### Overview

This tutorial is going to be mostly for advanced players, although even new player should find it helpful and amusing. We will discuss how effective hitpoints are calculated and walk through some examples.

If you have ever wondered if an armour upgrade is more effective than an HP upgrade or vice-versa, this is for you!

### What is Effective Hit Point (EHP)?

EHP is an amount of physical damage a unit can take before dying. The calculation includes the basic HP of a unit, its armour and evasion rate.

Basically it shows the tankiness of a unit excluding its HP regeneration, spell damage and damage modifiers (heavy vs magic, pierce vs light etc).

### EHP Calculation

The formula for EHP is:

$$E_{HP} = B_{HP} \cdot \frac{100}{ 100 – \epsilon} \cdot (1 + \frac{6A}{100} )$$

where $E_{HP}$ is effective hit points, $B_{HP}$ is basic hit points (normal HP), $\epsilon$ is the percent evasion and $A$ is the amount of armour.

### Example EHP Calculation

Let’s calculate the EHP of Ogremount’s *Ogre Lord*.

$$B_{HP} = 950$$

$$\epsilon = 10$$

$$A = 3$$

Thus,

$$E_{HP} = 950 \cdot \frac{100}{100 – 10} \cdot (1 + \frac{6 \cdot 3}{100})$$

$$E_{HP}= 1245.\overline{5} \approx 1245$$

For the sake of comparison, Labilia’s *Champion of Labilia* has an EHP of 1239. This means that compared to the *Ogre Lord* with an EHP of 1245, the *Champion of Labilia* is *almost* as “tanky” as an *Ogre Lord*. Tog Lagog’s *Chaos Assassin* has an EHP of 1232 so it can take almost as much physical damage as an Ogre Lord but of course it is weaker vs. spells. Dark Spire’s *Vampire Lord* at night time has 1516 EHP. Range units don’t have damage resistance and their armour is usually low so their EHP isn’t really impressive and at zero upgrades, their EHP is not far from their BHP. These are just a few examples. If you would like to see more EHP calculations, feel free to play with the form below.

### Armour upgrades vs HP upgrades

I have always criticised how players prefer to get HP upgrades first on high HP units or capture loads of bases with units like demon lords. But let us look at the numbers to see how effective it actually is.

First, we shall see how effective an HP upgrade is in terms of EHP. Dark Spire’s 75 HP book actually gives *Vampire Lords* (day time – 850 HP) 109 HP vs. physical damage if we multiply it by their armour and evasion. That is pretty impressive, but how much does a 100 gold armour upgrade give them? 114 EHP!

A 100 gold armour upgrade gives them 5 more EHP. Now you might be thinking: “meh, you do not need a blacksmith for a base upgrade and it also works on range and against spells”. First of all, almost nobody has good nukes early on, especially vs. high HP melee. Heroes are still low level. Firebolt hasn’t been upgraded etc. Secondly, *Vampire Lords* have only 850 HP during the day and they are not the perfect unit to take into consideration because as we know, the more HP a unit has, the more effective an armour upgrade is on him (by virtue of the EHP calculation). So let us consider this: at night time, *Vampire Lords* have 1050 HP so the book will give them 109 EHP, but an armour upgrade will instead give them a whopping 140 EHP! This is obviously way better than the best HP upgrade in the game in terms of tankiness for their melee.

### Another Example

Let’s take some other unit, Mount Hyak’s *Ursa Warrior*. This unit has 1000 HP and 3 armour. A research centre HP upgrade will give it 66 EHP and 1 armour upgrade will give it 133 EHR. Yes, that is how much more effective an armour upgrade is on high HP units and that is not even the highest HP unit in the game. The 10th armour upgrade on the *Ursa Warrior* is still more effective than 50 HP upgrade which results in 9 EHP (Yes, it is more expensive, we are just talking theory).

Ok now let us take some ranged unit, Mel Forth’s *Scout of Mel Forth* – 400 HP and 1 armour. 1 Armour upgrade will give this unit 48 EHP and an HP upgrade will give them 53 EHP. So in this case, an HP upgrade is more effective than an armour upgrade which is even more important because such units can be kill by low level nukes. For *Scouts of Mel Forth*, every continuous HP upgrade becomes less effective than an armour upgrade, so in-between HP upgrades, you should add some armour upgrades. For example, the 2nd HP upgrade with level 0 armour is 1 EHP less effective than the first armour upgrade. But since armour is an HP multiplier, you can work for your late game and get HP upgrades first if you know that you will not be able to research them later on. With Mel Forth’s *Huntress* whom has 700 HP and 3 armour, an HP upgrade will give 59 EHP and an armour upgrade will give 84 EHP. So even on 700 HP, an armour upgrade is more effective.

So, starting from a 450 HP unit with 1 armour and no evasion benefits more from an armour upgrade (just by a difference of 1 EHP) than from an HP upgrade. If a unit only has 450 HP, HP upgrades are probably still more important than spells but after 500-500 HP, an armour upgrade becomes increasingly effective.

That all said, most of the melee units will benefit more from armour upgrades than HP upgrades in the early game. Nukes are not a good enough reason to justify the cost of HP books. Hence, even the *Champion of Labilia’s* 6 armour still gets 34 EHP more from an armour upgrade than from a research centre upgrade (Whilstthe +75 HP base upgrade is 4 EHP better than the 1st blacksmith upgrade, the book is still not brilliant if you consider the prices). So, my recommendation would be to stop spamming HP books in the early game unless you are way ahead and will survive to the late game.

### Conclusion

I hope this small tutorial gave you some idea how tanky certain units are and how to actually calculate that. Also it should give you a general feeling when to add HP upgrades or armour upgrades. Below is a form which can help you calculate EHP for a particular unit.