Level Frequency of Wild Pokemon

Introduction

Note that this original research article was published before the April 2017 change to Pokemon GO. Starting in April 2017, trainers who clicked on the same Pokemon on the map might have had different results; trainers who were above level 30 would have Pokemon with the same IVs, moves, etc., but trainers below level 30 would see different moves, IVs, etc.

It's well established that if two trainers captured the same Pokemon spawn, their Pokemon will be near copies with identical:

Additionally, if the trainers are the same level, then the Pokemon they caught will also have the same CP and level. However, when trainer levels differ, their Pokemon levels differ as well. How are Pokemon level decided on each encounter?

GamePress investigates.

Results

Before the Pokemon GO API was deactivated, GamePress Researcher CreativiTimothy recorded 30,000 wild Pokemon encounters as a level 31 trainer.  The levels of Pokemon he encountered is shown in the following graph:

Conclusions

Wild Pokemon levels, and thus CP, are:

• Random
• Uniformly distributed
• Limited by your trainer level or the level 30 cap, whichever that is lower.

You are just as likely to encounter a level 1 Pokemon as one at your current level (or any levels in between).

If your trainer level is n, the chance of encountering a Pokemon at any level is 1/n (or 1/30, if n>30).

Fancy Math Below

To confirm that our conclusion is statistically significant, we ran a chi-square test against the sample. This test is used to see if the amount of times an outcome appeared relative to the total is equal to some probability.

Level Count Proportion Chi-Squared
1 1057 0.035233 3.249
2 1013 0.033767 0.169
3 1008 0.0336 0.064
4 1015 0.033833 0.225
5 1013 0.033767 0.169
6 1019 0.033967 0.361
7 1021 0.034033 0.441
8 1002 0.0334 0.004
9 968 0.032267 1.024
10 947 0.031567 2.809
11 1013 0.033767 0.169
12 1017 0.0339 0.289
13 1025 0.034167 0.625
14 990 0.033 0.1
15 1077 0.0359 5.929
16 965 0.032167 1.225
17 975 0.0325 0.625
18 963 0.0321 1.369
19 1030 0.034333 0.9
20 1036 0.034533 1.296
21 941 0.031367 3.481
22 937 0.031233 3.969
23 956 0.031867 1.936
24 1019 0.033967 0.361
25 980 0.032667 0.4
26 1004 0.033467 0.016
27 1018 0.033933 0.324
28 975 0.0325 0.625
29 1042 0.034733 1.764
30 974 0.032467 0.676
Grand Total 30000 1 34.594

p-value 0.218181537

Based on the test, the chi-squared value is 34.6 with a p value of 0.22 which is not statistically significant. Therefore, level seems to be uniformly distributed across encounters.