Raid Battles are the most accessible way for many travelers to obtain powerful Legendary Pokémon, but catching the reward Pokémon at the end of the battle is no trivial task. New and veteran players alike know the disappointment of watching a Mewtwo or Rayquaza evaporate in a cloud of smoke.
A small group of dedicated researchers have been investigating the mechanics of catching raid bosses for over a year, and have recorded 6,500 throws over the course of their investigation. Today we’re going to share an exciting discovery that they’ve unearthed!
- A dynamic catch bonus multiplier makes raid bosses easier to catch over the course of an encounter.
- It’s unclear what factors affect the multiplier: the number of Premier balls thrown, balls remaining, total number of times the raid boss has been hit, number of successive hits, or some other factor.
Background: The Catch Rate Formula
The probability of catching a Wild Pokémon was previously discovered by the GamePress group and can be stated as follows:
CR is the catch rate, or probability of catching the Pokémon on a particular throw. 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. As shown in our previous study, there is an additional bonus applied to some encounter methods, which we call the Encounter bonus.
All Multipliers start with a base value of 1 for standard conditions but can be increased with the right throwing strategies. For example, throwing a Curveball increases the Curve multiplier to 1.7, while using a Razzberry increases the Berry multiplier to 1.5. These increases make it more likely that the Pokémon will be captured. The Silph Research Group previously showed that the Encounter bonus is 2 for Pokémon rewards from Field Research and 1 for encounters with Wild Pokémon.
Researchers threw Premier Balls at raid bosses and recorded everything that is known to affect catch rates (see Background above) and whether the boss was captured or not.¹ Missed throws were also recorded. A final “hidden” multiplier was left as a free parameter, and we optimized its value such that the expected catches from the formula equaled the number of catches our researchers actually recorded.
A hidden multiplier value of 1 would indicate that the catch rate formula is accurately predicting catch results, while a value greater than 1 would indicate that the encounters are easier to catch than the formula predicts. We split the data set into the first ball thrown, second ball, third ball, etc. and found the best fit multiplier for each subset of the data. Optimized multiplier values along with their 95% confidence intervals are shown in the plot below.²
Considering only the results from the first throw of the encounter, we found a fitted multiplier near 1 (95% confidence interval of 0.82 – 1.19). This indicates that the catch rate formula accurately predicts the number of raid bosses caught on the first throw of the encounter. However, as researchers threw more balls, the fitted multiplier increased.³ In the analyses for throws 5 to 10, all the 95% confidence intervals excluded the expected value of 1, indicating that another multiplier must be involved in calculating the catch rate. We resampled the multipliers in this range 6,000 times, and only 17 (0.3%) were less than 1, providing strong evidence that this increase was not due to chance.
This result means that for the exact same throw conditions (e.g. using a Golden Razz Berry and performing a Great Curveball Throw), you are more likely to catch the raid boss on the 10th throw of the encounter than the 1st. In contrast, the fitted multiplier does not appear to increase when trying to catch Pokémon in the Wild, from Lures, from Incense, or after Photobombs.⁴
The mathematical details will require more data, but these initial results suggest a large catch bonus after many throws. By the 8-10th throw, it’s as if you’re throwing an Ultra Ball instead of a Premier Ball!
The increased catch rate throughout a raid boss encounter opens up new catching strategies for both hard-core and casual players. Travelers with limited berry resources might consider saving their berries for later in the encounter, rather than using them at the beginning. For example, if you only have five Golden Razz Berries to use, it is most efficient to use them on the last five Premier Balls. For travelers with virtually unlimited Pinap and Golden Razz Berries, these results also change the optimal candy gathering strategy, favoring the use of Pinap Berries until even later in the encounter.
Legendary Pokémon have the lowest base catch rate in the game, making the increased catch rate easier to detect. Further research will help clarify the exact mechanics of the multiplier and whether it applies to other encounter types. We are particularly interested in whether this multiplier also affects encounters with Shadow Pokémon, as travelers also use Premier Balls after battling Team GO Rocket.
This discovery fundamentally changes our understanding of catch mechanics and opens up a new area of research. We’re still collecting data and hope to provide more details about this finding in the near future. Thanks for tuning in, travelers!
Authors: Scientists Superion and Titleist
Analysis: Scientists Superion and Titleist
Project Leader: Scientist Superion
Graphics: Scientists WoodWoseWulf and Titleist
Editing: Scientist Cham1nade and Senior Researcher JinianD
Data collection: 36 fastidious researchers collected data for this study. These 14 went above and beyond.
¹ About 2/3 of the 6,500 throws at raid bosses were aimed at Legendary raid bosses, so their results dominate. There were no obvious differences between Legendary raid bosses and other raid bosses, but more data will be needed to conclusively determine that there is no difference. While these data account for missed throws, our proficient researchers rarely missed the raid boss. Because of this, our researchers will need to collect more data with purposefully missed throws to be able to determine whether the multiplier increase is a function of the balls thrown, balls remaining, total number of times the raid boss has been hit, number of successive hits, or some other factor.
² Confidence intervals around the hidden multiplier estimates were calculated using bootstrapping. Data meeting the specified throw condition was re-sampled with replacement 1,000 times. For each replicate, an optimized multiplier was fitted to the re-sampled data. The multipliers from these replicates were sorted, and the 25th and 975th value were used as the 95% confidence interval.
³ We confirmed that this increase is not reflected in the Pokémon’s catch circle during raid encounters. In contrast, the Encounter multiplier of 2 for Field Research encounters makes the catch circle more green.
⁴ The graphs below visualize the comparison between raid boss encounters (left) and Wild, Lure, Incense, and Photobomb encounters (right). The four other encounter types did not have enough data individually to completely rule out the existence of a dynamic catch rate multiplier. Taken together, it is likely that most of the four are not affected. Data from 7+ throws is excluded from the Other Encounters plot as there were fewer than 25 throws for each. Unlike the plot in the main article, the data set used for this figure does not account for missed throws. Therefore, the comparison between the two plots might be misleading if, for example, the multiplier is only applied after consecutive hits to the Pokémon and researchers miss more frequently or less frequently when throwing at raid bosses.