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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
On 12/8/2020 at 11:48 AM, Riesz said:

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

It's the same chance for each number on regular wild encounters. The only rigged encounters are from phenomena, event particle swarms, etc where the chance of a 30-31 is higher.

Edited by Rache
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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 :)

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  • 8 months later...

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