"[Analysis] Effect of Weather on Rate of Catching Raid Bosses"

#PokemonGO: Hello fellow travelers,With the recent addition of weather affects to boost the levels of wild pokemon and raid bosses caught, I was concerned about the lower catch chances for raid bosses that are being boosted by the weather, and I was considering waiting to raid Ho-oh's until the local clear weather boost went away. While it can be exciting to battle a boss boosted by the weather, is it a smart move because of the reduction in catch chance? I did some math to find out, and I wanted to share with all of you the data for Tier 5, EX, and other raids.Background:To briefly review how to calculate this [ref 1], the catch chance for catching any pokemon is governed by the following equation:Catch Probability for Throw = 1 – (1 – BaseCaptureRate/(2 X CPLevelMultiplier))BonusMultiplierswhereBaseCaptureRate is a percentage for each type of pokemon (ie. 2% for Ho-oh, Raikou, Entei, Suicune, and Lugia) It varies for different raid bosses [ref 2].CPLevelMultiplier is a constant number based on the level of the pokemonBonusMultipliers is the product of various bonuses such as using a golden razzberry, curving, and throwing a nice, great, or excellent.I would also like to state the following assumptions. I am assuming the case when you are trying your best to catch the boss with golden razz berries, all appropriate metals, and curve balls. We are also assuming that the raid group will be good enough to defeat the boss on a day its DPS is boosted.Now for the results:Tier 5 – Ho-oh and Other Raid Bosses with a 2% Base Capture Rate:Based on the above methods: I have calculated the following tables for great and excellent throws accounting for differences in the weather:BallsL20 T5 Boss - GreatL25 T5 Boss- GreatDifference112.7%11.5%1.3%223.8%21.6%2.2%333.5%30.6%3.0%442.0%38.5%3.5%549.4%45.6%3.8%655.8%51.8%4.0%761.4%57.3%4.1%866.4%62.2%4.1%970.6%66.6%4.1%1074.4%70.4%4.0%1177.6%73.8%3.9%1280.5%76.8%3.7%1383.0%79.4%3.5%1485.1%81.8%3.3%BallsL20 T5 Boss - ExcellentL25 T5 Boss - ExcellentDifference115.5%13.9%1.5%228.5%25.9%2.6%339.6%36.2%3.3%448.9%45.1%3.8%556.8%52.8%4.0%663.5%59.3%4.1%769.1%65.0%4.1%873.9%69.9%4.0%977.9%74.1%3.8%1081.3%77.7%3.6%1184.2%80.8%3.4%1286.7%83.5%3.2%1388.7%85.8%2.9%1490.5%87.8%2.7%Here’s how to read these tables: let’s say, I have 10 balls to throw on a Ho-oh on a day where there is not a fire or flying bonus (L20). If I am going to make 10 great throws, I have a 74.4% overall chance to catch the boss if I keep doing everything right. However, since all throws are independent events, if I make a great throw and the Ho-oh hops out, then I will have 9 balls and a 70.6% chance from that moment on.We can see in the comparison between the level 20 boss and the level 25 weather boosted boss on the great and excellent tables, that for a single great throw (or excellent), it is about 1.3% (or 1.5%) less likely to catch the boss, respectively. As a result, the overall chance of catching if you have a certain number of balls to throw is initially going to be around ~3-4% less for the level 25 boss than the level 20 boss. In other words, out of every 100 Tier 5 raids, you would expect to catch 3-4 fewer level 25 tier 5 raid bosses on average compared to level 20 tier 5 raid bosses.For a matter of perspective, we can see that this is a similar drop in catch probably as having one fewer damage ball to throw or consistently throwing with a larger circle size. The decrease in catch probably from a level 20 boss to a level 25 boss is actually less than the difference between excellent and a great (~2.8% per throw and ~5% to 7% overall). That said, many players should aim for a great throws since that is a throw most players can make more consistently and because missing the throw bonus makes the catch chance plummet to 8% for a single throw.Given the trade-off for having a 3-4% lower rate of catching the level 25 tier 5 boss for saving the 31,000 stardust and 28 candy for powering up a level 20 boss to the same level, I would say that this is a trade off many would be willing to make, since 31,000 stardust would take several hundred catches to earn and 28 rare candy can be hard to come by. Overall, I would say don’t be dissuaded from trying the raid boss on the day it is boosted just because of concern about not catching it.Special Case: EX Raid Mewtwo:Since the rollout of EX Raids, another consideration is how the weather would affect the catch chances of a precious chance at a mewtwo, which could be a source of stress even if it is something out of a trainer's hands. Since mewtwo has a base capture rate of 6%, the probability of catching a mewtwo on great throws is quite high whether the level is 20 or 25.BallsL20 Mewtwo - GreatL25 Mewtwo - GreatDifference134.0%31.0%3.0%256.4%52.4%4.1%371.3%67.1%4.1%481.0%77.3%3.7%587.5%84.3%3.2%691.7%89.2%2.6%794.5%92.5%2.0%896.4%94.8%1.6%997.6%96.4%1.2%1098.4%97.5%0.9%1199.0%98.3%0.7%1299.3%98.8%0.5%1399.5%99.2%0.4%1499.7%99.4%0.3%Because of the higher base capture rate, there is a 34% chance to catch a level 20 mewtwo on one great throw and a 31% chance to catch a level 25 mewtwo on one great throw (a 3% difference). Over 10 throws, this will translate into a less than 1% difference in overall catch probability, which is an almost negligible difference. This result is just another reason that it is important for groups to plan to maximize balls during an EX raid (as well to practice throwing at similarly far back pokemon like scyther so throws are not missed). While some would argue that they want to completely maximize the chance of catching the mewtwo, so that they might prefer a level 20 boss, in reality, maximizing individual and team damage balls is generally a much more important factor than the weather. That said, it is also worth commenting that with only 4 balls, the vast majority of trainers would be expected the catch the mewtwo at either level, so definitely it is important to keep calm, if you find yourself on a mewtwo catch screen with a few balls left. I would also add that unless the trainer is extremely confident with excellent throws, it is perhaps not worth shooting for excellent throws, which can be more likely to result in a missed throw bonus, given the high overall catch probably for over 10 great throws.Tier 4 –Tyranitar, Lapras, and Snorlax:Currently, the tier 4 raid bosses possess different catch rates, the most popular tier 4 raid bosses have been tyranitar, snorlax, and lapras, which also have the lowest base capture rate of 5%. The effect of throw bonus is correspondingly between the results for tier 5 legendaries and mewtwo.BallsL20 T4 - GreatL25 T4 - GreatDifference129.2%26.5%2.7%249.8%46.0%3.9%364.5%60.3%4.2%474.8%70.8%4.0%582.2%78.5%3.6%687.4%84.2%3.2%791.1%88.4%2.7%893.7%91.5%2.2%995.5%93.7%1.8%1096.8%95.4%1.4%1197.7%96.6%1.1%1298.4%97.5%0.9%1398.9%98.2%0.7%1499.2%98.7%0.5%In general, I would say that the reduction in catching chance is relatively small, < 2% overall catch chance, when starting with 9 or more balls. Once again it is relatively important to consider that it is more important to increase the number of balls. I would suggest that for these raid bosses since for most there will generally be more chances to raid in the future, it is a better trade off to get the savings in stardust and candy (31,000 stardust and 28 candy).Tier 3 to Tier 1:As is the case with Tier 4, the base capture rates for Tier 3, 2, and 1 raid bosses varies. Alakazam, Gengar, Machamp, Charmeleon, Wartortle, and Ivysaur are tied with the lowest base capture rate at 10%. The effect of weather is shown here:BallsL20 T3 - GreatL25 T3 - GreatDifference150.6%46.6%4.0%275.6%71.5%4.1%387.9%84.8%3.2%494.0%91.9%2.2%597.1%95.7%1.4%698.5%97.7%0.9%799.3%98.8%0.5%899.6%99.3%0.3%999.8%99.6%0.2%1099.9%99.8%0.1%11>99.9%99.9%0.1%12>99.9%99.9%<0.1%13>99.9%>99.9%<0.1%14>99.9%>99.9%<0.1%We see here that the reduction in the chance of capturing is negligible when starting with over 9 balls. If you are soloing/duoing and want to get a high IV pokemon to improve your team, if possible, definitely wait for the weather boost to the boss, if you have a team good/deep enough to take it down to get to the catch screen. If you find a high IV one and golden it and throw curve greats, you will almost certainly catch it at level 25 and save the 28 candies and 31,000 dust versus catching a level 20.Tldr: The reduction of chances of catching the raid boss because boosted level from 20 to 25 by weather is only a few percent or less in all cases. The effect of having another damage ball will be generally more significant. I recommend to not sit out on raiding because of concern about lower catch chance during a given weather based on the above tables. In fact, raiding a weather boosted boss will often lead to a savings of 31,000 stardust and 28 candy.ReferencesSee: http://ift.tt/2C6yDN4: http://ift.tt/2nRCpqs Information:Values used for circle size bonus were 1.46 for great and 1.8 for excellent as representative circle sizes, since there is slight variation based on radius within the great and excellent ranges.Edit: Minor text fixes, and adding supporting information about circle size for completeness. via /r/TheSilphRoad http://ift.tt/2jr8MLg