I've talked before about how TDO is kind of a fake metric in #PokemonGo However, for PvP, stat product is a real metric.

If you KO an opponent, obviously you're better off the more HP you have left afterwards.

You start with STamina HP.
/1

Each attack you do takes off proportional to ATTack damage to your opponent.

On the same move, your opponent takes off damage inversely proportional to your DEFense.
So, after one round, your opponent is at
OPP-a ATT
hitpoints, and you are at
ST - b / DEF
hitpoints
/2

Your opponent faints after n = OPP/(a ATT) rounds, at which point you have
ST - n b / DEF
or
ST - k / (ATT DEF)
hit points left.
k = b OPP / a, but a, b, and OPP are just constants that defend on your opponent, your own move set, etc. So k itself is just a constant...

Actually, I didn't do this math before starting this thread, and this reasoning is wrong (or at least doesn't lead to the stat product metric).

Instead of trying to maximize your own hit points when your opponent faints, try to minimize your opponents hit points when you faint.

So, after 1 round, your opponent is down to
OPP - a ATT
and you're down
ST - b / DEF.
After n rounds, your opponent is down
OPP - n a ATT
and you're down
ST - n b / DEF.
You faint after
ST - n b / DEF = 0 implies
n = ST DEF / b
rounds.

At this point, your opponent is down
OPP - (a/b) ATT DEF ST
hit points, which is obviously lower if the stat product
ATT DEF ST
is higher.
QED.

Now, why you might want low attack IVs for PVP.