"IV distribution for all encounter methods"

#PokemonGO: It started from one person's saying in my group chat that odds of ATK 15 is less rarer than odds of IV>=96%. (from lucky trade)I calculated the odds and confirmed it to be true, and realized it is easy to find general formula for IV n than I expected. So I tabulated the odds for all IV, then expanded it to all encounter types.Halfway through it I realized that many people already did this job... However, I couldn't find a recent one, and most of them were wrong, as they didn't consider lucky pokemon odds when calculating traded pokemon IV. Also, with new appraisal system and purified pokemons, I think this was maybe worth it.At this point tables are too many and too large, so I only attached the summarizing table and plots.​https://ift.tt/2YLR2Zv this post, just 'Lucky' means lucky trade, not lucky pokemon from random trade.Don't care about the 100.001. I summed rounded numbers.I assumed that lucky pokemon odds are 5%. (assuming recent pokemons, from https://ift.tt/2GQrgxi )I bolded most probable number of stars from each encounter.I ordered encounters in the order of odds of 3* pokemon, not 4*. (I'm a casual player) And, the order is different in each case.For 4*: Lucky = Purified w/ WB > Purified w/o WB > Raid > Best F > Ultra F > Great F > Good F > WB > no WBFor 3*: Lucky > Raid > Purified w/ WB > Best F > Purified w/o WB > Ultra F > Great F > WB > Good F > no WB​I drew plot for each encounters, for both individual odds and cumulative odds (from 100% backwards) I didn't include Ultra/Great/Good friend traded IV because they make plot too cluttered.​https://i.redd.it/p3knjmdotse31.png​https://i.redd.it/la6n5auptse31.pngThe reason Purified plot has jerk in it (more pronounced when weather boosted) is that IV 15 for each ATK/DEF/STA are more probable than others, (3/16 for purified w/o WB, 3/12=1/4 for purified w/ WB) so when IV allows two 15 it suddenly got higher (at 15+15+2=32 for purified w/o WB, 15+15+6=36 for purified w/ WB)Thanks to lucky pokemon odds, we can see Best friend trade odd plot makes a small bulge around 90% and less steep near 100% IV than others.(Except for purified ones, of course)​Application for mass evolvingAssume you want to leave (statistically) exact number of Pidgeys (assuming no WB) for mass evolving. You pinap them.For each Pidgey, you get 6 candies. And after you catch n Pidgeys, you get n*p candies additionally. (p is the probatility you transfer it) And for evolution, you need 10*m+2 candies for m Pidgeys. (You get one candy back when you evolve it, and you can transfer Pidgeotto) Now because m=n*(1-p),(6+p)n=10*n*(1-p)+2 =(similar when n is large)=10*n*(1-p)(6+p)=10(1-p)11p=4p=4/11=36%So if you transfer only 1* Pidgeys, without additional counting, you would have roughly needed number of Pidgeys when it comes to mass evolving time. (Considering we get WB sometimes) Same for other pokemons with candies needed to evolve are 12.​For candies needed to evolve = 25 (assuming no pinap)(3+p)n=23*n*(1-p)p=20/24=5/6=82%If you transfer all the 1* and 0*, it's almost same number. Be careful if you get pokemon from eggs often this would break.​For candies needed to evolve =50 (no pinap)(3+p)=48(1-p)p=45/49=92%So roughly, if you transfer all the 0* , 1* and ATK <=10 & 2*, you'll get similar number. Again you should make you own equation for pokemons which egg born is a major encounter source. via /r/TheSilphRoad https://www.reddit.com/r/TheSilphRoad/comments/cmoffn/iv_distribution_for_all_encounter_methods/?utm_source=ifttt