Lower star rating pp exponent and increase accuracy value on high SR maps

[MillhioreF]

As proposed here.

tl;dr
Lower exponential growth on StrainBase to deflate pp gains as star rating goes up
StrainMultiplier modification to rebalance values of different score ranges
Involve strain in accuracy pp to increase it for 960K+ scores

[PrismaticEffect]

This is Shoegazer; thank you very much for implementing this. The changes perfectly align with what is written in the document.

I will be fiddling around with the AccValue exponent to avoid 960-985K scores being too overpowered for certain SRs compared to 800-850K scores; I think that 960K-985K give a touch bit too much AccValue bonus as it is, but I need to find a proper exponent first.

edit: Line 140 (the line that gives a higher AccValue bonus to charts with more notes) should be removed. StrainValue already gives a multiplier based on the number of notes a chart has, and AccValue is based on StrainValue.

[WalterToro]

After reprocessing the mania scores, here is the Info from the top 2000 players: https://goo.gl/YJ7S3a
Need to note that players who are inactive cant be reprocessed so their pp is noted as 0.

Notable things:

• Jakads (AscensionDTWhen) loses 10300,9 pp (the only regular player losing over 10k pp)
• Only one regular player wins pp, Asrielly (130,7 pp), that is a good acc player without DT plays
• Top mania pp play drops from 2414pp to 1482,43pp

In conclusion, the proposal here seems to fulfill its objective and its one step forward into fixing and scaling the mania pp.

[peppy]

Looking better, but i think we should still add a post-scale to get the highest pp total down to the same level at osu!.

[MillhioreF]

There was already one in the code so I've modified it now. The #1 player would drop down to 15,300pp with this change with the rest scaled accordingly.

[PrismaticEffect]

Not that the specific linear multiplier would mean much (since a linear multiplier doesn't do much), but a multiplier of 0.75x would make it align closer to osu!standard. I feel that using the #1 osu!mania player for calibration is ill-advised since he is so far ahead of everyone else (7 out of 10 of o!m's highest PP plays are his with the new system). I would say that using the top 5 players in general to calibrate PP scaling would be a stretch, for those players are notably far ahead of everyone else.

There will be about 95 players would have 10,000+ pp with a 0.75x multiplier. In contrast, only 27 players will have 10,000+ pp with a 0.65x player. osu!standard currently has 188 players with 10,000+ pp, though the amount of players can be slightly lower with the HD/short map changes.

You could even use a 0.8x multiplier since there are so many osu!standard players with 10,000pp since the main goal is to adjust the PP values to align with osu!standard. About 150 players would have 10,000+ pp on osu!mania with a 0.8x multiplier, which is slightly lower than the amount of osu!standard players with 10,000+ pp.

It's really a matter of whether you want to use the very top players or "great" players as your benchmark -- I think the latter is better because of how the very top players seem to have a very marked gap in skill compared to the others.

edit: Here is a spreadsheet showing the PP values of each player after 0.65x, 0.75x, and 0.8x multipliers are applied: https://goo.gl/MCdofQ

There will be 27 players with 10,000pp or higher with a 0.65x multiplier, 94 players with a 0.75x multiplier, and 152 players with a 0.8x multiplier. I think a 0.8x multiplier would be the best option out of the three, but a 0.75x multiplier would be fine as well.

[MillhioreF]

I'm on board with 0.8 (or well I guess it's more like 0.73x since it was 1.1 before). Crunching pp values to be sane is fair, but I don't want to lower it too much either - scores are already extremely homogenous at beginner levels of play and changing the multiplier is only going to make them more so.

[PrismaticEffect]

The homogeneity was a concern of mine as well, thank you for the change. One last thing because Walter and I overlooked -- the multiplier should be 0.88x. There was a previous multiplier in the original PP system of 1.1, which means that changing the multiplier from 1.1x to 0.8x would reduce the multiplier by 27.7% instead of 20%. All of the calculations in the spreadsheet that I had linked were done under the assumption that the extant multiplier was 1.0 instead of 1.1.

Our mistake for overlooking that.

[WalterToro]

After discussing with @PrismaticEffect we came into an agreement that the 0.8x multiplier is good, looking at the possible new ranked maps in mania and the pp those can give in the long run.
With that, this proposal seems to be ready for merge.

[Tom94]

23k pp is still over 1.5x larger than 14k, which is the highest in standard. I think if we go with reducing the overall multiplier, then we should do it over-convervatively (i.e. aim to be below standard) rather than under-conservatively. The trend in mania is for pp to increase faster than standard due to more crazy maps getting ranked, so I believe this will all equalize out.

[WalterToro]

Yep, the 23k pp was still a big number, so we proceeded to change the scaling multiplier that was on the code (originally 1.1x, we dont know why), millhiore originally put 0.65x but we proposed 0.8x to be akin to the other leaderboards (more exactly the ctb leaderboard).
The results should be close to the numbers on the strong yellow column here https://goo.gl/YJ7S3a (tdlr, the drop will be from 33.4k to around 16.9k pp for the top player, and around 72 active players will get over 10k pp with this new scale)

[Tom94]

I see, looks like I misunderstood the sheet. Let's go then. :)

[iJinjin]

Cool stuff. Seems like a pretty solid fix, looking forward to the changes.

[nl-tata]

But why? I love the big pp, and I wish all gamemodes had big pp like mania. I want 1000pp plays, not 400pp plays. Especially taiko, the scaling in taiko is so slowww. I think the bigger pp is warranted, mania maps are WAYYYYYYYYYYYY more dense than osu!standard maps, so they should award more pp. Harder stuff should have bigger rewards.

[tailsdk]

I think this change is pretty good i dont think the pp reduction was needed as in the multiplier but i can see the accuracy focus being a good change. I can also see why peppy wants to lower the pp to a level like the other gamemodes since it would make sense as a develeper to keep some sort of balance between all the gamemodes.

[peppy]

The previous values were overflowing database/network values. It was unintended.