transferring between game modes. It would be reasonable to ask if such a goal is even even reasonable to begin with and if it really matters. Not that many players will bother to get good at every mode, more likely just a few and dabble in others, and those that do will necessarily start at the bottom and move up, but if the current 10 tier system ends up being too small and pushes into 12 instead, is it fine that one mode has maps that go to 12 and another only has maps that cap at 10? There seems to be a good amount of open question within this subject, and i'm not sure any of them have good answers.
