CLSW wrote:
I think setting the players' most frequency droplet misses as a point criteria is better.
Some maps are easy, but some maps (especially maps in 2008~2009s, http://osu.ppy.sh/p/beatmap?b=6097&m=2)are hard to SS.
Users' frequency Percent of pp Droplet misses
50%(the most) 10% 3
20% 13% 2
10% 20% 1
2% 30% 0
Like this, If you can't understand I'm sorry for poor language.
Notation used in this post:
AF = Acumulated Frequency of all groups with less droplet misses
DF = Diminishing Factor (where 0 < DF < 1)
BPF = Best Performance Factor (BPF > 1, here it is assumed that BPF = 1.01)
This seems like a good idea. And it can be worked, and here's an way: plays are sorted by droplet misses and the frequency of users with 'x' droplets misses is calculated. For the group with less droplet misses, pp given (BestPP) might be calculated as BestPP = MaxPP/BPF^(Droplet Misses). For the following groups, PP might be calculated as PP = floor(BestPP*(1- AF)^DF) (you'll see the reason for this DF later)
I'll do 4 examples, two assuming DF = 1 (Case A) and two assuming DF = 0.1 (Case B). In both cases, one example will be with players having 0 droplet misses and the other one with best plays having (at least) 1 droplet miss. Also, we'll assume the maps gives 100pp max and all scores are FC no mod.
Case A: DF = 1
A-1: There are plays with 0 droplet misses, so we'll consider the following distribution:
Group Class Users' frequency Droplet Misses
F 10% 5
E 15% 4
D 30% 3
C 25% 2
B 15% 1
A 5% 0
Group A would get 100pp (max possible, BestPP = 100/1.01^0 = 100)
For Group B, AF = 5%. So, PP_B= 100*(1-0.05) = 95
For Group C, AF= 5% + 15% = 20%. Therefore, PP_C = 100*(1-0.2) = 80
Similarly, PP_D = 55, PP_E = 25, PP_F = 10
A-2: Best play has (at least) 1 droplet miss, so we'll consider the following distribution:
Group Class Users' frequency Droplet Misses
E 10% 5
D 15% 4
C 30% 3
B 25% 2
A 20% 1
Group A would get BestPP = 100/1.01^1 = 99 pp
For Group B, AF = 20%. So, PP_B = 99*(1-0.2) = 79pp
Similarly, PP_C = 54, PP_D = 25, PP_E = 10
PP diminishing for missing droplets seems to harsh, so now I'll repeat the whole process considering DF = 0.1:
Case B: DF = 0.1
B-1: There are plays with 0 droplet misses, so we'll consider the following distribution:
Group Class Users' frequency Droplet Misses
F 10% 5
E 15% 4
D 30% 3
C 25% 2
B 15% 1
A 5% 0
Group A would get 100pp (max possible, BestPP = 100/1.01^0 = 100)
For Group B, AF = 5%. So, PP_B= 100*(1-0.05)^0.1 = 99
For Group C, AF= 5% + 15% = 20%. Therefore, PP_C = 100*(1-0.2)^0.02 = 97
Similarly, PP_D = 94, PP_E = 87, PP_F = 79
B-2: Best play has (at least) 1 droplet miss, so we'll consider the following distribution:
Group Class Users' frequency Droplet Misses
E 10% 5
D 15% 4
C 30% 3
B 25% 2
A 20% 1
Group A would get BestPP = 100/1.01^1 = 99
For Group B, AF = 20%. So, PP_B = 99*(1-0.2)^0.1 = 96
Similarly, PP_C = 93, PP_D = 86, PP_E = 78
Some ideas left:* BPF could change based on the difficulty of catching all the droplets: maps where catching the droplets is harder should have a lower BPF
* The term BPF^(Droplet misses) could be capped at some value, e.g., 1.1.
* How can this be incorporated considering all other variables (accuracy, spinners, mods)? Maybe it could be a percentage of "accuracy".
PS: Sorry if I made any mistakes while writing this!
EDIT: Just noticed this doesn't work for certain cases. Gonna think about it later
EDIT2: Ok, I think I got it. The special case it wasn't going to work was when there's a group class with ~0% frequency, as that class and the next one would get almost the same ammount of pp (thus making catching that extra droplet worthless).
UPDATEThe new approach I'd try would be: for each class, calculate its max pp possible (TopPP) according to droplet misses, using the same formula for BestPP, i.e., TopPP = floor(MapPP/BPF^(Droplet Misses)). Now, for each class, calculate its real pp using a diminishing formula based on acumulated frequency, as PP = floor(TopPP*(1-AF)^DF).
Now, I'll use one of the examples from above but calculate map pp worth using those new formulas. Also, I'll show one case of a harder to SS map.
Example 1:
Group Class Users' frequency Droplet Misses
F 10% 5
E 15% 4
D 30% 3
C 25% 2
B 15% 1
A 5% 0
TopPP_A = floor(100/1.01^0) = 100
PP_A = floor(100*(1-0)^0.1) = 100
TopPP_B = floor(100/1.01^1) = 99
PP_B = floor(99*(1-0.05)^0.1) = 98
TopPP_C = floor(100/1.01^2) = 98
PP_C = floor(98*(1-0.2)^0.1) = 95
TopPP_D = floor(100/1.01^3) = 97
PP_D = floor(97*(1-0.45)^0.1) = 91
TopPP_E = floor(100/1.01^4) = 96
PP_E = floor(96*(1-0.75)^0.1) = 83
TopPP_F = floor(100/1.01^5) = 95
PP_F = floor(95*(1-0.9)^0.1) = 75
Example 2: This is a harder to SS map, as there are 5% user with 0, 1 or 2 droplets misses.
Group Class Users' frequency Droplet Misses
F 30% 5
E 40% 4
D 25% 3
C 4% 2
B 0% 1
A 1% 0
TopPP_A = floor(100/1.01^0) = 100
PP_A = floor(100*(1-0)^0.1) = 100
TopPP_B = floor(100/1.01^1) = 99
PP_B = floor(99*(1-0.01)^0.1) = 98
TopPP_C = floor(100/1.01^2) = 98
PP_C = floor(98*(1-0.01)^0.1) = 97
TopPP_D = floor(100/1.01^3) = 97
PP_D = floor(97*(1-0.05)^0.1) = 96
TopPP_E = floor(100/1.01^4) = 96
PP_E = floor(96*(1-0.3)^0.1) = 92
TopPP_F = floor(100/1.01^5) = 95
PP_F = floor(95*(1-0.7)^0.1) = 84
When the map is harder to SS, less players concentrate on classes with less droplets misses and the decreasing factor based on AF is not that harsh.
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. I think the idea looks good, if I understand correctly you are calculating a maximum droplet pp contribution based on the map's difficulty. Then a player will get a higher fraction of that if it's more difficult to catch all of the droplets on that map. Also that droplet contrib would have less weight if everyone easily catches all of the droplets? This would fix most of the PF SS farming maps on ctb I think. What about the possibility where the map has few/no droplets and is still difficult to FC (maybe these 
