About stats distribution in PvP
For the CP cap leagues there is the question of what is the optimal stats distribution. In this calculation atk, def and sta include the IV and CP multiplier.
Assuming the winner will be the last Pokemon standing, TDO will be most important. So what stats distribution maximize TDO?
TDO=DPS*TIME when TIME is the time until the Pokemon faint.
DPS~atk (~indicate proportional).
CP~√(atk^2*def*sta) (√ is the square root).
TIME~def*sta (time until faint proportional to bulk).
from these we can say that:
TDO~atk*(CP/atk)^2=CP^2/atk.
When the CP is capped at say 1500, lower attack will lead to higher TDO. So the implications are that assuming same moves and typing, the Pokemon with the lower attack will be better. For example, Meganium>Venusaur.This calculation assumes the attack is high enough for the Pokemon to reach the cap, Shuckle will not become OP.
Answers
If TDO is going to be the only factor, a CP 1500 Pokemon with 1 ATK, 1 STA and sky high DEF will be the best ever.
If that is true, it's incredibly stupid of Niantic to use the current CP formula (that doubly accounts for ATK) as the league cap. We will have another Blissey (in 2500 league) and Chansey (in 1500 league) disaster.
And suddenly an ideal IV pokemon is the one with 0 ATK, 15 DEF and 0 STA.
Also, countering such Blissey/Chansey won't be easy.
It can't be a Fighting type - they both can hit a Fighting Pokemon super effectively with both of their moves. So, one needs to either resist Psychic, Fairy and Normal or have access to Fighting moves.
Here comes Bastiodon, Skarmory and Azumarill (for the 1500 CP cap).
And for 2500 CP cap, only Jirachi can beat Blissey. Next closest is Steelix, but it's at 366 TDO, but Blissey (with accounting for non-effective damage) is at 376.
No, they won't.
CP formula cap punishes badly Pokemons with high ATK.
Also, in my calculation, I forgot to account for the fact that Blissey and Chansey have ridiculously high HP - so, their TDO requirement to win is much lower than to win against them.
So, actually, NOTHING can get even close to beating Blissey and Chansey in the capped games, if DPS on its own does not matter (only TDO).
MM Metagross with 2500 CP cap is at 336 TDO (against neutral, "abstract", Pokemon). It wouldn't beat Blissey even if they both had the same HP, which they obviously don't.
Actually, things are not so simple after all.
The CP formula cap has a funny consequence: defense+stamina is buffed. So, let's play with the numbers.
Luckily for us, Metagross has almost exactly twice the ATK Blissey has, so let's use that.
For the sake of CP and damage soaking, both are calculated against DEF*STA, so it doesn't really matter (apart from rounding issues) what are they values, it's their product that effectively matters. So, to simplify, let's assume that for both our 'mons, DEF=STA.
At a given CP, the stats will be the following (ATK, DEF, STA):
2x y y
1x 2y 2y
As time to kill the other 'mon is proportional to a simple formula of (DEF * STA) / ATK, it's obvious that the 1x ATK 'mon kills the other one in half the time. So far so good.
To take into account not effective damage of Blissey's moves against Metagross, it's ATK gets divided by 1.4. OK, that's closer, but Blissey still wins.
Now, time for Weave Damage. There's a handy spreadsheet here:
https://docs.google.com/spreadsheets/d/1fLCxv0soOFyc4rGz7Hsm7A2BbaeSReVJ7X4ZT11ppBc/edit#gid=1401800577
Bullet Punch + Meteor Mash has weave of 2332 (takes STAB into account).
Pound + Dazzling Gleam has 1957, while Zen Headbutt has 1760.
So, even in the worse (for Blissey) case, 2 / (2332 / 1760) / 1.4 is still more than 1. Blissey wins, though it's not that far actually, so things like fast move rounding issues, actual IV values, and dodging (however it works with PvP) might tilt the balance a little.
However, it's clear that a maxed-out Registeel, especially with Focus Blast, will prevail here. Steelix should too, and a number of so far neglected low-ATK mons able to either resist Blissey's moves or hit her super-effectively without getting super-effectively back.
However, one more thing not accounted for here is energy gain due to damage taken. This is clearly going to work in Blissey's favor. With Blissey's HP, she well get around two more charges for free.
So I was wrong in general, though not about MM Metagross.
Oh well, one more thing that breaks this calculation.
At <2500CP, Blissey will be at 33-34 level, while Metagross will be 23-25.
This means that actual Blissey's ATK will be higher than 0.5 Metagross'es, shrinking her advantage.
I guess that at this point, more speculations are rather moot, because it really boils down to how Niantic handles the PvP mechanics.
So, I actually think that I was right initially - comparing the TDO calculated against a "neutral abstract" Pokemon is the number that's relevant. And it does what we want, because it is directly proportional to the ATK / (actual HP * DEF) formula, also takes STAB and weave damage into account.
However, effectiveness needs to be doubly accounted for here, as it affects both enemy's TDO and own TDO, so the TDO multiplier/divisor to be used here is 1.96, not 1.4 I have originally applied. And so, a number of Steel species is back in the game, including MM Metagross, though not by a huge factor. And both Steelix and Registeel will be better than Metagross in this new meta.
And Giratina is the best Dragon.
