Gold efficience for Health, Armor, and Magic Resist against %shred
Figured it would be useful to leave this here.
For every point of Armor or Magic Resist, it is an equivalent to 1% extra effective health. As a corollary, every health bought is effectively multiplied by your Armor and Magic Resist.
The basic formulas to determine your most gold efficient survival stats are the following:
**Resistance = ( (Health - 750) / 7.5); only if health >= 750, otherwise build health Health = ( (Resistances * 7.5 ) + 750 ) **
These formulas illustrate why Health is a much stronger purchase early game than amror or magic resist -- Most champions start around the 500 health range, and even at 1000 health, the ideal resistances are 33.3, which the entire cast will have from levels.
A good break point for tanky builds is 3000 health. If you reach 3000 health and have less than 300 resistances, it's more gold efficient to buy 400 gold worth of resistances instead of buying more health.
With the amount of %true damage conversion and armor/magic shred in the game, these formulas alter a bit.
Say you are against an attacker with 25% armor penetration. Effectively, this reduces your 300 armor to 225. It also reduces the effect of armor on health purchases, making it hard on the surface to tell which to buy. (The answer is health, which I'll go into below).
With 3000 health and effectively 225 armor, let's look at what 400 gold of each stat would give.
400 gold of health is 150 Health. Multiplied by are effective armor (1 + 2.25) buying a 
would give us effectively 487.5 extra health.
400 gold of armor is 20. But that gets shredded by 25%, dropping it to 15. Buying 400 gold of armor (say, upgrading from a 
to 
) would thus grant an effective 450 extra health, a little less than just buying health wholesale.
We need to compensate %shred in our formulas, which change them to:
Resistances = ( (Health - (750/R) ) ) / (7.5/R) ) ) Health = ( (Resistances * ( 7.5/R) ) ) + (750/R) )
Where R is the effective resistance multiplier. (For example, 25% armor shred means the effective armor multiplier is .75)
For our 25% shred, that makes fomula for armor
(3000 - 750/0.75 ) / (7.5/0.75) = 200
So if we are against 25% armor shred, and have less than 200 armor, armor should be built. If we already have 300 armor, we should have the following health before building any more against this opponent:
(300 * 7.5/0.75) + (750/0.75) = 4000 health; we need 1000 more health before more armor becomes a worthwhile purchase.
Hope this helps; at the very least I hope the basic formula helps when wondering what to build keeping some major thresholds in mind. The modified formula accounting for shred is mostly just an illustration that health becomes a more important purchase against shredding opponents.
1000 health \ 33 AR/MR 1150 health \ 50 AR/MR 1500 health \ 100 AR/MR 1875 health \ 150 AR/MR 2000 health \ 167 AR/MR 2250 health \ 200 AR/MR 2500 health \ 233 AR/MR 3000 health \ 300 AR/MR 3500 health \ 367 AR/MR 4000 health \ 433 AR/MR