Sorry for double post, but I made this intentionally, as I felt this deserves its own post
Update on the Formula
As I found the punishment for droplet misses wasn't enough, I thought of a new way to make it harsher. Also, I thought of a way to make it related to the total ammount of droplets in the maps (it's not the same to miss 1 out of 5 droplets than missing 1 out of 100). So, here's the notation I'll use:
MaxPP = Maximum Droplet pp Contribution
TopPP = Maximum pp posible for each class of players (based on droplet misses)
PP = Actual pp given to a class
AF = Acumulated Frequency of all groups with less droplet misses
DF = Diminishing Factor (where 0 < DF < 1)
LL = Lower Limit, percentage of pp a player missing all droplets will get (a number between 0 and 1), based only on droplet misses. It can't be 0.
TD = Total Droplets, the number of droplets of the map.
x = Number of droplet misses
1] Calculate the TopPP for each class using the following formula:
TopPP = floor(MaxPP*exp(x*ln(LL)/TD))
2] Calculate PP given using the diminishing formula based on AF:
PP = floor(TopPP*(1-AF)^DF)
So, now I'll work 4 different examples to show how this formula behaves. Two cases will have TD = 3 droplets and two will have TD = 7 droplets. Also, one map will be harder to SS than the other. They also assume LL = 0.5 and DF = 0.5
Case A: 3 Droplets total
For these maps, the TopPP for each class are:
TopPP_A = floor(100*exp(0*ln(0.5)/3)) = 100
TopPP_B = floor(100*exp(1*ln(0.5)/3)) = 79
TopPP_C = floor(100*exp(2*ln(0.5)/3)) = 62
TopPP_D = floor(100*exp(3*ln(0.5)/3)) = 50
Example A-1: Easy Map
For this distribution, the actual PP given for each class are:
PP_A = floor(100*(1-0)^0.5) = 100
PP_B = floor(79*(1-0.3)^0.5) = 66
PP_C = floor(62*(1-0.7)^0.5) = 33
PP_D = floor(50*(1-0.9)^0.5) = 15
Example A-2: Hard Map
For this distribution, the actual PP given for each class are:
PP_A = floor(100*(1-0)^0.5) = 100
PP_B = floor(79*(1-0.05)^0.5) = 76
PP_C = floor(62*(1-0.2)^0.5) = 55
PP_D = floor(50*(1-0.9)^0.5) = 15
Case B: 7 Droplets total
For these maps, the TopPP for each class are:
TopPP_A = floor(100*exp(0*ln(0.5)/7)) = 100
TopPP_B = floor(100*exp(1*ln(0.5)/7)) = 90
TopPP_C = floor(100*exp(2*ln(0.5)/7)) = 82
TopPP_D = floor(100*exp(3*ln(0.5)/7)) = 74
TopPP_E = floor(100*exp(4*ln(0.5)/7)) = 67
TopPP_F = floor(100*exp(5*ln(0.5)/7)) = 60
TopPP_G = floor(100*exp(6*ln(0.5)/7)) = 55
TopPP_H = floor(100*exp(7*ln(0.5)/7)) = 50
Example B-1: Easy Map
For this distribution, the actual PP given for each class are:
PP_A = floor(100*(1-0)^0.5) = 100
PP_B = floor(90*(1-0.3)^0.5) = 75
PP_C = floor(82*(1-0.5)^0.5) = 57
PP_D = floor(74*(1-0.65)^0.5) = 43
PP_E = floor(67*(1-0.75)^0.5) = 33
PP_F = floor(60*(1-0.8)^0.5) = 26
PP_G = floor(55*(1-0.9)^0.5) = 17
PP_H = floor(50*(1-0.95)^0.5) = 11
Example B-2: Hard Map
For this distribution, the actual PP given for each class are:
PP_A = floor(100*(1-0)^0.5) = 100
PP_B = floor(90*(1-0.05)^0.5) = 87
PP_C = floor(82*(1-0.1)^0.5) = 77
PP_D = floor(74*(1-0.2)^0.5) = 66
PP_E = floor(67*(1-0.4)^0.5) = 51
PP_F = floor(60*(1-0.7)^0.5) = 32
PP_G = floor(55*(1-0.85)^0.5) = 21
PP_H = floor(50*(1-0.95)^0.5) = 11
Comments
* In my opinion, this formula works well. Anyway, LL and DF can be adjusted.
Update on the Formula
As I found the punishment for droplet misses wasn't enough, I thought of a new way to make it harsher. Also, I thought of a way to make it related to the total ammount of droplets in the maps (it's not the same to miss 1 out of 5 droplets than missing 1 out of 100). So, here's the notation I'll use:
MaxPP = Maximum Droplet pp Contribution
TopPP = Maximum pp posible for each class of players (based on droplet misses)
PP = Actual pp given to a class
AF = Acumulated Frequency of all groups with less droplet misses
DF = Diminishing Factor (where 0 < DF < 1)
LL = Lower Limit, percentage of pp a player missing all droplets will get (a number between 0 and 1), based only on droplet misses. It can't be 0.
TD = Total Droplets, the number of droplets of the map.
x = Number of droplet misses
1] Calculate the TopPP for each class using the following formula:
TopPP = floor(MaxPP*exp(x*ln(LL)/TD))
2] Calculate PP given using the diminishing formula based on AF:
PP = floor(TopPP*(1-AF)^DF)
So, now I'll work 4 different examples to show how this formula behaves. Two cases will have TD = 3 droplets and two will have TD = 7 droplets. Also, one map will be harder to SS than the other. They also assume LL = 0.5 and DF = 0.5
Case A: 3 Droplets total
For these maps, the TopPP for each class are:
TopPP_A = floor(100*exp(0*ln(0.5)/3)) = 100
TopPP_B = floor(100*exp(1*ln(0.5)/3)) = 79
TopPP_C = floor(100*exp(2*ln(0.5)/3)) = 62
TopPP_D = floor(100*exp(3*ln(0.5)/3)) = 50
Example A-1: Easy Map
Group Class Users' frequency Droplet Misses
D 10% 3
C 20% 2
B 40% 1
A 30% 0
For this distribution, the actual PP given for each class are:
PP_A = floor(100*(1-0)^0.5) = 100
PP_B = floor(79*(1-0.3)^0.5) = 66
PP_C = floor(62*(1-0.7)^0.5) = 33
PP_D = floor(50*(1-0.9)^0.5) = 15
Example A-2: Hard Map
Group Class Users' frequency Droplet Misses
D 10% 3
C 70% 2
B 15% 1
A 5% 0
For this distribution, the actual PP given for each class are:
PP_A = floor(100*(1-0)^0.5) = 100
PP_B = floor(79*(1-0.05)^0.5) = 76
PP_C = floor(62*(1-0.2)^0.5) = 55
PP_D = floor(50*(1-0.9)^0.5) = 15
Case B: 7 Droplets total
For these maps, the TopPP for each class are:
TopPP_A = floor(100*exp(0*ln(0.5)/7)) = 100
TopPP_B = floor(100*exp(1*ln(0.5)/7)) = 90
TopPP_C = floor(100*exp(2*ln(0.5)/7)) = 82
TopPP_D = floor(100*exp(3*ln(0.5)/7)) = 74
TopPP_E = floor(100*exp(4*ln(0.5)/7)) = 67
TopPP_F = floor(100*exp(5*ln(0.5)/7)) = 60
TopPP_G = floor(100*exp(6*ln(0.5)/7)) = 55
TopPP_H = floor(100*exp(7*ln(0.5)/7)) = 50
Example B-1: Easy Map
Group Class Users' frequency Droplet Misses
H 5% 7
G 5% 6
F 10% 5
E 5% 4
D 10% 3
C 15% 2
B 20% 1
A 30% 0
For this distribution, the actual PP given for each class are:
PP_A = floor(100*(1-0)^0.5) = 100
PP_B = floor(90*(1-0.3)^0.5) = 75
PP_C = floor(82*(1-0.5)^0.5) = 57
PP_D = floor(74*(1-0.65)^0.5) = 43
PP_E = floor(67*(1-0.75)^0.5) = 33
PP_F = floor(60*(1-0.8)^0.5) = 26
PP_G = floor(55*(1-0.9)^0.5) = 17
PP_H = floor(50*(1-0.95)^0.5) = 11
Example B-2: Hard Map
Group Class Users' frequency Droplet Misses
H 5% 7
G 10% 6
F 15% 5
E 30% 4
D 20% 3
C 10% 2
B 5% 1
A 5% 0
For this distribution, the actual PP given for each class are:
PP_A = floor(100*(1-0)^0.5) = 100
PP_B = floor(90*(1-0.05)^0.5) = 87
PP_C = floor(82*(1-0.1)^0.5) = 77
PP_D = floor(74*(1-0.2)^0.5) = 66
PP_E = floor(67*(1-0.4)^0.5) = 51
PP_F = floor(60*(1-0.7)^0.5) = 32
PP_G = floor(55*(1-0.85)^0.5) = 21
PP_H = floor(50*(1-0.95)^0.5) = 11
Comments
* In my opinion, this formula works well. Anyway, LL and DF can be adjusted.