Ode to Penrose - Ranking

By uMathA

Background image: #14

Ranking

Shown below are the absolute statistical rankings of all the mints. The "Rarest" piece is often not visually rare looking or even that obvious as to why it's rare.

The absolute rarity takes into account all the traits, which can often include things like "starting angle" or "number of dots in the background." Traits where all the values are very spread out across all of the pieces.

Consider a drop with 100 pieces and 50 palettes. Because of the wide range of palettes, there will be a whole bunch of mints that are 1-of, 2-of and 3-of. But one palette isn't particularly rarer than another. But another feature of which only 4 are true, and the remaining 96 are false, is mathematically less rare than any of the palettes but is probably more desirable to a collector. But people have been asking for this, and who am I not to give the people what they want.

By rank

Rank id Rarity Links
1 169 0.000000503269457871017183%
2 92 0.000000955907289251856036%
3 12 0.000001910276740558515800%
4 183 0.000002803232912502269856%
5 271 0.000003590655235120281345%
6 108 0.000005414141455228512228%
7 263 0.000005520643846080331065%
8 134 0.000006372485346337133057%
9 65 0.000007484626156748281504%
10 295 0.000008893822721083796147%
11 126 0.000009591704849301649729%
12 244 0.000010462077261362534079%
13 90 0.000012994016822703662300%
14 157 0.000014317661185621095656%
15 221 0.000014902290867062364957%
16 50 0.000016220860730064761226%
17 35 0.000016286614720072082593%
18 25 0.000016809466854041561361%
19 22 0.000017533121984807949174%
20 174 0.000019172800783632280906%
21 256 0.000019530360403804494806%
22 239 0.000019574474849180523986%
23 213 0.000019845327071725823396%
24 41 0.000020823759938643466943%
25 178 0.000020970043027300395457%
26 96 0.000021298673415240130998%
27 154 0.000025198878232452329216%
28 43 0.000027801373169204159384%
29 140 0.000027968525840942248448%
30 249 0.000029021104488261574822%
31 278 0.000029024304143284080005%
32 113 0.000032373851149833966507%
33 225 0.000032655513122510049467%
34 170 0.000034148830931242133238%
35 236 0.000034179697859426095544%
36 194 0.000034267276602704854391%
37 205 0.000034674154878665075865%
38 237 0.000034983534261401991899%
39 275 0.000035559534673052600425%
40 16 0.000036184275778802637571%
41 95 0.000036869188912429064274%
42 72 0.000037635264428093728034%
43 255 0.000037989988356216759303%
44 223 0.000038507618302852381217%
45 166 0.000039436638322769505935%
46 202 0.000039512771102448620956%
47 59 0.000041770916891372601872%
48 276 0.000042140721227148261697%
49 119 0.000042262440198501750920%
50 175 0.000042527342268708026194%
51 37 0.000044500321469332576130%
52 106 0.000044513935833995622697%
53 181 0.000046321991244317448132%
54 151 0.000047845306261285443033%
55 103 0.000050040097465410080121%
56 222 0.000050412959245939425860%
57 63 0.000054720805159188959724%
58 163 0.000055429642732170566956%
59 46 0.000056381108631069283186%
60 130 0.000057882360072600661535%
61 297 0.000058516316968532929932%
62 197 0.000060816184015999400500%
63 279 0.000061352440587872112483%
64 219 0.000061434401468191544480%
65 101 0.000061695688209317738429%
66 216 0.000062299216916336029549%
67 7 0.000065181810173800739500%
68 177 0.000066140153668279029584%
69 184 0.000066142174568382567658%
70 146 0.000067251878308095114486%
71 114 0.000067923206317203332362%
72 245 0.000068424679313276414437%
73 83 0.000071464117042837030000%
74 18 0.000071470046509292475562%
75 128 0.000072273297079279895058%
76 32 0.000075164244372600511491%
77 234 0.000076312490491672340287%
78 204 0.000076783009381903186098%
79 189 0.000077227389468211558084%
80 214 0.000077766493350908073227%
81 258 0.000081508598693755601934%
82 179 0.000082975169934583627813%
83 138 0.000083923114891465891278%
84 147 0.000085767571426608756372%
85 131 0.000089145974160387218810%
86 124 0.000091187026998441005456%
87 164 0.000094616167023302649134%
88 167 0.000094636110271745924115%
89 49 0.000094979336316322216936%
90 28 0.000097476108135177813824%
91 246 0.000098702725539136180739%
92 274 0.000100961359862163001992%
93 54 0.000103266278247098156366%
94 270 0.000108567804493261334405%
95 62 0.000110755578749505411438%
96 5 0.000111294289262527690038%
97 27 0.000111335760807882409602%
98 261 0.000112582591023665718236%
99 291 0.000112770045663962634728%
100 129 0.000112788008420872755194%
101 207 0.000120209894827254273300%
102 14 0.000123115382641924631709%
103 203 0.000129847282115119207853%
104 73 0.000130240023329623226620%
105 31 0.000130896518620039059707%
106 13 0.000131126058929283129378%
107 80 0.000132927663421644818827%
108 117 0.000135492177468887021541%
109 186 0.000138187493993780353800%
110 33 0.000141463281009107189144%
111 250 0.000141847842060082617510%
112 105 0.000143972140844463123311%
113 11 0.000145569521908384173986%
114 15 0.000148643344111916620885%
115 227 0.000149911793335358881291%
116 210 0.000150173104261166703464%
117 42 0.000151677820001264065768%
118 91 0.000152724807654018964386%
119 251 0.000153718245224846919829%
120 45 0.000154964189090391811455%
121 262 0.000155944913372340796757%
122 122 0.000160495447719509443628%
123 243 0.000165074600161917856012%
124 64 0.000165564865347673823189%
125 69 0.000165907056152766866665%
126 277 0.000167267841902638773194%
127 283 0.000168379575351634060707%
128 267 0.000171175833656594196443%
129 75 0.000173322865666754105055%
130 53 0.000177282120955400468226%
131 107 0.000177443224593290337738%
132 206 0.000179127326099309916755%
133 240 0.000179163044271980211822%
134 1 0.000180177796359424320042%
135 265 0.000180526341075104275555%
136 201 0.000183465626703421884032%
137 125 0.000183627484274303203306%
138 235 0.000185857073957894786955%
139 121 0.000185951961184361170675%
140 215 0.000186183182496102298583%
141 193 0.000187288863118579104088%
142 260 0.000188588751515859448472%
143 115 0.000190339019875818555834%
144 292 0.000191963022921165852013%
145 3 0.000194022700922229457497%
146 220 0.000195472629026701441796%
147 112 0.000195708925263017791737%
148 71 0.000198516365390933934932%
149 180 0.000201136112513603990647%
150 264 0.000201767758598094681813%
151 198 0.000205161427845306149672%
152 285 0.000206142391447054870897%
153 139 0.000207082528959535766468%
154 39 0.000207858317914399857605%
155 47 0.000210664646105192569173%
156 257 0.000211935253835689727583%
157 266 0.000212446216608556996902%
158 187 0.000217239181143064860905%
159 158 0.000218797647787102996983%
160 48 0.000220895392794969434337%
161 74 0.000222031446122337289533%
162 30 0.000224233879157746364896%
163 142 0.000226702997896317186115%
164 136 0.000229853339363805364137%
165 2 0.000230184676111066551093%
166 34 0.000232598336585396935289%
167 228 0.000232688025142572586269%
168 94 0.000234798828290331759727%
169 196 0.000241029109827478680694%
170 99 0.000246095652423774450667%
171 36 0.000257292340283659759330%
172 150 0.000258130889532355459279%
173 52 0.000258186954882384952191%
174 195 0.000262936633781690992217%
175 26 0.000264254394089478831555%
176 296 0.000267393356105885223774%
177 254 0.000268840016845244716460%
178 182 0.000269551598964848512178%
179 145 0.000269569511252538453194%
180 284 0.000271354342033290596957%
181 218 0.000278123340977598769875%
182 29 0.000284137163005950866852%
183 153 0.000286452590667260139929%
184 57 0.000287929231133551074163%
185 172 0.000289078645462288177318%
186 165 0.000290279952113006928845%
187 104 0.000293975566178341382682%
188 259 0.000297979511733149698364%
189 159 0.000298293411765928901530%
190 269 0.000314497939240938992507%
191 241 0.000318935984093196426333%
192 4 0.000322251029152724845824%
193 289 0.000334799021160925487379%
194 77 0.000339192927541613164881%
195 238 0.000344491605870243181985%
196 280 0.000349974755388294416804%
197 88 0.000366142005571706093039%
198 191 0.000377042810216420389360%
199 10 0.000389450325204864725853%
200 200 0.000394964117773011701932%
201 173 0.000395842906743868285565%
202 86 0.000399219939012749962769%
203 199 0.000403238627528160718805%
204 97 0.000404478448159643997218%
205 110 0.000404943838099425528106%
206 232 0.000406079819437770946945%
207 66 0.000408378536550878528007%
208 294 0.000411140031516619877498%
209 247 0.000412270878575325835057%
210 298 0.000414521770607876064926%
211 281 0.000422420568928660053552%
212 87 0.000451250037489615515342%
213 242 0.000458213218874876731211%
214 268 0.000459588672502413272611%
215 176 0.000460776825269386392219%
216 70 0.000464337860214152509802%
217 23 0.000465088524003557941388%
218 51 0.000467596057784685050288%
219 109 0.000470353673330937082329%
220 190 0.000471374039368340337717%
221 102 0.000471956425132330264962%
222 133 0.000474602694658428022906%
223 288 0.000477065739538888502341%
224 120 0.000478118077758539928180%
225 100 0.000491208916785064453325%
226 116 0.000495920420456241067310%
227 67 0.000496558300889628125713%
228 78 0.000497358708384346018608%
229 253 0.000498520756433472084397%
230 0 0.000499458956047365231455%
231 143 0.000500616414925085777970%
232 160 0.000505292118366671024442%
233 144 0.000516709036752400455335%
234 211 0.000517656863705565745658%
235 21 0.000520604387814143135770%
236 171 0.000536591172324116347410%
237 8 0.000539615739460533837268%
238 93 0.000540835910523324307937%
239 84 0.000545243170785259358493%
240 192 0.000546108216409421642901%
241 272 0.000547213764920996287994%
242 135 0.000548883871351657504079%
243 290 0.000553595577322916619807%
244 82 0.000560886860266243138760%
245 60 0.000568667714843834647478%
246 209 0.000569049911661937096556%
247 149 0.000578882455649898852376%
248 111 0.000579850238352328135882%
249 156 0.000583446180082194541978%
250 217 0.000583909239569597635598%
251 230 0.000586760559258268791019%
252 19 0.000597123844136771735405%
253 282 0.000612629224001701362147%
254 76 0.000617180412054161675432%
255 20 0.000619069937827974978335%
256 6 0.000620018266871909294949%
257 9 0.000639318890938727788995%
258 231 0.000645730498432225789862%
259 233 0.000665719792916720184452%
260 229 0.000668634950540650404259%
261 38 0.000682544288076870398797%
262 123 0.000700421500986595749368%
263 252 0.000720904673456714841472%
264 55 0.000733735970048888120482%
265 61 0.000734794097345570283546%
266 89 0.000734938487053615730447%
267 44 0.000755320817943981397645%
268 208 0.000755550991529854330461%
269 188 0.000757600180684829386558%
270 24 0.000758232033913097225146%
271 127 0.000764959318535745258147%
272 161 0.000771005332453533623674%
273 118 0.000775889412954999281580%
274 56 0.000777176311843205745548%
275 287 0.000777915260328876411247%
276 185 0.000795877382691935605571%
277 168 0.000830477447395797855993%
278 68 0.000833707456098506014507%
279 248 0.000834044347178236611384%
280 293 0.000838685230656059394622%
281 212 0.000839001038678472126769%
282 152 0.000839817216939561447808%
283 141 0.000847855428592747127799%
284 299 0.000853192981993974538558%
285 132 0.000854574365964195993735%
286 155 0.000859152695521905548394%
287 58 0.000874320047002307147894%
288 286 0.000875866188099985666822%
289 224 0.000887849669379421374722%
290 137 0.000900489543899354785012%
291 226 0.000923377738998406487683%
292 148 0.000930881119322134794464%
293 162 0.000987055149734057538438%
294 79 0.000993893710953447839448%
295 40 0.001000416798370552893399%
296 98 0.001084332373656306117496%
297 273 0.001225074245297537315139%
298 81 0.001249182787069256063764%
299 17 0.001298452512502177918705%
300 85 0.001361922380597384773723%

By id

id Rank Rarity Links
0 230 0.000499458956047365231455%
1 134 0.000180177796359424320042%
2 165 0.000230184676111066551093%
3 145 0.000194022700922229457497%
4 192 0.000322251029152724845824%
5 96 0.000111294289262527690038%
6 256 0.000620018266871909294949%
7 67 0.000065181810173800739500%
8 237 0.000539615739460533837268%
9 257 0.000639318890938727788995%
10 199 0.000389450325204864725853%
11 113 0.000145569521908384173986%
12 3 0.000001910276740558515800%
13 106 0.000131126058929283129378%
14 102 0.000123115382641924631709%
15 114 0.000148643344111916620885%
16 40 0.000036184275778802637571%
17 299 0.001298452512502177918705%
18 74 0.000071470046509292475562%
19 252 0.000597123844136771735405%
20 255 0.000619069937827974978335%
21 235 0.000520604387814143135770%
22 19 0.000017533121984807949174%
23 217 0.000465088524003557941388%
24 270 0.000758232033913097225146%
25 18 0.000016809466854041561361%
26 175 0.000264254394089478831555%
27 97 0.000111335760807882409602%
28 90 0.000097476108135177813824%
29 182 0.000284137163005950866852%
30 162 0.000224233879157746364896%
31 105 0.000130896518620039059707%
32 76 0.000075164244372600511491%
33 110 0.000141463281009107189144%
34 166 0.000232598336585396935289%
35 17 0.000016286614720072082593%
36 171 0.000257292340283659759330%
37 51 0.000044500321469332576130%
38 261 0.000682544288076870398797%
39 154 0.000207858317914399857605%
40 295 0.001000416798370552893399%
41 24 0.000020823759938643466943%
42 117 0.000151677820001264065768%
43 28 0.000027801373169204159384%
44 267 0.000755320817943981397645%
45 120 0.000154964189090391811455%
46 59 0.000056381108631069283186%
47 155 0.000210664646105192569173%
48 160 0.000220895392794969434337%
49 89 0.000094979336316322216936%
50 16 0.000016220860730064761226%
51 218 0.000467596057784685050288%
52 173 0.000258186954882384952191%
53 130 0.000177282120955400468226%
54 93 0.000103266278247098156366%
55 264 0.000733735970048888120482%
56 274 0.000777176311843205745548%
57 184 0.000287929231133551074163%
58 287 0.000874320047002307147894%
59 47 0.000041770916891372601872%
60 245 0.000568667714843834647478%
61 265 0.000734794097345570283546%
62 95 0.000110755578749505411438%
63 57 0.000054720805159188959724%
64 124 0.000165564865347673823189%
65 9 0.000007484626156748281504%
66 207 0.000408378536550878528007%
67 227 0.000496558300889628125713%
68 278 0.000833707456098506014507%
69 125 0.000165907056152766866665%
70 216 0.000464337860214152509802%
71 148 0.000198516365390933934932%
72 42 0.000037635264428093728034%
73 104 0.000130240023329623226620%
74 161 0.000222031446122337289533%
75 129 0.000173322865666754105055%
76 254 0.000617180412054161675432%
77 194 0.000339192927541613164881%
78 228 0.000497358708384346018608%
79 294 0.000993893710953447839448%
80 107 0.000132927663421644818827%
81 298 0.001249182787069256063764%
82 244 0.000560886860266243138760%
83 73 0.000071464117042837030000%
84 239 0.000545243170785259358493%
85 300 0.001361922380597384773723%
86 202 0.000399219939012749962769%
87 212 0.000451250037489615515342%
88 197 0.000366142005571706093039%
89 266 0.000734938487053615730447%
90 13 0.000012994016822703662300%
91 118 0.000152724807654018964386%
92 2 0.000000955907289251856036%
93 238 0.000540835910523324307937%
94 168 0.000234798828290331759727%
95 41 0.000036869188912429064274%
96 26 0.000021298673415240130998%
97 204 0.000404478448159643997218%
98 296 0.001084332373656306117496%
99 170 0.000246095652423774450667%
100 225 0.000491208916785064453325%
101 65 0.000061695688209317738429%
102 221 0.000471956425132330264962%
103 55 0.000050040097465410080121%
104 187 0.000293975566178341382682%
105 112 0.000143972140844463123311%
106 52 0.000044513935833995622697%
107 131 0.000177443224593290337738%
108 6 0.000005414141455228512228%
109 219 0.000470353673330937082329%
110 205 0.000404943838099425528106%
111 248 0.000579850238352328135882%
112 147 0.000195708925263017791737%
113 32 0.000032373851149833966507%
114 71 0.000067923206317203332362%
115 143 0.000190339019875818555834%
116 226 0.000495920420456241067310%
117 108 0.000135492177468887021541%
118 273 0.000775889412954999281580%
119 49 0.000042262440198501750920%
120 224 0.000478118077758539928180%
121 139 0.000185951961184361170675%
122 122 0.000160495447719509443628%
123 262 0.000700421500986595749368%
124 86 0.000091187026998441005456%
125 137 0.000183627484274303203306%
126 11 0.000009591704849301649729%
127 271 0.000764959318535745258147%
128 75 0.000072273297079279895058%
129 100 0.000112788008420872755194%
130 60 0.000057882360072600661535%
131 85 0.000089145974160387218810%
132 285 0.000854574365964195993735%
133 222 0.000474602694658428022906%
134 8 0.000006372485346337133057%
135 242 0.000548883871351657504079%
136 164 0.000229853339363805364137%
137 290 0.000900489543899354785012%
138 83 0.000083923114891465891278%
139 153 0.000207082528959535766468%
140 29 0.000027968525840942248448%
141 283 0.000847855428592747127799%
142 163 0.000226702997896317186115%
143 231 0.000500616414925085777970%
144 233 0.000516709036752400455335%
145 179 0.000269569511252538453194%
146 70 0.000067251878308095114486%
147 84 0.000085767571426608756372%
148 292 0.000930881119322134794464%
149 247 0.000578882455649898852376%
150 172 0.000258130889532355459279%
151 54 0.000047845306261285443033%
152 282 0.000839817216939561447808%
153 183 0.000286452590667260139929%
154 27 0.000025198878232452329216%
155 286 0.000859152695521905548394%
156 249 0.000583446180082194541978%
157 14 0.000014317661185621095656%
158 159 0.000218797647787102996983%
159 189 0.000298293411765928901530%
160 232 0.000505292118366671024442%
161 272 0.000771005332453533623674%
162 293 0.000987055149734057538438%
163 58 0.000055429642732170566956%
164 87 0.000094616167023302649134%
165 186 0.000290279952113006928845%
166 45 0.000039436638322769505935%
167 88 0.000094636110271745924115%
168 277 0.000830477447395797855993%
169 1 0.000000503269457871017183%
170 34 0.000034148830931242133238%
171 236 0.000536591172324116347410%
172 185 0.000289078645462288177318%
173 201 0.000395842906743868285565%
174 20 0.000019172800783632280906%
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