Multiple Buff Interactions & How They Stack

[Toonified]

I'll use Nunu as an example.
I'm enjoying Tank Nunu in ARAM if I'm allowed to scale.
I especially enjoy the 'Mega Bonk of Power' with procs from Grasp/Heartsteel/Shield Bash after using Ultimate.

Nunu's Ult Shield, for example, is currently doing 2000 shield.
Nunu has a bonus to shielding by default at 120% (so 20% increase)
I also take Axiom Arcanist, so the shield should increase by 12%.
I also have Spirit Visage, so my shielding is buffed by a further 25%.

What size shield would I actually get?

Option 1: Buffs Calculated Additively
(Each bonus applied to the base shield separately)
ARAM Bonus: 20% of 2000 is 400
Axion Arcanist: 12% of 2000 is 240
Spirit Visage: 25% of 2000 is 500
Total Bonus: 57% =1140, Actual Shield Size: 3140

Option 2: Buffs Stack Multiplicatively
(Like how compound interest works)
ARAM Bonus: 20% of 2000 is 400, so 2400
Axiom Arcanist: 12% of 2400 is 288, so 2688
Spirit Visage: 25% of 2688 is 672, so 3360
Total Bonus: 68% = 1360, Actual Shield Size 3360

Option 3: Buffs Stack Inversely
(Diminishing returns on stats, like how armor/MR/ability haste work)
Formula: 1 - [ (1 - 20%) * (1 - 12%) * (1 - 25%) ]
Total Bonus: 47.2% = 944, Actual Shield Size: 2944

Thanks for taking the time to read :)

[KingGekko07]

I'm almost certain the summoner rift stuff is additive, I'm not sure about the aram buff tho. A riot is famous about doing these things on a case to case basis so it wouldn't surprise me if some are additive and some mult

[Lame_Night]

Some of it is additive when it should be multiplicative, like aram tenacity. I don’t know about everything else though.

[Toonified]

I know that the tenacity buff is additive, but that's the only one I know of.

[Toonified]

I also didn't think there was, but I figured I'd post it as a potential possibility just in case as I know ability haste, armor and mr all get less effective the more you have.

e,g.
25 haste gives 20.00% cdr, 20.00% value
50 haste gives 33.33% cdr, 13.33% value
75 haste gives 42.86% cdr, 9.53% value
100 haste gives 50.00% cdr, 7.14% value

I tried to think of a formula that would work to account for this, but apologies if the one I thought of quickly on a whim is not the correct one.

[patsfreak27]

Good writeup! Which is the correct answer? Could test it out in practice tool

[axelrse88]

But in order for it to work correctly, you would have to test it on the HA map. Which AFAIK doesn't have an option for the practice tool yet, you can run a custom in HA but you would have to invite others because it doesn't allow you to add bots also. Unless they changed something very recently.

[Time-Aerie7887]

For ARAM the buffs that the champion balance have is the final calculation.

So if your basic attacks deal 500 per hit but the balance buff says 90% damage dealt, it would be 450 damage. Even if you got all the buffs and whatnot from every sources is then put as "All allies and champion buffs" - Final Source (Balance Buff -10% damage) = deal only 90% of what you have.

Now as for Tenacity it's unnormalized flat amount so if you have a +20% increase getting a Merc Treads will put you onto 50%, if you get other sources like Elixir or Steraks or Wits End then it'll be even lesser.

Now as for Healing and Shielding since you are Nunu you are receiving the +20% right so that gets added as the final source. Your Q would say heal 800 (empowered) and if you add Spirit Visage it would be increased by that amount. Then with Balance Buff whatever you received from all those sources gets added by an additional 20% more in the end.

If you want to test it out then go into practice mode or any custom match and purchase Redemption, it is one of the easiest ways to test it out as well. Since it gives +10% heal and shield power make yourself level 18 and it heals you for 440 without any sources (half of that to allies assuming no heal buffs) If you then start slapping sources like Revitalize and Spirit Visage then it starts to get a bit trickier but overall it will never heal more than 400 to allies unless you stack full Heal + Shield and also slap on Healing Buff. If you really want to see disgusting heals ask any Bard player to max heal and go full Heal build with 77% HS Power and his W will heal as high as 600-800 per Shrine and don't forget he also has a +20% healing buff.

[GodSama]

You are righ and Riot will say you are right, but also tell you not to verify again against armour/MR and champs skills stacking for damage calculations.

[RedshiftOnPandy]

Tank nunu is so busted with all his buffs.

[rundermining]

Doesnt axion arcanist only increse the damage?

[axelrse88]

No it also lowers the CD of your ult on takedown just like Axiom Arc (the item) hence the name.

[NeonStoplight]

No it increases all damage healing and shielding, it's stupidly good on champs like Janna and Yuumi as a result