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Silph Study: #046

Published:
05.24.2021

A Window into Egg Transparency

Egg Transparency is finally here! For the first time in Pokémon GO, the species that can hatch from each egg are prominently shown in the game. This feature provides travelers a glimpse inside eggs acquired after the release of Egg Transparency on April 7, 2021. In addition, species are grouped into Rarity Tiers (on a scale of one to five eggs), which suggest how likely each species is to hatch. While the Egg Transparency feature has been a game-changer for egg hatching, travelers have been left with one major question: what do the Rarity Tiers actually mean?

Eager to crack into the mechanics behind this new feature, Silph Researchers compared the Rarity Tiers with the results of our egg tracking efforts. In this article, we’ll examine some of the recent hatch pools for each egg distance.¹ Without further ado, let’s unscramble the Egg Transparency feature!

Key Findings

  1. Species may change Rarity Tiers when other species are added or removed from the egg pool.
  2. Rarity Tiers likely represent a range of hatch probabilities, not relative weights.
  3. Species within a single Rarity Tier can have different hatch rates.

Rarity Tiers at Work

With the ability to see the hatch pool for each egg, changes to the pool are easy to detect. We have observed that the addition or removal of Pokémon can shift the Rarity Tiers of other Pokémon in the pool. As an example, let’s take a look at 5 km eggs collected during March 2021, with a focus on Drowzee and Voltorb.

In the first image, Drowzee and Voltorb appear in the most common group (Tier 1) alongside two regional Pokémon. When the number of regional Pokémon is increased to three or more — as shown in the second image — Tier 1 is eliminated completely, shifting Drowzee and Voltorb to Tier 2. The last image shows an egg from Rivals Week with featured event Pokémon occupying Tiers 1-3. Drowzee and Voltorb shift all the way down to Tier 4, with former Tiers 35 combining into the rarest Tier 5.

In past studies, we showed that it was possible to assign underlying weights to each species in a 1:2:4:8 ratio. Could Rarity Tiers visually represent a weight system like that? Not according to this example. If the Rarity Tiers represented weights, then Drowzee’s hatch probability would be calculated as its weight over the sum of the weights of all Pokémon in the pool. As other Pokémon enter the pool, Drowzee’s weight would remain unchanged, even as its hatch probability decreases. But Drowzee’s Rarity Tier does change, as seen in the above example. This contradiction leads us to believe that a Pokémon’s Rarity Tier cannot be directly mapped to a relative weight.

Tiers as an indication of hatch rates

Alternatively, we propose that the visible Rarity Tiers represent a range of hatch probabilities. As Pokémon are added to the pool, the probability of hatching Drowzee decreases, causing its Rarity Tier to change as well. Furthermore, the Rarity Tiers cannot represent fixed percentages, as the species in Tier 3 (Eevee, Ralts, etc.) with two regionals do not change Rarity Tiers when five regionals are present, while Drowzee and Voltorb do shift tiers.

Let’s see how this probability range model fits our egg hatching data. In the figure below, the probability of hatching each species is graphed according to its respective Rarity Tier.


Plot of each species by its Rarity Tier and hatch rate. The vertical bars represent a 95% confidence interval of the hatch rate. The grey areas indicate the estimated percentage range of each Rarity Tier. Some Pokémon are shown multiple times because event shifts caused their Rarity Tiers to change. Regional Pokémon are combined in the case of Pansear, Pansage, and Panpour (shown as Pansear), and in the case of Mime Jr., Kangaskhan, Tauros, and Farfetch’d (shown as Mime Jr.) Other 5 km regionals are excluded.

The majority of Pokémon hatching from each Rarity Tier tend to fall within distinct ranges, indicated by the grey areas. It should be stressed that each point is an estimation of the hatch rate, given our data. (Outliers such as Golett and Mime Jr. are likely due to low sample size.)

While we cannot pinpoint the exact rate of each individual species, we can get a clearer view by examining the overall hatch rate of all species within a Rarity Tier. This is done by combining the rates of all the species available within each Rarity Tier across all egg distances.² The table below shows the mean hatch rate of each Rarity Tier and what percentage range we believe each tier represents.

Rarity Tier Number of Hatches Mean Hatch Rate Estimated
Range
2,078 14.32% > 10 %
1,987 9.00% 7 – 10%
1,510 5.46% 4 – 7%
333 3.15% 2 – 4%
196 0.96% < 2%

The data above represent an aggregate of all Pokémon from multiple egg distances, telling us the mean Rarity Tier rate and not any specific Pokémon’s hatch rate. Ideally, though, we would want a way to assign each Pokémon a hatch rate based on its Rarity Tier and egg distance. Could this be possible using the new Egg Transparency feature? Let’s take a look!

Variable Hatch Rates within Tiers

While the Rarity Tiers do correspond to a rough range of hatch rates, they cannot be mapped directly onto a set hatch rate, even among eggs with the same hatch distance. As an example, let’s review the Tier 1 species in 12 km eggs.

Pokémon Count Proportion of
12 km Hatches
95% Confidence Interval
Vullaby 315 23.44% 21.17 – 25.70%
Larvitar 232 17.26% 15.24 – 19.28%
Absol 199 14.81% 12.91 – 16.71%
Scraggy 169 12.57% 10.80 – 14.35%
Pawniard 141 10.49% 8.85 – 12.13%


As you can see, the hatch rates are not evenly distributed. Vullaby hatches at a significantly higher rate than the other species, despite being in the same Rarity Tier and distance group.³ This variability in the hatch distribution means that it is impossible to assign a hatch rate for each species using the Egg Transparency information alone. Even when Pokémon appear in the same Rarity Tier, there is no guarantee that they will hatch at the same rate. At present, we are most confident that this affects the Tier 1 hatch pool. Significantly more data would be required to effectively test the lower-probability Rarity Tiers in the same manner.

Parting words

With egg pools constantly changing due to events, the Egg Transparency feature makes it easier than ever before to see what is in each egg! The convenience of having this information in-game has redefined how players hatch eggs and how the Silph Research group tracks them.

Unfortunately, Egg Transparency may not quite satisfy travelers’ expectations, as Rarity Tiers do not completely disclose a Pokémon’s hatch rate. We can easily see this with the overrepresentation of Vullaby compared to others found within the same Rarity Tier. In an extreme case, this could mean a Pokémon which hatches from 1 in 50 eggs and one that hatches from 1 in 500 would misleadingly share the same Rarity Tier. Unless we receive the exact hatch rate for each species, we advise travelers to use the Egg Transparency feature as an estimate rather than a comprehensive hatch guide. That’s it for now, travelers. Keep up with what’s hatching on the Road!


Acknowledgements

Article authors: Lead Researchers archer and DeeDillyDawn and Scientist CaroKann
Analysis: Scientists Darkmighty, CaroKann, and Titleist
Graphics: Scientists WoodWoseWulf and CaroKann
Editing: Scientists Cham1nade and skyeofthetyger and Senior Researcher JinianD
Project Leaders: Scientists Ansku and Cham1nade and Lead Researcher SarcasmCloud

Since the launch of Egg Transparency, 50 dedicated senior researchers have contributed to the Silph egg database. These researchers went above and beyond the call of duty:

  • AlertedFancy
  • alohanico
  • badmusicfan
  • Bectile
  • lindabayes
  • MrPrunez
  • otarie
  • Pancake
  • racheliptak
  • RDC-DCIfan68

Footnotes

¹ Egg pools can change with each new event, Pokémon release, or regional inclusion. To account for this, we looked at specific time periods where the egg pools did not experience this type of fluctuation. The table below shows the time periods with stable data sets that were used for the egg distance analysis.

Egg Distance Date Range Number of Hatches
2 km March 1 – May 4 1,823
5 km March 1 – May 4 435
7 km October 22, 2020 – May 3 2,186
10 km February 23 – May 4 316
12 km February 2 – May 4 1,344

The Celebrate Spring 2021 event featured an expanded pool of 2 km eggs, for which we collected 811 observations. All other special event egg pools with fewer than 500 data points were excluded from our analysis. Adventure Sync eggs were excluded from both the 5 km and 10 km hatch results.

Regional Pokémon have a significant impact on the 5 km Rarity Tiers. We divided 5 km eggs into two regions of interest. Region A contained one or two regionals, which appeared in Tier 1. Regionals such as Panpour, Pansage, and Pansear were combined into a single regional “slot.” Each slot’s hatch rate was the combined observations of all species in the slot divided by the total number of species in Region A. Our analysis considered only eggs from Region A when calculating the hatch rate of Pokémon in 5km eggs

Region B contained three or more regional Pokémon, which caused the Tier 1 Pokémon to shift to Tier 2. Insufficient data was obtained from Region B to estimate hatch rates. Regional Pokémon also appear in 2 km eggs (Illumise/Volbeat), and 10 km eggs (Sigilyph); however, the Rarity Tiers were unaffected by their inclusion.

² The mean rate for a Rarity Tier is calculated using the weighted harmonic mean of the individual hatch rates. Each species in a Rarity Tier is assigned a weight w based on the total number of hatches for that species, and a rate R equal to the number of hatches over all hatches in the distance pool. The harmonic mean rate of the Rarity Tier can be expressed as:

    \[H=\frac{\sum\limits^n_{i=1}{w_i}}{\sum\limits^n_{i=1}{\frac{w_i}{R_i}}}\]\]

³ Using a Pearson’s Chi-Squared goodness-of-fit test, we compared the number of hatches for each species to the number of hatches we would expect if the hatch rates were uniform. The Tier 1 pool of 12 km eggs differed significantly from our expectations (χ2(4) = 85.534, p < 0.001). Pairwise comparisons for each individual species showed that Vullaby was observed significantly more than every other species in the 12 km egg pool (Bonferroni-corrected p-value = 0.004 for Larvitar and p-values < 0.001 for Absol, Scraggy, and Pawniard).