Average Pokemon GO Plus Catch Rate by Trainer Level

GamePress would like to acknowledge trainer /u/sowok as the inspiration for this post.

When catching Pokemon with the Pokemon GO Plus, you're constrained in three ways:

  • Use Poke Ball only
  • One opportunity - Pokemon flees if fail
  • No throw bonuses whatsoever (except medal bonus, which we'll not cover in this article)

Because of the limited variables involved, sowok proposed "what is the per trainer level catch rate of PGO+" as an open question.

GamePress' recent research into level distributions of wild Pokemon is the last piece of the puzzle necessary to solving this.

Average Pokemon Go Plus Catch Rate by Trainer Level
Plotted with Average BCR=.38

Note that this catch rate will be improved by medal bonuses. We will update this page once information on medal bonuses is out.

Solution

A trainer's average catch rate is the average catch rate of all the Pokemon they encountered. As such, several questions need to be answered before Trainer Catch Rate can be solved:

  1. What is the Pokemon catch rate of GO Plus?
  2. What is the local distribution for wild Pokemon?
  3. What is the level distribution for wild Pokemon?
What is the Pokemon catch rate of GO Plus?

GamePress answered Question #1 in when we published GO Plus catch rate:

$$Capture Rate = \frac{Base Capture Rate}{2 * CP Multiplier} $$

GO Plus catch rate is exactly the same as throwing a Poké Ball without any throw bonuses.

What is the local distribution for wild Pokemon?

This question appears insurmountable on the surface, because Pokemon spawns depend so much on where you live, but it turns out much simpler than it initially appear.

This is because we don't actually need the Pokemon distribution, just the Base Capture Rate distribution. It turns out that 37 of the 74 base form Pokemon have Base Capture Rate (BCR) of 40%.  

Critically, those 37 include every common spawn (with an important exception of Magikarp at 56% BCR):

    base-capture-rate

    Because most spawns will have 40% BCR, we can expect for the actual base capture rate distribution for most trainers to hover around 40% as well:

    • If Magikarp and Oddish aren't common, then average BCR will end up slightly below 40%.
    • If Magikarp and Oddish are common, then their higher BCRs will bring the average back up to near 40%.
    • If the local area frequently spawns low BCR Pokemon (Growlithe, Eevee, and the starters, for example), then the average BCR will be lower still.

    To confirm this theory, we checked the average BCR of several catch samples we have on hand:

    TrainerAverage BCRSamples
    homu (0.37)36.6%222
    homu (0.41)36.8%270
    doublefelix39.2%353
    Spidertotz40.7%527
    heldertb38.1%240
    Karingan37.9%425

    The trainers are from 5 independent locations including Munich, California, and Belgium. In total, two-thirds of Pokemon in the collective sample have a BCR of 40%, as expected.

    The average BCR of the catch batches fall within a small range about 40%. The lowest among the average BCR, homu's, have a sizeable presence of Growlithe and Eevee because of the desert climate, which drags down the BCR average. The highest among the average BCR, Spidertotz's, is almost 15% Magikarp.

    We estimate the average BCR to fall within 41%-to-35% range for most trainers, with most around 38%.

    What is the level distribution for wild Pokemon?

    Because the other factor that affect capture rate with GO Plus is CPMultiplier, which in turn depends on a Pokemon's level, it is important to know the distribution of Pokemon level in the wild. In the recent article "Level Frequency of Wild Pokemon", we found that wild Pokemon levels are:

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

    Using the average base catch rate and level distribution, it is now possible to calculate the catch rate for a trainer where N is equal to the number of pokemon encountered since the trainer last leveled up.

    $$TrainerCatchRate = \frac{\displaystyle\sum_{i=1}^{N} \frac{BCR_i}{2 CPM_i}}{N}$$ $$ \approx \overline{BCR} \frac{\displaystyle\sum_{i=1}^{level} \frac{1}{2 CPM_{level}}}{level}$$
    Level \ BCR 35% 38% 41%
    1 100% 100% 100%
    2 100% 100% 100%
    3 94% 96% 98%
    4 87% 91% 94%
    5 82% 86% 89%
    6 77% 81% 85%
    7 73% 77% 81%
    8 70% 74% 78%
    9 67% 71% 75%
    10 65% 68% 72%
    11 62% 66% 70%
    12 60% 64% 68%
    13 58% 62% 66%
    14 57% 60% 64%
    15 55% 59% 62%
    16 54% 57% 61%
    17 53% 56% 60%
    18 51% 55% 58%
    19 50% 54% 57%
    20 49% 53% 56%
    21 48% 52% 55%
    22 47% 51% 54%
    23 46% 50% 53%
    24 46% 49% 52%
    25 45% 48% 51%
    26 44% 47% 50%
    27 43% 46% 50%
    28 43% 46% 49%
    29 42% 45% 48%
    30 41% 44% 47%
    31 41% 44% 47%
    32 41% 44% 47%
    33 41% 44% 47%
    34 41% 44% 47%
    35 41% 44% 47%
    36 41% 44% 47%
    37 41% 44% 47%
    38 41% 44% 47%
    39 41% 44% 47%
    40 41% 44% 47%

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