"An Attempt to Understand Raid Boss Tiers"

#PokemonGO: Hi! I am a student currently studying statistics as part of a Master’s degree, and as revision for our exam, my Professor suggested practicing using the software (SPSS) at home. As someone who enjoys playing Pokémon Go and has done so since the game’s release, I thought I would make revision somewhat enjoyable, and see if I could answer a question that has bothered me since the raid boss rotation:Why are Pokémon allocated a certain difficulty tier as raid bosses? Is it due to their base stats?(Also, apologies for any formatting issues - this is the first time I have made a lengthy post and tried to use reddit's formatting style!)Preliminary IssuesI wanted to look at the raid bosses that have been in the game since the gym rework, and see if there is a reason why certain Pokémon are allocated to a specific tier. Note, my focus was on raid bosses that were available generally (so ignoring the special T4 raids in Yokahama), and only on Tiers 1-4, as T5 is reserved purely for legendary Pokémon.We know that Niantic uses base stats to work out the overall power and CP of the raid boss, using the formula here. The formula ignores Stamina, and instead focuses on Attack and Defence, applying a superficial HP stat based on the tier allocated. To make my life easier, I decided to compare the difficulty tier to the resulting value from that formula (henceforth Stat Value) minus the HP boost, rather than compare the difficulty tier to both attack and defence separately. Therefore, using this version instead:Stat Value = (baseattack+15)*sqrt(basedefence+15)This means, for example, that Bayleef would be allocated a single score of 1786.26, making my life easier (instead of having to compare all 3 base stats).AnalysisTo begin with, I looked at correlation: was there a link or relationship between the difficulty tier and the Stat Value? As the data is not continuous (the Pokémon are split into 4 groups, making the data ordinal, rather than interval or ratio), I had to use a non-parametric test. This resulted in a value of r=0.474, that there is a generally significant positive correlation between the difficulty tier and the Stat Value.This was promising. However, correlation does not equal causation; there may be other factors at work here. So, I had to go further and conduct what’s called an Analysis of Variance. Basically, this would work out whether the Pokémon has statistically significant differences in their Stat Values between the different tiers (so if T1 < T2 < T3 < T4).This came back with a surprising result. In relation to Tier 1, there was an incredibly high statistical significance between the Stat Values of those Pokémon and those in the other tiers (p<0.001, as significant as you can get really). However, in relation to the other tiers, there was no statistical significance between the Stat Values (p ranged from 0.365 to 1.000; p needs to be equal to or less than 0.05 to have significance).So, it seems evident that all raid bosses found in Tier 1 are statistically weaker than the other bosses, but those in Tiers 2, 3 and 4 are all statistically equal. This also is evident if you ‘switch’ the tier allocated to current bosses, and look at the resulting CP:a Tier 3 Tentacruel would have a CP of 15737, which matches up with other T3 bosses.a Tier 4 Omastar would have a CP of 29908, which matches up with other T4 bosses.a Tier 2 Venasaur would have a CP of 13188, which matches up with other T2 bosses.This has exceptions – Sableye has much lower stats than the rest of the T2 bosses (it is just as strong as the T1 bosses), and Porygon has much lower stats than the rest of T3 bosses. Other factors may have an impact, which will be discussed below.Now, this somewhat inconclusive result may also be because we have only had 42 raid bosses, meaning our sample size is rather low. If Niantic does another switch of the raid bosses, we might be able to look again and see if anything changes here.So What Else?What else could cause the allocation of difficulty tiers? From what we have seen, a few other factors are apparent, which could help explain why a Pokémon will be found in a certain difficulty tier:Pokémon rarity – the rarer a Pokémon generally, the higher the difficulty tier. Wild spawn rates of Snorlax, Lapras and Tyranitar are a lot lower than those of Sandslash or Sableye (a generalisation – biomes of course have an impact also). Also, T4 Pokémon and/or their families generally hatch out of eggs with higher distances than Pokémon in other tiers. This ‘rarity’ argument may explain why Sableye is not a T1 raid and why Porygon is not a T2 raid.Difficulty – the HP of the boss is calculated based on difficulty tier, so the ‘strength’ of the boss is dependent on what tier it is placed in. Cloyster is solo-able as a T2 raid, but it wouldn’t be if it was T3. Likewise, Ninetails has been proven to be a challenge to solo raiders as a T3 boss (just like Flareon), but would definitely need multiple people if it was in Tier 4.Place in the Meta – generally speaking, the more useful Pokémon in the meta will be found in the higher tiers. This is very much a generalisation: Exeggutor is the best grass-type attacker, but was a T2 raid boss, whereas Poliwrath, Nidoqueen and Nidoking are all out-classed by others, and are current T4 raid bosses). Also, usefulness is in the eye of the beholder – some people may consider Lapras less useful than Machamp, due to a preference of attackers over defenders.Evolution – the stage of evolution is also a factor; un-evolved and 1st evolution Pokémon are found more in T2 and T3, and 2nd evolution Pokémon are found in T3 and T4.Each of these factors cannot explain the placement of Pokémon into difficulty tiers by themselves; they all have obvious loopholes and exceptions. But together, they show a variety of different considerations that are made when choosing the difficulty tier of a raid boss. They also help explain why base stats alone do not dictate which difficulty tier a Pokémon will be in if it becomes a raid boss.Tl;dr – base stats of Pokémon explain why Pokémon are placed as Tier 1 raid bosses, but not why they would be placed in either Tiers 2, 3 or 4. Other factors must be in force here.Edits - formatting (I knew it would happen). via /r/TheSilphRoad http://ift.tt/2ABWJh8