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Silph Study: #041

Published:
02.05.2021

A Guide to Candy XL: Part 2 – Catching

Note from the Editor: Due to updates in Pokémon GO since this article’s publication, some of the information regarding Go Battle League Encounters, Evolved Pokémon and Legendary/Mythical Pokémon may be out of date. Please stay tuned for future publications addressing these changes.


This article is the second in a three-part series discussing the various methods of obtaining Candy XL. In the first article, we took a close look at how Candy XL is rewarded from hatching eggs and discovered that Candy XL is awarded in a simple tier system based on the egg distance. In this study, we’ll take a closer look at Candy XL rewards from catching Pokémon. Since the launch of the GO Beyond update, researchers have collected data on over 16,000 catches during our investigation, allowing a deep dive into the underlying mechanics of the feature. Let’s see what we’ve uncovered!

Key Findings:

  1. The amount of Candy XL received is dependent on the level of the caught Pokémon, with higher level Pokémon giving more Candy XL.
  2. The Candy XL rate is likely broken into distinct level ranges.
  3. The distribution of Candy XL received from catching Pokémon is well-described by a binomial distribution (flipping a weighted coin).

The Effect of Level on Candy XL

When catching Pokémon, researchers recorded the number of Candy XL received, the weather, the encounter type, and CP and IVs for each catch. The CP and IVs were used to calculate the caught Pokémon’s level.

Plot of the average number of Candy XL received as a function of caught Pokémon level with a 95% confidence interval (black). The dashed lines represent the predicted rate for the Stair-step model (blue) and the mixed Linear model for levels 15-25 (red).

Plot of the average number of Candy XL received as a function of caught Pokémon level with a 95% confidence interval (black). The dashed lines represent the predicted rate for the Stair-step model (blue) and the mixed Linear model for levels 15-25 (red).

The graph above shows the average number of Candy XL received and the 95% confidence interval as a function of Pokémon level for wild encounters or Pokémon spawned from incense. As discussed in our initial publication, the rate of Candy XL is positively correlated with the level of the caught Pokémon. The amount of Candy XL received begins increasing at level 15 and flattens at level 31.

Notably, the rates themselves appear to break off into distinct “stair-stepped” values, modeled by the blue dashed line. The table below shows how the rate of Candy XL can be broken into these level ranges along with their 95% confidence interval. Each level “step” is separated by rate increments of 0.15 every three to five levels, suggesting a ratio in values for level 15 and above.

Step Range Number of Catches Average Candy XL per Catch Estimated Fraction Probability per Flip

(See XL Bundle Distribution below)

Levels 1-14 5,751 0.03 ± 0.004 3/100 1/100
Levels 15-19 2,119 0.17 ± 0.02 3/20 1/20
Levels 20-22 1,288 0.31 ± 0.03 6/20 2/20
Levels 23-25 1,369 0.45 ± 0.03 9/20 3/20
Levels 26-30 2,271 0.61 ± 0.03 12/20 4/20
Levels 31-35 837 0.87 ± 0.06 18/20 6/20

While the stair-step model presented above provides a strong fit to the data, there is not a clear explanation for the placement of the steps. The steps cover uneven level ranges, with ranges 20-22 and 23-25 covering only three levels apiece. While the step ranges may seem arbitrary, we’ll see them again in the next article in the series!

A combination of linear growth and stepped ranges could also explain the data. Using a chi-squared goodness-of-fit test, we evaluated various combinations of linear and stepped models at a significance level of 0.01. We were unable to reject either the stair-stepped model or a mixed linear growth model for levels 15-25, both of which are pictured on the graph above.¹

XL Bundle Distribution

The average Candy XL rate is useful, but does not give a full picture of its distribution. After each catch, a player can receive a bundle containing a variable amount of Candy XL. In over 16,000 catches, our researchers observed bundle sizes ranging from zero to three, which are tabulated below.

Bundle Size Occurrences Probability
13,277 78.70%
2,961 17.55%
586 3.47%
47 0.28%

This data is an aggregate of all catches regardless of encounter type or Pokémon level. As we discussed in the article on Candy XL from hatching eggs, we suspect that several weighted coin flips are performed each time Candy XL can be awarded. Given that researchers never received more than three Candy XL from a single catch, we hypothesized that a binomial model with three coin flips could accurately predict Candy XL bundle sizes. The graph below shows the observed and predicted likelihood of receiving each bundle size per Pokémon level.

As the average rate of Candy XL increases with level, so does the likelihood of receiving larger bundle sizes.² To assess the accuracy of the coin-flip model, we compared the theoretical distribution and observed distribution of Candy XL from levels 20-35 using a chi-squared goodness-of-fit test.

We also explored models with more coin flips. Models with flips ranging from three to five sufficiently fit the observed data and could not be rejected at a 0.01 significance level.³ It is noteworthy that a three-coin model matches the three regular candies normally received when catching Pokémon. This observation nicely parallels our previously proposed model for Candy XL rewards from hatching eggs.

What Doesn’t Influence Catch Candy XL?

Other factors were examined for possible effects on Candy XL rates. Using a series of Student’s t-tests, we evaluated mean Candy XL rates compared to a control group of wild and incensed Pokémon.

  • Field Research Pokémon (all level 15) did not significantly differ from level 15 Pokémon caught in the wild or from incense, and Shadow Pokémon did not differ from level 8 Pokémon (p-values=0.30 and 0.13 respectively). Candy XL rates for Pokémon caught in the wild and spawned by incense also did not differ (p-value=0.45).
  • Weather-boosted catches had a significantly higher rate of Candy XL than unboosted catches; however, this was explained by the increase in Pokémon level. For Pokémon with levels from 6-30, there was no significant difference between boosted and unboosted catches (p-value=0.66).
  • Despite receiving five or more regular candies for catching certain evolved Pokémon, there was no difference in their overall Candy XL rate when compared to catching unevolved forms (p-value=0.13).
  • Increasing regular candy for caught Pokémon (via Pinap berries or double catch candy events) did not significantly change the rate of Candy XL received (p-value=0.25).
  • So far, the research group has not found evidence of specific species having boosted Candy XL drop rates. Eighteen species were captured more than 250 times during the course of the study. None of these species differed from their expected average Candy XL under the proposed model (one-sample t-test, all p-values>0.05).⁴

The Candy XL rate for Raid and GO Battle League encounters have yet to show a significant difference from wild Pokémon, but more data is required before drawing a strong conclusion (n=595 and 256, respectively).

Parting Words

While Candy XL still remains a scarce resource for many travelers, catching wild Pokémon is the largest and most accessible source currently available. Weather-boosted Pokémon are especially profitable due to their higher than normal levels, with the average boosted Pokémon netting 64% more Candy XL than the average unboosted spawn (0.36 compared to 0.21). If there’s a specific Pokémon you want to power up, be sure to check the weather forecast!

Thanks for reading, travelers. Stay tuned for the third article in the series, which will take a look at transferring Pokémon!


Acknowledgements

Article author: Scientist CaroKann
Analysis: Scientist CaroKann and Titleist, and Lead Researchers Pancake and Gustavobc
Graphics: Scientists WoodWoseWulf and CaroKann
Project Leaders: Scientists Draxado and CaroKann
Editing: Scientists Cham1nade and skyeofthetyger
Data collection: 53 fastidious researchers collected data for this project. These 10 greatly exceeded our expectations:

  • Cloysterband
  • DeeDillyDawn
  • jinian
  • lunarite
  • marye
  • NeroXP
  • Pancake
  • RDC-DCIfan
  • Sean3116
  • topseeser

Footnotes

¹ We also evaluated mixed models which include linear growth from levels 15-30 and levels 15-35 and stair-step growth for the other levels. Comparisons of the expected counts for each model to the observed data was rejected using a chi-squared goodness-of-fit test at a 0.01 significance level.

² The number of 2 Candy XL bundles for level 26 Pokemon caught in the wild is significantly higher than the model. While this outlier could be due to an artifact in random number generation or general variance in our data, we are unable to come up with a logical explanation for this deviation.

³ For evaluating each coin-flip model, we first set the probability of success as the modeled Candy XL rate at each level divided by the number of flips. The expected counts of each Candy XL bundle are defined by the number of catches times the binomial function per level. We compared to the expected and observed counts of each bundle across each level using a chi-squared goodness-of-fit test, at a significance level of 0.01. As greater than one bundle sizes are rarer at lower levels, each model was only evaluated comparing the observed and expected counts of levels 20 and above.

Likewise, we evaluated a Poisson distribution model for the Candy XL bundle sizes. We first fit λ to each level using the maximum likelihood estimate (the sum Candy XL divided by the total number of catches at each level). The expected count for each bundle size was set as the number of catches per level times the Poisson probability mass function. When compared to observed bundle distribution using a chi-squared goodness-of-fit test, the expected values of the Poisson distribution model was rejected at a significance level of 0.01.

⁴ The following table shows the eighteen species along with their sample sizes, expected Candy XL rates, observed Candy XL rates, and p-values. All encounter methods are combined, and the expected rates of Candy XL were calculated from the level distributions of the species using the proposed stair-step model. Species that were more often caught at a high level tend to have higher expected rates of Candy XL. For example, species that were more often caught weather-boosted had higher expected rates.

Species Observations Expected Candy XL rate Observed Candy XL rate Student’s one-sample t-test p-value
Meltan 1,071 0.26 0.27 0.51
Machop 716 0.32 0.33 0.76
Wooper 648 0.23 0.24 0.64
Pikachu 497 0.21 0.19 0.32
Weedle 436 0.31 0.30 0.87
Snover 432 0.21 0.19 0.21
Seel 432 0.21 0.20 0.68
Bunnelby 404 0.26 0.31 0.12
Litleo 372 0.31 0.31 0.89
Spheal 357 0.23 0.27 0.21
Eevee 354 0.25 0.27 0.49
Cubchoo 342 0.23 0.27 0.28
Mareep 325 0.21 0.24 0.39
Hoothoot 320 0.25 0.28 0.39
Makuhita 310 0.31 0.31 0.88
Jigglypuff 290 0.30 0.36 0.14
Misdreavus 283 0.22 0.24 0.37
Woobat 268 0.22 0.26 0.26