Ranking Points & Cosmetic XP

Ranked-Points System

The points you earn from your time on a map is the sum of the points awarded from each of these 3 systems described below: WR/top10 points + formula points + group points.

The systems described here are complete; we are in agreement that this is what the Ranked-Points should look like. The values chosen for percentiles, WR points, etc. are still up for debate; however, these should be simple to change later, should we decide to change them, because of the design of the system. For now, we consider the values to be informed-guess placeholders.

There are no “base completion points”; the formula system somewhat accounts for this, but we’ve determined that it is not worth having a system of its own

Aside – Motivation;

Times ranked beyond the top10 are awarded points according to 2 systems: the Group system, and a Formula system. The group system rewards discrete bundles of points for players ranking within certain “percentile” blocks. The formula system awards points simply according to a formula with a single parameter – the player’s rank. The group system should award more points than the formula system; it should be the primary goal of the player to improve to the next group. The formula system simply provides bonus ranked points for improving within a group, so the player does not feel like intermediate improvements are a waste of effort.

WRs and Top10s system

WRs award a fixed number of points for all maps. For now, we set this to be 3,000 points. Ranks 2-10 award some percentage of the WR points.

Rank 1 = 3000 points = 100% of WR
Rank 2 = 2250 points = 75% of WR
Rank 3 = 2040 points = 68% of WR
Rank 4 = 1830 points = 61% of WR
Rank 5 = 1710 points = 57% of WR
Rank 6 = 1590 points = 53% of WR
Rank 7 = 1515 points = 50.5% of WR
Rank 8 = 1440 points = 48% of WR
Rank 9 = 1365 points = 45.5% of WR
Rank 10 = 1290 points = 43% of WR

Formula system

Points awarded is some equation of the form A / (rank + B), where A is a scaling constant, and B is a smoothing constant.
We choose A = 50000, B = 49.
In this case the graph shows our equation Points = 50000 / (rank + 49)
Formula Graph

X axis designates player rank on a map,
y axis designates points awarded

Ex:
Player sets a time of rank 468 on a map with 1333 completions.
Formula points awarded = 50000 / (468 + 49) = 96.7 => 97 points. (Note that the # of completions on the map did not affect the points awarded!)

(New) Group System

(based on @Joe’s & Jux’s comments about minimum group sizes)
(plus lots of help from Jux and Aux)

4 groups, loosely “percentile”-based (in fact, a function of #completions, but not as simple as a percentage). Instead of calculating group boundaries directly from percentiles, we calculate group sizes based on a simple maximizing function –

Group size = max(A(x), minSize)

max(A, B) simply returns the value of the larger parameter.
A is a function of #completions, minSize

Group 1 always starts at rank 11, and its size is determined from its group size formula.

The formula to determine group size, A(x) (where x is the # of completions of the map), is
_A(x) = SF * (x^E), where SF and E are defined uniquely for each group:
SF = Scale factor, E = Exponent

Group 1: E = 0.5, SF = 1
Group 2: E = 0.56, SF = 1.5
Group 3: E = 0.62, SF = 2
Group 4: E = 0.68, SF = 2.5

minSize is another parameter which varies per group:

Group 1: minSize = 10
Group 2: minSize = 45
Group 3: minSize = 125
Group 4: minSize = 250

Ex.
On a map with 400 completions:

Group 1 size = max(1 * 400^0.5, 10) = max(20, 10) = 20
Group 2 size = max(1.5 * 400^0.56, 45) = max(42.98, 45) = 45
Group 3 size = max(2 * 400^0.62, 125) = max(82, 125) = 125
Group 4 size = max(2.5 * 400^0.68, 250) = max(147, 250) = 250

Therefore:

Group 1 = ranks 11-30 (begins from rank 11, contains 20 spots)
Group 2 = ranks 31-75 (begins from rank 31 = end of G1, contains 45 spots)
Group 3 = ranks 76-200 (begins from rank 76 = end of G2, contains 125 spots)
Group 4 = ranks 201-450 -- note this exceeds #completions (400)! So it extends all the way to rank 400, and anyone who completes the map is automatically in at least group 4.

Group Points:
(going by WR points = 3000) (no particular pattern; eyeballed). Keep in mind that you also get points from the formula!

Group 4 = 90 points = 3% of WR
Group 3 = 210 points = 7% of WR
Group 2 = 390 points = 13% of WR
Group 1 = 600 points = 20% of WR

Cosmetic XP

For more advanced info about cosmetics
Make a copy of The spreadsheet

0 - 50

Level Exp in level Total exp
001 21,000 21,000
002 22,000 43,000
003 23,000 66,000
004 24,000 90,000
005 25,000 115,000
006 26,000 141,000
007 27,000 168,000
008 28,000 196,000
009 29,000 225,000
010 30,000 255,000
011 42,000 297,000
012 44,000 341,000
013 46,000 387,000
014 48,000 435,000
015 50,000 485,000
016 52,000 537,000
017 54,000 591,000
018 56,000 647,000
019 58,000 705,000
020 60,000 765,000
021 83,000 848,000
022 86,000 934,000
023 89,000 1,023,000
024 92,000 1,115,000
025 95,000 1,210,000
026 98,000 1,308,000
027 101,000 1,409,000
028 104,000 1,513,000
029 107,000 1,620,000
030 110,000 1,730,000
031 144,000 1,874,000
032 148,000 2,022,000
033 152,000 2,174,000
034 156,000 2,330,000
035 160,000 2,490,000
036 164,000 2,654,000
037 168,000 2,822,000
038 172,000 2,994,000
039 176,000 3,170,000
040 180,000 3,350,000
041 225,000 3,575,000
042 230,000 3,805,000
043 235,000 4,040,000
044 240,000 4,280,000
045 245,000 4,525,000
046 250,000 4,775,000
047 255,000 5,030,000
048 260,000 5,290,000
049 265,000 5,555,000
050 270,000 5,825,000

50 - 100

Type Amount Percentage
Per-level increase 750,000 277.78%
Total exp difference 31,180,000 635.28%
Level Exp in level Total exp
051 326,000 6,151,000
052 332,000 6,483,000
053 338,000 6,821,000
054 344,000 7,165,000
055 350,000 7,515,000
056 356,000 7,871,000
057 362,000 8,233,000
058 368,000 8,601,000
059 374,000 8,975,000
060 380,000 9,355,000
061 447,000 9,802,000
062 454,000 10,256,000
063 461,000 10,717,000
064 468,000 11,185,000
065 475,000 11,660,000
066 482,000 12,142,000
067 489,000 12,631,000
068 496,000 13,127,000
069 503,000 13,630,000
070 510,000 14,140,000
071 588,000 14,728,000
072 596,000 15,324,000
073 604,000 15,928,000
074 612,000 16,540,000
075 620,000 17,160,000
076 628,000 17,788,000
077 636,000 18,424,000
078 644,000 19,068,000
079 652,000 19,720,000
080 660,000 20,380,000
081 749,000 21,129,000
082 758,000 21,887,000
083 767,000 22,654,000
084 776,000 23,430,000
085 785,000 24,215,000
086 794,000 25,009,000
087 803,000 25,812,000
088 812,000 26,624,000
089 821,000 27,445,000
090 830,000 28,275,000
091 930,000 29,205,000
092 940,000 30,145,000
093 950,000 31,095,000
094 960,000 32,055,000
095 970,000 33,025,000
096 980,000 34,005,000
097 990,000 34,995,000
098 1,000,000 35,995,000
099 1,010,000 37,005,000
100 1,020,000 38,025,000

100 - 150

Type Amount Percentage
Per-level increase 1,000,000 98.04%
Total exp difference 86,480,000 327.43%
Level Exp in level Total exp
101 1,520,000 39,545,000
102 1,520,000 41,065,000
103 1,520,000 42,585,000
104 1,520,000 44,105,000
105 1,520,000 45,625,000
106 1,520,000 47,145,000
107 1,520,000 48,665,000
108 1,520,000 50,185,000
109 1,520,000 51,705,000
110 1,520,000 53,225,000
111 1,520,000 54,745,000
112 1,520,000 56,265,000
113 1,520,000 57,785,000
114 1,520,000 59,305,000
115 1,520,000 60,825,000
116 1,520,000 62,345,000
117 1,520,000 63,865,000
118 1,520,000 65,385,000
119 1,520,000 66,905,000
120 1,520,000 68,425,000
121 1,520,000 69,945,000
122 1,520,000 71,465,000
123 1,520,000 72,985,000
124 1,520,000 74,505,000
125 1,520,000 76,025,000
126 2,020,000 78,045,000
127 2,020,000 80,065,000
128 2,020,000 82,085,000
129 2,020,000 84,105,000
130 2,020,000 86,125,000
131 2,020,000 88,145,000
132 2,020,000 90,165,000
133 2,020,000 92,185,000
134 2,020,000 94,205,000
135 2,020,000 96,225,000
136 2,020,000 98,245,000
137 2,020,000 100,265,000
138 2,020,000 102,285,000
139 2,020,000 104,305,000
140 2,020,000 106,325,000
141 2,020,000 108,345,000
142 2,020,000 110,365,000
143 2,020,000 112,385,000
144 2,020,000 114,405,000
145 2,020,000 116,425,000
146 2,020,000 118,445,000
147 2,020,000 120,465,000
148 2,020,000 122,485,000
149 2,020,000 124,505,000
150 2,020,000 126,525,000

150 - 200

Type Amount Percentage
Per-level increase 1,000,000 49.50%
Total exp difference 135,480,000 207.08%
Level Exp in level Total exp
151 2,520,000 129,045,000
152 2,520,000 131,565,000
153 2,520,000 134,085,000
154 2,520,000 136,605,000
155 2,520,000 139,125,000
156 2,520,000 141,645,000
157 2,520,000 144,165,000
158 2,520,000 146,685,000
159 2,520,000 149,205,000
160 2,520,000 151,725,000
161 2,520,000 154,245,000
162 2,520,000 156,765,000
163 2,520,000 159,285,000
164 2,520,000 161,805,000
165 2,520,000 164,325,000
166 2,520,000 166,845,000
167 2,520,000 169,365,000
168 2,520,000 171,885,000
169 2,520,000 174,405,000
170 2,520,000 176,925,000
171 2,520,000 179,445,000
172 2,520,000 181,965,000
173 2,520,000 184,485,000
174 2,520,000 187,005,000
175 2,520,000 189,525,000
176 3,020,000 192,545,000
177 3,020,000 195,565,000
178 3,020,000 198,585,000
179 3,020,000 201,605,000
180 3,020,000 204,625,000
181 3,020,000 207,645,000
182 3,020,000 210,665,000
183 3,020,000 213,685,000
184 3,020,000 216,705,000
185 3,020,000 219,725,000
186 3,020,000 222,745,000
187 3,020,000 225,765,000
188 3,020,000 228,785,000
189 3,020,000 231,805,000
190 3,020,000 234,825,000
191 3,020,000 237,845,000
192 3,020,000 240,865,000
193 3,020,000 243,885,000
194 3,020,000 246,905,000
195 3,020,000 249,925,000
196 3,020,000 252,945,000
197 3,020,000 255,965,000
198 3,020,000 258,985,000
199 3,020,000 262,005,000
200 3,020,000 265,025,000