Pseudo Synergies in Defensive Stats
Suppose you have a shield that grants +10% max health. Many people would incorrectly think that stacking health maximizes the value of this shield.
In fact, what maximizes defense generally also maximizes the value of this shield.
That is, effective health versus physical damage is given by:
EH = HP*(100 + Armor)/100
To maximize effective health with gold G and price of heath PH for bonus health BH and price of armor PA, you maximize the lagrangian
HP*(100+Armor)/100 + lambda(G - PH*Armor - PH*BH) HP = BaseHealth + BonusHealth
If you have a % HP shield, you get the lagrangian
(1+%HPShield)*HP*(100+Armor)/100 + lambda(G - PH*Armor - PH*BH) HP = BaseHealth + BonusHealth
The (1+%HP_Shield) term cancels out when you divide first order conditions, so it does not affect the optimal choice of armor and bonus health. This implies that what maximizes effective health without the shield is also what maximizes effective health with the shield.
Because it looks like stacking health maximizes the value of the shield but this is not true, I call this a pseudo-synergy
Most shields and temporary resistance buffs feature this pseudo synergy scaling.
The same sort of thing happens when a champion gets %bonus armor.
Real shield synergies allow for more strategic builds and more windowed power
RIOT -- it would be more interesting to create true build synergies with sheilds and resistance buffs. Have the size of the shield scale with bonus resists. Or have bonus resists scale with health.
What this would do is allow players to opt into building more windowed power. If your shield scales with resists, then your champion's defense will be much stronger during the shield if you build resists and neglect health (frozen heart, iceborn gauntlet, wits end). But when the shield is on cooldown you will be much weaker because you do not have enough health to benefit from the resists. This would make choice of build more strategic -- do I want to be extremely tanky when my shield is up but squishy when my shield is down? Or do I want to be moderately tanky all the time?
Instead of following through with proposed buffs to nautilus, replace his %bonus health shield with a %bonus armor shield -- every 100 bonus armor and 100 bonus magic resist adds 300 HP to his shield, or something like that.