I think that we don't need separate leaderboards, as they are by score, not PP.
The high aim PP from touchscreen plays is problem, right? We just need to detect touchplay then!
We don't need to nerf aim too, maybe just push some other skills up by little (especially on highest star rating?), but that's another matter that falls into PP system and should probably be discussed separately. So, let's focus on touchscreens.
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I think that very good idea for solution could be this simple one (simple idea, not implementation) :
→ Detect touchscreen play and evaluate it using different algorithm.
Let's assume that we have an algorithm to detect touchscreen play.
That is, to almost certainly say, if it's a touchscreen play, where by almost certainly I mean a case, where probability for it not being touchscreen play is very close to zero.
Technically, I think it shouldn't be hard in theory, but I am not sure about "precision" of current replays, maybe on lower performance and rapid jumps it can be little problematic with how currently replays works? Well, increasing precision can probably create other problems, there will be much bigger data transfer required to submit all new, bigger replays, etc., I don't really know much about this stuff, in terms of how much of it osu! requires, but let's assume that if there's this kind of problem, then we can eventually "improve" the replays and solve submission issues too.
Now, basing on how fast cursor changes position, giving enough precision, it should be relatively easy to conclude, if it's a touchscreen play, right? And by touchscreen play I mean "teleporting movement", an instantaneous shift in cursor position.
The changes in position that are very small could be disregarded, as stuff like clicking overlapping circles isn't really important here (the big jumps are our issue) and replay's precision requires us to set some limits.
Now, when the score gets submitted, it's being processed and if a "touchscreen play" segments are detected, they are evaluated with different PP algorithm. Or the whole score is simply marked as "touchscreen" and evaluated differently.
What do you think about this?
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There are at least 2 issues or things to do, that we have with this from the very start though:
(1) New PP algorithm for touchscreen segments is needed. Or maybe more like just touchscreen aim PP tweak, while leaving some of the rest of PP (streaming, acc?) as normal?
(2) Not sure how much more computational resources it would take, to analyze every new best submitted score in search of touchscreen play segments, but maybe there's actually no real problem here? If we was to simply mark a whole score as a touchscreen play, we just need to find an instances of touchscreen plays in it, so probably not much of trouble here?
(I assume that it could be an overkill, if we would want to go ham and try to judge which parts of score are touchscreen play, and which are not, in case of mixed plays? It's so marginal that just marking play as normal/touchscreen should be okay, especially as doing something like this would require to "analyze" whole score, which is redundant here)
(optional)(And if we decide to not simply mark the whole play as touchscreen, in case of "mixed input devices" plays, then we would need to reasonably fuse "normal" and "touchscreen" PP)