"Mathematical analysis of Darkrai SB vs DP"

#PokemonGO: TL;DR : By my analysis Dark Pulse is better when boss DPS against Darkrai is larger than 11.4065, which include (Armored) Mewtwo, Deoxys-N, Deoxys-A, and Lugia. Generally, DP is more consistent, while SB has more potential to be faster.Mathematical proof: ( I tried to link docdroid pdf, but TSR filtered my post, moderators not responding, so I attach it as picture)​DerivationIt's based on a Gamepress article https://ift.tt/2MvQ2pF . (Warning: that article is not easy to read.)​Comparison with Pokebattler simulation :We should first check which bosses has DPS larger than 11.4065.On Gamepress DPS/TDO chart ( https://ift.tt/32IE2qF ), if you set Enemy species as Darkrai (we're trying to find boss DPS), Enemy fast move as Snarl, and you can also customize Darkrai as not having Focus Blast so chart averages only DP and SB not DP/SB/FB, but last one doesn't make much difference. And search for(psychic,ghost)&(legendary,deoxys,armored)&!dragon&@*currentBecause, Darkrai is SE against Psychic and Ghost, and we're trying to see T5 raid bosses (and I found out somewhat weirdly Armored Mewtwo doesn't count as a legendary in Gamepress database), and Dragon is better against Dragon (Lati@s and Giratina), and bosses always use current moves.Then we get some 7 pages of result. In principle I need to compare each case by case, but I was not willing to spend that much time, and we want our Darkrai to be consistent counter. Which means we (well, I) want to see it's performance against bosses most difficult moves. So I checked on the Best checkbox, then we get​​T5 bosses DPS against S/SB or S/DP DarkraiNow, according to our result, best moveset for Darkrai against (Mewtwo, Deoxys-A/N, Armored Mewtwo, Lugia) should be S/DP, and against (Deoxys-S,D / Cresselia, Lake trio) should be S/SB.When I check Pokebattler simulation ( https://ift.tt/2s3Mja0 ) with L40 counters, (I checked both general best moveset and best moveset against one in the above table) all of these cases agree with my conclusion. Only difference was 'general' best moveset for Armored Mewtwo is S/SB not S/DP, but best moveset against IT/DP is S/DP, and when I search all the armored mewtwo it's DPS average should be below 11, so it does not invalidate my result.​I did additional check, this time for Mewtwo's each moveset.​Mewtwo's DPS against S/SB or S/DP DarkraiAccording to our result, against Psychic best moveset should be S/SB, and against all the rest best moveset should be S/DP. But this time there were some discrepancies. Extreme cases (DP and Psychic) agree well, but Pokebattler says against (PC/TB, PC/IB, C/IB) SB is better. So my prediction is only 70% correct here, but considering we used many approximations during derivation, I think this is fine. And I had fun.+ Oh, and all of this assumes that we don't dodge. If we dodge we can distort Enemy DPS function form to our advantage, so SB would be better.It would be good if Gamepress modify their equation to consider cases in which Pokemon faints while trying to use charge move. There might be better way than my crude equations. I can tell they should have better mathematician than me from the above linked article.​If you had fun reading my proof, my previous math article:https://ift.tt/35S7zju via /r/TheSilphRoad https://ift.tt/2W15JIl