First of all I would like to thank Tom for putting in effort to make a change to the CTB pp system to begin with even though there are rooms for major improvement.
Here's how I dissect the problem with pp: (Umineko style :3)
Red statement: Core conclusion
Blue statement: Sub conclusion
Gold statement: Final conclusion
1. A good pp system is where the system credits map purely dependent on difficulty, and scale the rewards in pp proportionately. In other words, a more difficult map should always get more pp than an easier map no matter what, and ideally if Map A is twice as hard as Map B it shall reward twice as much of pp, or whichever proportion that is most fit be it purely multiple or logarithmic or exponential. I don't think anyone disagrees on this point.
Conclusion (1): Harder map = more pp
2. CTB is absolutely timing based just like Taiko and Mania. Unlike say Osu!Standard, where clicking on time (rhythm ---> time accuracy) and clicking at the right place (aim ---> spacial/positional accuracy) are two separate parameters. Having either variable heavily compromised will result in a miss no matter how good the other variable is being mastered. E.g. a perfectly timed click at a completely wrong place will always be a miss, a perfectly positioned click at a completely wrong timing will always be a miss as well. However for CTB, if one pressed the keys perfectly in time, one will never miss no matter what. That's because the platter moves at a fixed speed, and all combos unreachable with that speed will be caught with a hyperdash. Therefore the only parameter that affects CTB gameplay is the timing where the keys are being pressed (and held on to).
Conclusion (2): Timing = Everything in CTB
3. Since timing is the only affecting factor for CTB, then the more stringent the timing window the more difficult the map is to FC, therefore, is harder and deserves more pp.
Conclusion (3): Less forgiving timing window = More difficult = More pp
Mapping factors that affects timing/difficulty:
4. An AR too high requires great reaction speed, therefore can cause delay in a player's timing in pressing the keys correctly.
Conclusion (4): Extremely high AR deserves more pp.
5. An AR too low confuses the player as the platter becomes "slippery" (moves way too fast as compared to the dropping fruits), the fruits are harder to read and timings are harder to judge.
Conclusion (5): Extremely low AR deserves more pp.
6. High HP drains doesn't affect the key-press timing at all, but it multiplies the consequences of not being able to keep in time, which is to entirely fail the map.
Conclusion (6): Higher HP deserves more pp.
7. High CS makes the fruit hit-circle smaller, thus there is less room for mistake in terms of the position of the platter, since position of the platter is absolutely controlled by the timings of the keys pressed, the higher the CS the smaller the error in key-press timing there can be. Therefore a very high CS is very difficult.
Conclusion (7): Higher CS deserves more pp.
8. OD in all other modes: E.g. AT OD10 if you hit the object more/less than 15ms in timing you miss, that applies for every combo. For OD9 may be 20ms.
OD in CTB: Pattern A requires player to just move left by 3 platter length and you are given 5 seconds to do so. And then 3 more seconds to move right 1 platter length away. Easy. Pattern B requires player to move left right left right consecutively 20 times with 10ms of error window for each combo. Hard. Other modes use Meter OD, which is a fixed timing window exactly the same for every combo, that is invariable. CTB uses Pattern OD, which is dependent on how much room for timing error to successfully get from one combo to another, which varies with different combos. Meter OD has no effect on difficult, while Pattern OD affects difficulty. The harder the pattern, the less forgiving the timing, the more difficult the map becomes.
Conclusion (8): Harder pattern = less room for timing error.
Conclusion (9): Harder pattern deserves more pp.
9. Longer maps require a player to consistently hit the timing window despite the long duration, it requires more timing accuracy as compared to if the map was shorted. Thus more difficult.
Conclusion (10): Longer maps deserve more pp.
Clearly from the explanation above you can see which factor affects the gameplay difficulty the most, at I will list it as my final conclusion.
Conclusion (11): Arranged in order of greater pp emphasis: Pattern OD > CS > AR (high/low) > HP > Meter OD = 0
Of course there are a lot more questions left unanswered by my conclusions.
1. What is consider too high/too low AR?
2. Is AR difficulty more subjective or objective?
3. Which are the patterns that are less forgiving?
4. Since every combo has different timing error window, how does one accurately account for the overall difficulty of a map containing thousands of combos?
5. I find low CS as hard to read as high CS, is that not a valid point?
6. What is the easiest CS/AR to benchmark on?
7. How does modifiers (mods) affect the above mentioned parameters?
8. How does spinners and droplets play a part in the pp system?
9. So many things to change so much work to be done, is that even possible?
10. Is it worth the effort to strive for a perfect pp system?
11. Is difficulty overall a subjective matter of pure human experience, or is it simply a matter of neurology mathematics and physics, or maybe both?
12. Should we scale elements that are or potentially could be subjective as objective pp?
13. WTF were you talking about the whole time, were you smoking weed?
And many more questions. Which I hope we can discuss in an mature and constructive manner in the future.
the bananas are actually spinners so they just function as bonus points, the full amount of possible seems to be only done by auto.