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IV's probabilities while catching wild pokemon


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IV’s is determinate between 0 and 31, so there is 32 possibilities for each stat.

32^6 = 1 073 741 824 combinations of different pokemon IV's.

Chance to get a 6*31 wild catch:

31 31 31 31 31 31

There is just one combination with theses IV’s, so the probability is 1 / 1 073 741 824.

The probability to catch a 6*0 wild pokemon is the same, 1 / 1 073 741 824.

Chance to get a 5*31 wild catch:

X 31 31 31 31 31

31 X 31 31 31 31

31 31 X 31 31 31

31 31 31 X 31 31

31 31 31 31 X 31

31 31 31 31 31 X

Considering X could be between 0 and 30, there is 31 possibilities for each case.

6 * 31 = 186.

1 073 741 824 / 186 ≈ 5 772 806.

The probability to catch a 5*31 wild pokemon is approximately 1 / 5 772 806.

 

Chance to get a 4*31 wild catch:

X X 31 31 31 31

X 31 X 31 31 31

X 31 31 X 31 31

X 31 31 31 X 31

X 31 31 31 31 X

31 X X 31 31 31

31 X 31 X 31 31

31 X 31 31 X 31

31 X 31 31 31 X

31 31 X X 31 31

31 31 X 31 X 31

31 31 X 31 31 X

31 31 31 X X 31

31 31 31 X 31 X

31 31 31 31 X X

Considering X could be between 0 and 30, there is 31*31 = 961 possibilities for each case. 15 * 961 = 14 415.

1 073 741 824 / 14 415 ≈ 74 488.

The probability to catch a 4*31 wild pokemon is approximately 1 / 74 488.

 

 

Chance to get a 3*31 wild catch:

X X X 31 31 31
X X 31 X 31 31
X X 31 31 X 31
X X 31 31 31 X
X 31 X X 31 31
X 31 X 31 X 31
X 31 X 31 31 X
X 31 31 X X 31
X 31 31 X 31 X
X 31 31 31 X X
31 X X X 31 31
31 X X 31 X 31
31 X X 31 31 X

31 X 31 31 X X
31 X 31 X X 31
31 X 31 X 31 X
31 31 X X X 31
31 31 X X 31 X

31 31 X 31 X X
31 31 31 X X X

Considering X could be between 0 and 30, there is 31*31*31 =  29 791 possibilities for each case. 20 * 29 791 = 595 820.

1 073 741 824 / 595 820 ≈ 1 802.

The probability to catch a 3*31 wild pokemon is approximately 1 / 1 802.

 

 

Chance to get a 2*31 wild catch:

31 31 X X X X
31 X 31 X X X
31 X X 31 X X
31 X X X 31 X
31 X X X X 31
X 31 31 X X X
X 31 X 31 X X
X 31 X X 31 X
X 31 X X X 31
X X 31 31 X X
X X 31 X 31 X
X X 31 X X 31
X X X 31 31 X
X X X 31 X 31
X X X X 31 31

Considering X could be between 0 and 30, there is 31*31*31*31 = 923 521 possibilities for each case. 15 * 923 521 = 13 852 815.

1 073 741 824 / 13 852 815 ≈ 78.

The probability to catch a 2*31 wild pokemon is approximately 1 / 78.

 

 

Chance to get a 1*31 wild catch:

31 X X X X X
X 31 X X X X

X X 31 X X X

X X X 31 X X

X X X X 31 X

X X X X X 31

Considering X could be between 0 and 30, there is 31*31*31*31*31 = 28 629 151 possibilities for each case. 6 * 28 629 151 = 171 774 906.

1 073 741 824 / 171 774 906 ≈ 6,25.

The probability to catch a 1*31 wild pokemon is approximately 1 / 6,25.

 

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

 

After this, i decided to calculate the probability for every sum of possible IV.

It would take 10000 years to do it by myself, so I made a little program in C++ which will do this in 3 seconds.

The program:

program.png.8decac503f67927e0b877e64db5f030f.png

 

And the result of the program:

 

Total IV : Number of combination

0 : 1
1 : 6
2 : 21
3 : 56
4 : 126
5 : 252
6 : 462
7 : 792
8 : 1287
9 : 2002
10 : 3003
11 : 4368
12 : 6188
13 : 8568
14 : 11628
15 : 15504
16 : 20349
17 : 26334
18 : 33649
19 : 42504
20 : 53130
21 : 65780
22 : 80730
23 : 98280
24 : 118755
25 : 142506
26 : 169911
27 : 201376
28 : 237336
29 : 278256
30 : 324632
31 : 376992
32 : 435891
33 : 501906
34 : 575631
35 : 657672
36 : 748642
37 : 849156
38 : 959826
39 : 1081256
40 : 1214037
41 : 1358742
42 : 1515921
43 : 1686096
44 : 1869756
45 : 2067352
46 : 2279292
47 : 2505936
48 : 2747591
49 : 3004506
50 : 3276867
51 : 3564792
52 : 3868326
53 : 4187436
54 : 4522006
55 : 4871832
56 : 5236617
57 : 5615966
58 : 6009381
59 : 6416256
60 : 6835872
61 : 7267392
62 : 7709856
63 : 8162176
64 : 8623146
65 : 9091452
66 : 9565682
67 : 10044336
68 : 10525836
69 : 11008536
70 : 11490732
71 : 11970672
72 : 12446566
73 : 12916596
74 : 13378926
75 : 13831712
76 : 14273112
77 : 14701296
78 : 15114456
79 : 15510816
80 : 15888642
81 : 16246252
82 : 16582026
83 : 16894416
84 : 17181956
85 : 17443272
86 : 17677092
87 : 17882256
88 : 18057726
89 : 18202596
90 : 18316102
91 : 18397632
92 : 18446736
93 : 18463136
94 : 18446736
95 : 18397632
96 : 18316102
97 : 18202596
98 : 18057726
99 : 17882256
100 : 17677092
101 : 17443272
102 : 17181956
103 : 16894416
104 : 16582026
105 : 16246252
106 : 15888642
107 : 15510816
108 : 15114456
109 : 14701296
110 : 14273112
111 : 13831712
112 : 13378926
113 : 12916596
114 : 12446566
115 : 11970672
116 : 11490732
117 : 11008536
118 : 10525836
119 : 10044336
120 : 9565682
121 : 9091452
122 : 8623146
123 : 8162176
124 : 7709856
125 : 7267392
126 : 6835872
127 : 6416256
128 : 6009381
129 : 5615966
130 : 5236617
131 : 4871832
132 : 4522006
133 : 4187436
134 : 3868326
135 : 3564792
136 : 3276867
137 : 3004506
138 : 2747591
139 : 2505936
140 : 2279292
141 : 2067352
142 : 1869756
143 : 1686096
144 : 1515921
145 : 1358742
146 : 1214037
147 : 1081256
148 : 959826
149 : 849156
150 : 748642
151 : 657672
152 : 575631
153 : 501906
154 : 435891
155 : 376992
156 : 324632
157 : 278256
158 : 237336
159 : 201376
160 : 169911
161 : 142506
162 : 118755
163 : 98280
164 : 80730
165 : 65780
166 : 53130
167 : 42504
168 : 33649
169 : 26334
170 : 20349
171 : 15504
172 : 11628
173 : 8568
174 : 6188
175 : 4368
176 : 3003
177 : 2002
178 : 1287
179 : 792
180 : 462
181 : 252
182 : 126
183 : 56
184 : 21
185 : 6
186 : 1

The sum of all theses numbers is 1 073 741 824, so it works perfectly.

 

Graphics view:

probabilty (%)

graphic.png.e340f9d4bdd96e0e263ebd8d3b1a7b27.png  

 

Another graphic view, thanks to the member TohnR for the idea:

graphic2.thumb.png.2c16b5f25a5b143fc292648faec1cc10.png

 

 

Edited by Galekingex
Link to comment
On 12/8/2020 at 1:48 AM, Riesz said:

This maybe true but we do not know if it is same probability for each number (0-31)

Thanks for your comment, your right.

I think I will probably caught some ditto (like 3000-4000) and check all the IV's to see if the distribution is equal or not ^^

 

9 minutes ago, xenkiller said:

Magnifique ! Merci Bro

De rien ;)

 

On 12/8/2020 at 1:56 AM, Ovale said:

Thank you very much my friend. I like the statistics.

 

Muchas gracias mi amigo. Me gustan las estadisticas.

Ty :)

Edited by Galekingex
Link to comment

I'd just add that the chance to have

AT LEAST 1*31 when catching a Pokémon would be 6/32 so around 1/5.5

AT LEAST 2*31 when catching would be 15/32² which is around 1/68.5

After all, no one is gonna complain about getting a better result than the goal, so what really matters is the interval not the exact value imo :) 

Funny sheet tho ! 

 

Using your data, we can calculate the chance to have IV in certain ranges

IV [0 to 20] = IV [166 to 186] = 230 227 / 1 073 741 824 which approximates to 1/4664 

IV [0 to 10] = IV [176 to 186] = 8 005 / 1 073 741 824 which approximates to 1/134k (winning a catch event is much harder than finding a shiny these days kek)

Link to comment
On 12/19/2020 at 7:51 PM, TohnR said:

I'd just add that the chance to have

AT LEAST 1*31 when catching a Pokémon would be 6/32 so around 1/5.5

AT LEAST 2*31 when catching would be 15/32² which is around 1/68.5

After all, no one is gonna complain about getting a better result than the goal, so what really matters is the interval not the exact value imo :) 

Funny sheet tho ! 

 

Using your data, we can calculate the chance to have IV in certain ranges

IV [0 to 20] = IV [166 to 186] = 230 227 / 1 073 741 824 which approximates to 1/4664 

IV [0 to 10] = IV [176 to 186] = 8 005 / 1 073 741 824 which approximates to 1/134k (winning a catch event is much harder than finding a shiny these days kek)

Thank you my friend, I had another graphic view with the probability for different intervals.

Hope theses data will be useful to you :)

Link to comment
  • 8 months later...
  • 1 year later...

You can use this website https://anydice.com/ and use the command : output 6d{0..31}

Go to "export" to show the real values in % and change values for "at least" or "at most".

Just go for an 100/value to calculate the probabilities in a 1 to XX encounter format.

For people who don't get it, there is the numbers : 

AT LEAST 
0,100
1,99.99999990686774
2,99.9999993480742
3,99.99999739229679
4,99.99999217689037
5,99.99998044222593
6,99.99995697289705
7,99.9999139457941
8,99.9998401850462
9,99.99972032383084
10,99.9995338730514
11,99.99925419688225
12,99.99884739518166
13,99.99827109277248
14,99.99747313559055
15,99.99639019370079
16,99.9949462711811
17,99.99305112287402
18,99.99059857800603
19,99.9874647706747
20,99.98350627720356
21,99.97855816036463
22,99.97243192046881
23,99.96491335332394
24,99.95576031506062
25,99.94470039382581
26,99.93142848834401
27,99.9156042933465
28,99.8968496918679
29,99.874746054411
30,99.8488314449788
31,99.8185977339745
32,99.7834876179696
33,99.7428921051324
34,99.6961484663189
35,99.6425386518241
36,99.5812881737948
37,99.5115654543043
38,99.4324816390873
39,99.343090876937
40,99.242391064763
41,99.129325058311
42,99.002782348543
43,98.86160120368
44,98.704571276903
45,98.53043667972099
46,98.33789952099299
47,98.12562391161899
48,97.89224043488498
49,97.63635108247398
50,97.35653465613697
51,97.05135263502598
52,96.71935550868498
53,96.35908957570798
54,95.96910420805199
55,95.54795958101698
56,95.09423486888399
57,94.60653690621199
58,94.08350931480499
59,93.52384209632798
60,92.92628169059698
61,92.28964149951898
62,91.61281287670099
63,90.89477658271798
64,90.13461470603998
65,89.33152165263898
66,88.48481420427598
67,87.59394064545698
68,86.65848895907499
69,85.67819409072499
70,84.65294428169499
71,83.58278647064499
72,82.467930763955
73,81.308753974735
74,80.105802230535
75,78.859792649745
76,77.571614086625
77,76.242326945065
78,74.873162060975
79,73.46551865339501
80,72.02096134424501
81,70.54121624678501
82,69.02816612273502
83,67.48384460806501
84,65.91042950749501
85,64.31023515761501
86,62.68570385873501
87,61.03939637541501
88,59.37398150562501
89,57.69222471862501
90,55.99697586148501
91,54.29115593432501
92,52.57774293421501
93,50.85975676773501
94,49.14024323223501
95,47.422257065755005
96,45.708844065645
97,44.003024138485
98,42.307775281345
99,40.626018494345004
100,38.960603624555006
101,37.314296141235005
102,35.689764842355004
103,34.089570492475005
104,32.516155391905
105,30.971833877235003
106,29.458783753185003
107,27.979038655725002
108,26.534481346575003
109,25.126837938995003
110,23.757673054905002
111,22.428385913345004
112,21.140207350225005
113,19.894197769435003
114,18.691246025235003
115,17.532069236015005
116,16.417213529325004
117,15.347055718275003
118,14.321805909245004
119,13.341511040895004
120,12.406059354513003
121,11.515185795694002
122,10.668478347331002
123,9.865385293930002
124,9.105223417252002
125,8.387187123269003
126,7.710358500451003
127,7.073718309373003
128,6.476157903642003
129,5.9164906851650025
130,5.393463093758003
131,4.905765131086003
132,4.452040418953003
133,4.030895791918003
134,3.640910424262003
135,3.280644491285003
136,2.9486473649440033
137,2.6434653438330034
138,2.363648917496003
139,2.107759565085003
140,1.874376088351003
141,1.662100478977003
142,1.469563320249003
143,1.295428723067003
144,1.1383987962900028
145,0.9972176514270028
146,0.8706749416590028
147,0.7576089352070028
148,0.6569091230330028
149,0.5675183608827028
150,0.48843454566570277
151,0.41871182617520275
152,0.35746134814590275
153,0.30385153365110273
154,0.2571078948376027
155,0.2165123820004027
156,0.18140226599550272
157,0.1511685549912027
158,0.1252539455590027
159,0.10315030810210271
160,0.08439570662350271
161,0.06857151162600271
162,0.055299606144202706
163,0.04423968490940271
164,0.03508664664608271
165,0.027568079501212706
166,0.021441839605392705
167,0.016493722766462705
168,0.012535229295312705
169,0.009401421963992705
170,0.006948877096002705
171,0.005053728788912705
172,0.003609806269232705
173,0.0025268643794727048
174,0.0017289071975417048
175,0.0011526047883697048
176,0.0007458030877777048
177,0.00046612691862070476
178,0.0002796761391827048
179,0.00015981492382970478
180,0.00008605417592020478
181,0.00004302707297300478
182,0.000019557744092704782
183,0.000007823079652504783
184,0.0000026076732346547824
185,0.0000026077032089205
186,0.000000000931322574615


AT MOST :

0,
1,0.000000006519258022305
2,0.0000026077032089205
3,0.0000078231096267705
4,0.0000195577740669705
5,0.0000430271029472705
6,0.0000860542058944705
7,0.0001598149538039705
8,0.0002796761691569705
9,0.0004661269485949705
10,0.0007458031177519705
11,0.0011526048183439705
12,0.0017289072275159705
13,0.0025268644094469704
14,0.0036098062992069705
15,0.005053728818886971
16,0.006948877125976971
17,0.009401421993966971
18,0.012535229325286971
19,0.01649372279643697
20,0.02144183963536697
21,0.02756807953118697
22,0.03508664667605697
23,0.04423968493937697
24,0.05529960617417697
25,0.06857151165597697
26,0.08439570665347697
27,0.10315030813207697
28,0.12525394558897696
29,0.15116855502117696
30,0.18140226602547696
31,0.21651238203037695
32,0.25710789486757696
33,0.303851533681077
34,0.357461348175877
35,0.418711826205177
36,0.488434545695677
37,0.567518360912677
38,0.656909123062977
39,0.757608935236977
40,0.8706749416889771
41,0.997217651456977
42,1.138398796319977
43,1.2954287230969772
44,1.4695633202789773
45,1.6621004790069773
46,1.8743760883809772
47,2.107759565114977
48,2.3636489175259774
49,2.643465343862977
50,2.948647364973977
51,3.280644491314977
52,3.640910424291977
53,4.030895791947977
54,4.4520404189829765
55,4.9057651311159765
56,5.393463093787976
57,5.916490685194976
58,6.476157903671976
59,7.073718309402976
60,7.710358500480975
61,8.387187123298975
62,9.105223417281975
63,9.865385293959974
64,10.668478347360974
65,11.515185795723974
66,12.406059354542975
67,13.341511040924976
68,14.321805909274977
69,15.347055718304976
70,16.417213529354974
71,17.532069236044975
72,18.691246025264974
73,19.894197769464974
74,21.140207350254975
75,22.428385913374974
76,23.757673054934976
77,25.126837939024977
78,26.534481346604977
79,27.979038655754977
80,29.458783753214977
81,30.971833877264977
82,32.51615539193498
83,34.08957049250498
84,35.68976484238498
85,37.31429614126498
86,38.960603624584984
87,40.62601849437498
88,42.30777528137498
89,44.00302413851498
90,45.70884406567498
91,47.42225706578498
92,49.140243232264986
93,50.859756767764985
94,52.57774293424499
95,54.29115593435499
96,55.99697586151499
97,57.69222471865499
98,59.37398150565499
99,61.03939637544499
100,62.68570385876499
101,64.31023515764498
102,65.91042950752498
103,67.48384460809498
104,69.02816612276499
105,70.54121624681498
106,72.02096134427498
107,73.46551865342498
108,74.87316206100498
109,76.24232694509497
110,77.57161408665498
111,78.85979264977497
112,80.10580223056498
113,81.30875397476498
114,82.46793076398498
115,83.58278647067498
116,84.65294428172497
117,85.67819409075497
118,86.65848895910497
119,87.59394064548697
120,88.48481420430596
121,89.33152165266897
122,90.13461470606997
123,90.89477658274797
124,91.61281287673097
125,92.28964149954896
126,92.92628169062696
127,93.52384209635797
128,94.08350931483497
129,94.60653690624197
130,95.09423486891397
131,95.54795958104697
132,95.96910420808197
133,96.35908957573797
134,96.71935550871497
135,97.05135263505596
136,97.35653465616696
137,97.63635108250396
138,97.89224043491497
139,98.12562391164897
140,98.33789952102298
141,98.53043667975098
142,98.70457127693298
143,98.86160120370998
144,99.00278234857298
145,99.12932505834098
146,99.24239106479298
147,99.34309087696698
148,99.43248163911728
149,99.51156545433429
150,99.58128817382479
151,99.64253865185408
152,99.69614846634889
153,99.74289210516238
154,99.78348761799958
155,99.81859773400448
156,99.84883144500878
157,99.87474605444099
158,99.89684969189788
159,99.91560429337649
160,99.931428488374
161,99.9447003938558
162,99.9557603150906
163,99.96491335335392
164,99.97243192049879
165,99.97855816039461
166,99.98350627723354
167,99.98746477070469
168,99.99059857803601
169,99.993051122904
170,99.99494627121109
171,99.99639019373078
172,99.99747313562054
173,99.99827109280247
174,99.99884739521164
175,99.99925419691223
176,99.99953387308139
177,99.99972032386083
178,99.99984018507618
179,99.99991394582409
180,99.99995697292704
181,99.99998044225592
182,99.99999217692036
183,99.99999739232678
184,99.99999934810418
185,99.99999990689773
186,100.0000000000

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