Wild, Field Research, and Shadow Pokémon Secret Multipliers

Secret multiplier header

Speculations have long circulated that Pokémon granted as Field Research rewards felt “easier” to catch than their wild counterparts. Unfortunately, evidence supporting this “feeling” was only anecdotal. That changes today!

The Silph Research Group is excited to share that the first large-scale study of these encounter mechanics is complete. A small team of researchers collected, recorded, and analyzed 10,000 catch attempts across Field Research, Wild, and Shadow encounters to determine whether all three encounter types fit the previously-established catch mechanics.

Spoiler… They break the mold! We have discovered the following:

Field Research Encounters:

A newly discovered secret catch multiplier applying to Field Research encounters increases their effective catch rate. The net effect is such that standard Poké Balls are as potent in Field Research encounters as Ultra Balls are in wild encounters!

Shadow Encounters:

Shadow encounters appear difficult to catch due to their red “catch circle” color. It turns out that this is deceptive. Shadow Pokémon are exactly as difficult to catch as their non-Shadow counterparts. Don’t let the red circle fool you!

For a deeper dive into the analysis that revealed these discoveries, read on!

Background: The Previous Catch Rate Formula

The probability of catching a Pokémon was previously discovered by the GamePress group, and can be stated as follows:

 \mathrm{CR = 1 - (1 - \frac{BCR}{2 \cdot CPM})^{Multipliers}}

CR is the catch rate, or probability of catching the Pokémon. BCR is the base catch rate, which is a value unique to each Pokémon species. Legendary Pokémon have a low BCR, while common Pokémon like Rattata and Pidgey have a high BCR. CPM stands for Combat Power Multiplier, and is a scaling factor that increases with the level of the Pokémon, making higher-level Pokémon more difficult to catch. Finally, Multipliers is given by the product of the ball type, berry, throw circle size, curve ball, and type medal bonuses that apply to a particular encounter:

 \mathrm{Multipliers = Ball \cdot Berry \cdot Throw \cdot Curve \cdot Medal}

Several tools exist for calculating the CR for given conditions and species according to known mechanics. 

Methods

The initial hypothesis was that if Pokémon of a certain encounter type were easier to catch, then the discrepancy between the observed catch rate and the theoretical catch rate could be explained by a hidden multiplier, dubbed the Encounter multiplier. This multiplier would be applied to the catch rate formula together with the multipliers for different balls, berries, throw circle sizes, curve balls, and type medals.

For each catch attempt, researchers recorded all possible variables known to affect catch rate (species, ball, berry, etc.) and whether the Pokémon was caught or not. The catch rate formula shown above was used to calculate the theoretical catch rate for each catch attempt, accounting for all known bonuses. Summing all theoretical catch rates for a given encounter type (Wild, Research, and most recently, Shadow encounters) gave an expected number of catches for each category. The number of expected catches was then compared to the number of observed catches to look for inconsistencies. An extra parameter (the Encounter multiplier) was then added to the model in order to calculate an “observed” catch rate such that the sum matched the observed number of catches.

Finally, we needed to calculate the uncertainty around the Encounter multiplier for each category. Confidence intervals for the parameters were calculated using bootstrapping. Data points were re-sampled with replacement and the Encounter multiplier was fitted to minimize the error between the observed and theoretical catch rate, as described above. Re-sampling and parameter estimation were repeated 10,000 times. The parameter estimates were used to calculate a first moment pivotal (or reversal percentile interval) confidence interval around the parameter estimate at an α of 0.01. 

Findings

Wild Encounters

Wild encounters were used as the control condition. We wanted to rule out a bug (or previously unknown feature) affecting all encounter types and to confirm the methodology. Assuming the catch rate formula was correct and our methodology was sound, we would expect to find an estimated Encounter multiplier of 1, and indeed it was found to be

Encounterwild = 1.042
with a 99% confidence interval of 0.915-1.192, N = 3,667.

This indicates that Wild encounters do not have a secret multiplier associated with them, as the theoretical catch rates correspond to the observed catch rates. This corroborates GamePress’s catch rate model and confirms that our methodology for investigating other encounter types is meaningful.

Field Research Encounters

Next we examined Field Research encounters (not including weekly Breakthrough rewards) using the same methodology. Surprisingly, we found a multiplier of

Encounterquest = 2.017
with a 99% confidence interval of 1.89-2.151, N = 5,336.

The proximity of this multiplier to 2 leads us to believe that this is the multiplier being used to make Field Research encounters easier to catch. To put this in practical terms, the effect of this multiplier is like using Ultra Balls instead of regular Poké Balls.

Shadow Encounters

Shadow Pokémon, despite having a BCR of 0.05 for all species in the GAME_MASTER file¹, are noticeably easier to catch. This could perhaps be explained by a large Encounter multiplier. However, if the game were truly using a BCR of 0.05 for all species, then identical throws would have the same catch probability for all Pokémon species. It was clear from our data that this was not the case — comparisons between species with different default BCRs made it clear that the Shadow versions of species with a high BCR remained easier to catch than Shadow versions of species with a low BCR.

This observation suggests that Shadow Pokémon use a BCR value different from 0.05. One simple hypothesis is that Shadow Pokémon actually use the normal BCR associated with their species. Indeed, when the theoretical catch rate was calculated with the different default BCR of each species (instead of the GAME_MASTER value of 0.05), the two values agreed, resulting in an Encounter multiplier of

Encountershadow = 1.044
with a 99% confidence interval of 0.862-1.226, N = 1,418.

These results provide evidence that Shadow encounters do not have an additional Encounter multiplier like Field Research encounters. Instead, each Shadow Pokémon uses the default BCR for their species. In other words, Shadow Pokémon are exactly as difficult to catch as their non-Shadow counterparts. The BCR value of 0.05 is likely used to set the color of Shadow Pokémon’s throw circle, but is not used to calculate their catch probability. This is reminiscent of Ditto-disguised species, where the circle color matches that of the disguised species, but the (anecdotally) observed catch probability matches Ditto’s BCR

Parting words

Thanks to our persistent team of researchers, this study was able to establish the existence of a secret Encounter multiplier that can be applied to different encounter types:

 \mathrm{Multipliers = Ball \cdot Berry \cdot Throw \cdot Curve \cdot Medal \cdot \boldsymbol{Encounter}}

This study was able to estimate these multipliers for Wild, Field Research, and Shadow encounters. Several other encounter types, including Raids and Field Research Breakthroughs, are still under study. Stay tuned for later updates! In the meantime, we hope this information helps you to use your balls and berries more wisely and deepens your understanding of the Pokémon GO world.

Until next time, see you on the Road, travelers!


Footnotes

¹During the latest wave of Shadow Pokémon additions, Niantic deviated from their previous practice of giving Shadow Pokémon a uniform (albeit, as shown above, visual-purposes-only) BCR of 0.05. Instead, the new Shadow Pokémon had the same BCR as their wild counterparts. One notable example was Meowth. However, upon quick examination we concluded that the underlying catch mechanics remained the same. Since then, the new species’ BCRs were changed to 0.05 in the GAME_MASTER file.