Diff adjust mod multipliers

[bad-faith]

Difficulty adjust should have mod multipliers based on the base map diff settings and how they are changed, not just flat 0.5x.

I'm thinking having interpreting it as 3 mods and multiplied together makes most sense.

CS increase -> multiplier increased (based on how much the circle radius changes)
CS decrease -> multiplier decreased (bigger circles)

AR increased -> multiplier decreased (lower density = easier to read/acc)
AR decreased -> multiplier increase (higher density)

OD increase -> multiplier increased (based on how much the 300 window changes)
OD decrease -> multiplier decreased (easier to acc)

HP increase -> 1x
HP decrease -> same as NF (0.5x)

All 3 settings should have quantized steps at which multiplier changes similar to how rate change has.
I imagine this is how we can rank DA (or rate change) in the future as well, by either only ranking the quantized steps only, or by ranking every possible combination, but then assuming the play was set at an easier step.

How to quantize the settings:

• I believe the values of CS/AR/OD are very non-linear in difficulty, so we need to do some extra work, simply having constant steps wouldn't work well.
• Take the base values of CS/AR/OD and convert them to circle radius/preemt period/300 window.
• Multiply those values by x^n where x is the quantization parameter (x is close to 1) and n is the quantization step (integer, can be both positive and negative).
• The multiplier for the set diff setting could would be y^n. (y is close to 1)
• The values of x/y could be different for negative/positive n.
• Convert the values of (circle radius/preemt period/300 window) back into the CS/AR/OD values.
• We can then either round or not round the CS/AR/OD values:
• We can then either round the value of n or the value of CS/AR/OD on the 0.1 based grid.
• If we round the CS/AR/OD values the mod selection has a similar interface, but some steps are marked at being quantized. With extended limits this has a problem that two values of n might map to the same value after rounding.
• If we round the n value (I personally prefer this variant) the steps on the CS/AR/OD values would map to the corresponding n value. This also solves the issue of the extended limits on the CS/AR/OD values because any value of n makes a technically valid CS/AR/OD. This also makes the mod multiplier map-independent.
• I think most people are familiar with HR making cs4 cs5.2, so this could be either one or two quantized steps in terms of CS adjust. I think HR is harder than 1.1x (and 1.05x) and so we could have 2 steps here.

I'd be happy to implement this and test what quantization steps and multiplier values work best.

• if we made 1 step for CS in between 4 and 5, the value of x would be ((54.4 - 4.48 * 4)/(54.4 - 4.48 * 5)) ≈ 1.14
• if we made 2 steps for OD in between 9 and 10, the value of x would be sqrt((80 - 6 * 9)/(80 - 6 * 10)) ≈ 1.14
• if we made 2 steps for AR in between 9 and 10, the value of x would be sqrt((1200 - 150 * (9 - 5))/(1200 - 150 * (10 - 5))) ≈ 1.15

I made a graph which shows how cs values would grow based on the step of 4->5 together with an example mod multiplier.
https://www.desmos.com/calculator/9fswnc48x6

[Newbie1st]

CS increase doesn't always mean a universal increase in difficulty, at CS values below 4 making the circles smaller can potentially make the map easier, due to larger circles often being harder to read and the decrease in reading difficulty from smaller circles being more impactful than the increase in aim difficulty up to a certain point.

Overall, simply changing the multiplier to 1x when only increasing OD/HP would already be a massive improvement and a good first step.

[shiumano]

DA, when the same multiplier as EZ or HR is applied, must not have a higher multiplier.

[peppy]

This is coming soon 🤞 .