Do IVs matter in the PvP battle league?
In the Great League and the Ultra League the maximal CP of a Pokemon are capped at 1500 and 2500. Furthermore the IVs of a Pokemon matter in the CP calculation.
As I do not know the CP calculation I try to use Pokemon with good IVs in the PvP fights. Therefore I prefer Pokemon which have a 13+ Attack IV, 13+ Defense IV and 13+ HP IV.
But is this really the best option?
I found the following site which seems to suggest that a 1/15/15 Alolan Raichu is better in PvP than a 15/15/15 Alolan Raichu. But I can not find an explanation why this is the case.
And the most important part, does it matter in an actual battle?
I have seen that there are similar questions (this one Do individual values (IVs) really matter at lower levels? or this one What is better to have? A pokemon with higher IV but lower CP or vice versa?) but they do not consider PvP at all.
Solution 1:
Yes, it does matter, and yes, it does matter in an actual battle (example in the end).
It is because attack more heavily impacts the CP than defense or HP. See for example the answer here, with the formula:
CP = (Base Atk + Atk IV) * (Base Def + Def IV)^0.5 * (Base Stam + Stam IV)^0.5 * Lvl(CPScalar)^2 / 10
What happens with a higher attack, is that your level cannot get as high to still stay under 1500CP, and that results in a lower total stats. This is also depicted in your example, where a perfect (15/15/15) IV Alolan Raichu only reaches level 22.5, whereas the perfect PvP (1/15/15) IV can go to level 24.5. This results in a Stat Product (that are all stats multiplied with each other) of that is lower for the perfect (15/15/15) IV vs perfect PvP (1/15/15) IV. This Stat Product is a made-up metric, but it shows you the relative potential of a certain species very well.
To demonstrate it really could make a difference, compare these two battles:
Battle Perfect (15/15/15) IV
Battle Perfect PvP (1/15/15) IV
In the first case, you lose against a Magnezone. The second one, you win, with 1HP left. The difference in defense and HP was enough to keep it alive.
Sidenote, it does not always guarantee it's better. Even so, if you simulate the perfect (15/15/15) IV vs perfect PvP (1/15/15), the perfect (15/15/15) IV will win. This is because when two Pokémon use a charge move at the same time, the one with a higher Attack stat uses its charged move earlier, making the latter one faint.
EDIT:
As noted in the comments, the moves have been updated, so I needed to find a different battle. I found one, where a Seadra is battling an Alolan Raichu:
Battle Perfect (15/15/15) IV
Battle Perfect PvP (1/15/15) IV
In short, the Perfect IV looses (Raichu has 6HP left) and the Perfect PvP IV wins (and Seadra has 1HP left).