Multiplicative Scaling and Frontline + Backline Balance

Basic Multiplicative Item Scaling

Diversifying your stats is the most efficient way to use your limited resources due to multiplicative scaling. I like to conceptualize this starting with a simple example. If you had 10 swords giving +10% AD each, you would hit twice as hard, dealing double your total damage. If you had 10 bows giving +10% AS each, you would attack twice as fast, also dealing 100% more damage. However, if you had 5 swords and 5 bows, you would deal 1.5x1.5-1 = 125% more total damage using the same number of components.

Applying Scaling Principles

Of course in TFT we aren't hand picking our items, but we can play around what we hit. If you are offered a lot of items that give hit points (in Magic N' Mayhem, this could be something like Warmog's Armor, Anima Visage, and Moonstone Renewer), you may want to prioritize playing a frontliner that naturally gains resistances rather than shields.

Frontliners can mix durability, armor+magic resist, and hit points (can come in the form of heals or shields). Physical champions may want a mixture of attack damage, attack speed, damage amp, critical strike chance+crit damage, and armor penetration. Magic casters often want a mixture of items that increase their cast frequency, and items that increase the output of the cast. Historically, a common synergistic best in slot item combination for mages is a mana item, attack speed item, and damage item such as Spear of Shojin + Nashor's Tooth + Jeweled Gauntlet which is much stronger than 3 repeated copies of any one of those items.

Frontline and Backline Balance

This is the part that I most frequently see players make mistakes on. Balancing your frontline and backline scales multiplicatively, just like unit stats. Let's start with a simple example. You are level 4 and can add backline units that deal 100 dps, or frontline units that give your team 10 seconds survivability. If you split 1 carry and 3 tanks, your team will deal a total of 100 dps x 30 seconds = 3000 damage. If you split evenly with 2 carries and 2 tanks, it will deal 200 dps x 20 seconds = 4000 damage.

TFT is more complex where frontliners deal some damage, backliners can tank, etc., but the general idea is that you want to invest your limited resources so that you aren't neglecting either your frontline or backline. Most strong meta comps are designed to do this naturally when given an even mix of item components.

Bonus: Melee Compositions

Melee comps prefer not to expend resources on tanks since there is no effective way to ensure that your tanks are targeted before your carries; instead, they want to take advantage of multiplicative scaling with omnivamp. If you have invested most of your resources into a melee unit that deals 15,000 damage per fight, adding 20% omnivamp with only 1 item on that unit is an extremely efficient way to gain 3000 HP, as much as 3 Warmog’s Armors.

While it can’t hurt, it is not necessary to know the exact details of the math behind various combinations as long as you understand the fundamentals of multiplicative scaling. If you have any questions, let me know in the Discord and I will answer as many as I can!