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Orb of the Magi or Berith’s Agony? Crimson Banner or The Aegis? In a game of Arena of Valor, you’ll constantly come across the decision to purchase either HP or armor (or magic defense). If we simply compare the gold value of each stat (based on tier 1 items), 1 armor is equivalent to 2.4 HP. However, comparing them this way ignores the fact that armor and magic defense rise in value the more HP you have – after all, if armor makes 100 hit points difficult to get through, then it will make 1000 hit points that much harder to penetrate.
To illustrate this fact more clearly, let’s take a look at Effective HP. We first utilized Effective HP when comparing Arcana, borrowing the concept from a Reddit post from February 2018. Effective HP describes how much damage it actually takes to bring a hero down, taking armor into account. For example, if Arthur has 100 HP remaining, but has 600 armor (or 50% – armor calculation formula here), then it will take 200 physical damage to take him out.
In order to easily determine Effective HP for less round numbers, let’s take a look at the standard armor formula:
x * (1 – y / (y+600)) = z
where x is the incoming damage, y is the raw armor amount and z is the actual damage dealt after accounting for armor. Another way to look at this equation is to treat the actual damage dealt (z) as the HP amount of the receiving hero, which means that the incoming damage (x) – the amount of damage our hero can withstand when accounting for armor – is the Effective HP. Solving for x gives us:
x = z / (1 – y / (y+600))
Following our first example, Arthur with 600 armor would have 600/(600 + 600) = 50% physical damage resistance. Then, setting Arthur’s HP (z) to 100 and solving for x (Effective HP) gives us 200. Hurray!
Diminishing Returns Debunked
The more armor you have, the less armor percentage you gain with each armor addition:
Therefore, armor suffers from diminishing returns, right? Well, no. Effective HP does a good job of debunking this myth. Let’s take a look at the same armor amounts, for a hero with 1000 HP:
|Armor||Armor Percentage||HP||Effective HP|
With each addition of 300 armor, our hero’s Effective HP rose by the same 500, even though the armor percentage gains decreased every time.
Another way to look at the above table is to consider Hero B with 100 AD attacking our Hero A with 1000 HP and varying armor amounts. With 0 armor, it takes 10 attacks (assuming no HP regeneration) to kill hero A. At 600 armor, Hero B’s attacks now effectively deal 50 damage, meaning it would take 20 attacks to take down Hero A. At 1200 armor, Hero A’s attacks deal 33 damage – only a 17 damage drop, rather than 50 the first time – but it takes 30 attacks to defeat Hero A, the same 10-attack difference from 0 armor to 600 armor.
Side note, for the super nerdy: if, for example, the armor formula made it so that 1200 armor gave 75% damage resistance (and 1800 armor 87.5%, and so on), the Effective HP of Hero A would go up exponentially (1000 → 2000 → 4000 → 8000), which is obviously not a desired outcome.
Armor More Effective the More HP You Have (and vice versa)
No matter how much armor you have, if you’re multiplying by a small HP amount, your Effective HP won’t climb very high. Using the example from above, if going from 0 to 600 armor doubled the number of required attacks, then requiring more attacks in the first place is a surefire way to increase Effective HP.
Given the way armor percentage is calculated, it turns out that every 100 armor increases your Effective HP by one-sixth of your current HP. In the table below, the armor goes up 300 at a time, which increases the Effective HP by one-half the original HP. To make the table symmetric, I’ve set the HP to increase by intervals of one-half the original HP number of 4000:
|Effective HP Given HP (Left) and Armor (Top)|
As you can see, the higher the HP, the more our hero gains from purchasing armor, and vice versa. Thus, it’s always better to have a good balance of HP and armor, rather than simply stacking one or the other. In the same way that 5 * 5 > 4 * 6, having 8000 HP and 600 armor will give you more Effective HP than 6000 HP and 900 armor, or 10000 HP and 300 armor.
Should I Buy HP or Armor?
Determining whether armor or HP will be more beneficial (assuming the opponent has only physical damage) is dependent on the amount of HP you currently possess. Specifically, the value of armor in terms of Effective HP is:
1 armor = (Current HP) / 600
Therefore, if you currently have 6000 HP, then 1 armor is worth 6000 / 600 = 10 Effective HP. And if you’re considering buying an item that grants 100 armor, then the item will be worth 6000 * 100 / 600 = 1000 HP to you.
Going back to the example from the first sentence of this article, comparing the 270 armor of Berith’s Agony to the 1100 maximum health gained from Orb of the Magi, we have
(270 / 600) * (Current HP) = 1100
A bit of math then tells us that our current HP would only need to be 2444 in order for Berith’s Agony to start providing us with more Effective HP (again, given only physical damage on the opposing team), which is less than all heroes’ starting HP.
The Aegis versus Crimson Banner is a bit trickier math-wise, as there are two separate starting points for the “current HP”:
(360 / 600) * (Current HP) = (200 / 600) * (HP after adding 1500 from Crimson Banner) + 1500
In the end, the HP at which The Aegis begins to outdo Crimson Banner in terms of Effective HP is 7500.
What About Asterion’s Buckler?
Asterion’s Buckler, as well as some heroes’ abilities, applies a flat damage reduction rather than listing armor or magic defense. But don’t worry, we can calculate the equivalent armor and magic defense you get with 10% damage reduction with – you guessed it – Effective HP. Using the equation at the top of the page (the one with x’s, y’s, and z’s), and using z = .9 * x for Asterion’s Buckler, then solving for y (the armor or magic defense amount), we get:
y = 66.7 armor and/or magic defense
So Asterion’s Buckler will give you (and allies within 200 units around you for 2-3 seconds) around 67 armor and magic defense (and true damage defense) on top of its other benefits.
Applying the same calculation to other heroes’ abilities, we get the equivalent of roughly 106 physical/magic/true defense for Max‘s Smooth Moves and Wonder Woman‘s Sword and Shield, 150 physical/magic/true defense for the ultimates of Max, Lu Bu, and Zanis, between 600 and 1400 defense (depending on level) for Omen‘s Untouchable, and a whopping 2400 defense when Wonder Woman charges Bracelets of Submission.
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