After I saw the post debating the efficacy of Steraak’s Gage vs. Warmog’s Armor, I remembered there was another new item that has some interesting properties. I’m talking about Heartsteel… I mean Steadfast Heart!
Steadfast Heart has the unique property of % damage reduction. Unlike Bramble Vest, this damage reduction is to ALL damage. As a result, there is a way to mathematically model the % damage reduction effectively as a % max HP bonus. Just like Warmog’s Armor!
Warmog’s Armor has a flat 8% max HP bonus. Steadfast Heart, however has its bonus split. For the first 50% of your HP, you get 15% damage reduction, while for the second 50% of your HP you get 8%.
So how do we model this as HP? Let’s use the first 50% as an example. While you are above 50% HP, any amount of damage becomes 85% of its original value. 100 damage becomes 85. That means that for an amount of damage “x”, we get 0.85x.
Now, to find the effective % max HP bonus, we solve the equation 100 = 0.85x. When we solve for x, we see that x = 117.647. In other words, every 100 HP we have is effectively 117.647 HP, giving us a 17.647% HP bonus.
When we are lower than 50%, our bonus is 8.696%. When we average out the bonus, we get a 13.165% HP bonus from Steadfast Heart. The interesting conclusion to this is that if we disregard the other flat stats we get from the item itself, Steadfast Heart is more effective HP than Warmogs. This conclusion also holds true as we get more health, which means that Steadfast Heart scales better as well.
However, Warmog’s gives us 600 health as well, while Steadfast Heart only gives us 250. This means that we get 350 extra health in exchange for a 5% HP bonus and some Armor and crit. 350 health might not seem like a lot, but 5% HP only outweighs 350 health when you get to 7,000 HP. That’s a lot of HP. For reference, a 3 star 3 cost tank has about 3000 HP. This means that if we are ignoring calculations for armor and magic resistance, and just calculating based on total HP, Warmog’s Armor is usually going to give you more HP. Not from the % bonus, but from the actual 600 health it gives you.
Okay, so that’s just when we are looking at flat HP. TFT is a complicated game, even for tanks. Armor and MR also provide a damage reduction effect, which complicates effective HP calculations. Which comes first? Armor and MR or flat damage reduction? Are they additive or multiplicative? From what I understand, the formula is something like this:
<aside> 🐒 DR = Damage Reduction in decimal form
</aside>
Now, all I care about is the middle part for now. We are going to operate under the assumption that the other values are 1. If I feel like it, I’ll make some pretty graphs to model the whole equation later. I did in fact make some graphs.
In TFT every unit has abilities. Usually, a tank has some kind of ability to heal or shield themselves. Heals effectively increase the amount of HP a tank has to work with. This means they aren’t just limited to their starting health pool when calculating Shields work exactly the same as health does, although they usually have an expiration timer. This means that damage reduction also applies to shields.
As a result, that 7,000 HP number we were talking about before becomes a bit more reachable if we account for effective HP from sources like healing and shielding from other items or units. Still a bit hard though.
All of these calculations are also done assuming that the healing and shielding has the same damage reduction effect on average. The reality of the situation is that a lot of the time, the shield or heal will be in the >50% threshold, making the bonus 17.5% instead of 13%.
Finally, another really unique principle comes from stacking multiple steadfast hearts.