Welcome to the second part in this Battle Mechanics article series. In Part I, we constructed the basic battle formula, showing the relation between attack and life, and buffs and debuffs. Although we could go from there into other territory, I feel this second part is needed to avoid any confusion afterwards. In this part we will look at the different types of buffs and how they (possibly) interact.
- Other parts in this series:
- 1. Recap
- 2. The different Buffs
- 3. Difference between additive and multiplicative
- 4. What matters in the end
Let’s start with the formula we ended up with in Part I. I’ll be taking the colored version as it is easier to understand:
If we look at a case in which we are the attacking force, we need to fill in the orange factors in this formula. For the “Life debuff” part this is straightforward, as the only source of debuff is Gems*. For the “Attack buff” part, things are a little bit more complicated, as many more buffs are involved, which interact together in some way. In Part I, I took a shortcut and presented this simply as the (1+attack buff) factor, but behind this simple statement is some more complex math. For now, as we did in Part I, let’s focus on the Attack factor alone to avoid doing double work. Also, because Attack debuff belongs to the enemy, we will also not take this into account (we don’t have to). So the formula we will work with in this article will be formula (eq. 2):
(* new Hero skills also work with debuffs, but for the sake of clarity I will leave these out at the moment, but a similar article to this could be written, and might in fact be written once the Skills are better understood)
2. The different buffs
Focusing on attack, we have quite some buffs we need to take into account. The list is as follows:
- Hero level
- Perm buffs
- Gear and Gems
- City Guardian
But how do these interact? Do they simply stack, or do they multiply each other? Basically, what we need to solve is the following riddle:
3. Difference between multiplicative and additive
Before figuring this out, first a little mathematical background. In many games and of course in mathematics in general, formulas can have many different terms in them. In this case, every single attack buff type is called a term by the way. Now all these terms as stated in above can be implemented in two basic forms: multiplicative and additive. Using an example with just a few example buffs, additive looks like this:
While multiplicative looks like this:
In most cases, additive is used when a buff adds directly to a certain number. For example, in the Diablo games, you can find weapons that have a +3 damage bonus. This +3 is a hard constant, so if your base attack was 2, now it will be 5. If it was 20, now it is 23. In short, additive tends to be unrelated to the base value of whatever is being increased (or decreased).
In contrast, multiplicative bonuses usually come in the form of percentages, such as we see in KoM. In fact, I have no knowledge of any constant, absolute, additive bonuses in this game. Different percentages lead to different multiplication factors. A 100% attack buff leads to a “2” multiplication factor.
Besides the mathematical difference, the outcome of the effects of buffs also changes with what type of math is used. Let’s say we have 3 buffs of 100% each, and fill them in in (eq. 12) and (eq. 13). In the strictly additive formula, we end up with (assuming 1 base attack) 4 attack. In the multiplicative formula, we end up with 8 attack.
In general, multiplicative is better and increases faster, but of course, this is just some theoretical math background and this still tells us nothing about the real situation in KoM, so let’s get back into the actual game.
4. Possible scenario’s
So, with this many buffs, there are many possible scenario’s. Just working with two attack buffs from gear and perm buffs, we can piece together some combinations:
Assuming that the base attack value is a number and the buffs percentages/100, formula (C) corresponds to a strict additive form s given in (eq. 12), while (E) corresponds to multiplicative as in (eq. 13).
Formulas (A), (B) and (D) only work if the base Attack value is expressed as a percentage, and thus will give a percentage increase. To give an actual number for attack, we need to multiply the base attack value with the combination of buffs, be they either additive or multiplicative. So what is the real situation?
While it is completely possible to figure this out yourself, we need to know only the position and type of one buff, namely the gear buff. Now from all information from other sources and testing done by myself, it is almost certain that KoM uses a mix of additive and multiplicative, such as shown here in (eq. 14):
Now we need to figure out how many factors the real equation has and which buffs belong to each other. As it turns out, the most important one, the gear buffs, form a separate factor in this equation (A factor is one of the ‘parts’ in a multiplication, like the (eq. 14) has three: The base attack factor and two buff factors). All other buffs either reside in one large additive factor, such as:
or form multiple multiplicative factors themselves or in small groups:
5. What matters in the end
So what does this lead us all to? Well, as I have stated, this article series focuses on Battle Mechanics, but it specifically focuses on gear and gear choices. Why? Because that is basically all we as players have in terms of trying out different combinations. Only in gear(+Gems) can we shift some in the percentages buff versus debuff. ALL other buffs, such as Guardian/runes/Hero lvl are static and cannot be changed (for the better at least). You try to get these as high as possible and that’s it.
Secondly, I have also stated that the goal will not be to construct a complete and working battle simulator predicting exact outcomes, as this is impossible for PvP and we are also not looking too much into Campaign simulating. Nonetheless this could serve as a starting point for that.
So if we focus on gear in (eq. 15), and we do not care about the exact outcome of battle, but rather the relative impact of gear and Gem choices, it no longer matters what all the other buffs are, and it doesn’t matter how they factor into equation 15. Why? Well fairly simply stated: Whatever the exact form of (eq. 15) is regarding each buff type, we know two things:
- The “Gear attack” buff will be a separate factor in the formula
- The entire formula will be formed by a number of factors, all multiplicative
This means that the relative effectiveness of your gear buffs is not affected by your other buffs. What this means is basically that a 100% attack buff will always double your TK’s. Always? ALWAYS! Try it for yourself: Put either (eq. 15.1) or (eq. 15.2) into Excel. Fill in a range of different combinations of values for the other buffs. Now test the outcomes between having a 0 for the “Attack gear” value against a 1 (for 100%). Every single time you will see the TK doubling when inputting 1.
Now, if we replace the factors with some constants, we see that X = A*B*C*D is equal to X=(A*B*C)*D, and if we define E=A*B*C, this becomes X=E*D. Doing the same for (eq. 15.1) we get:
is equal to:
And redefining the left factor above into:
We substitute that into (eq. 16) again and we get:
Which is identical to the formula (eq. 2) with which we started! What I have explained here in even more detail basically is how we are not going to go for a full-on combat simulator, but only look at the relative impact of gear buffs/debuffs, why we therefor can discard the other buffs, and why this makes working out gear performances much easier. Equation 11 from Part I becomes slightly more specific:
I agree it is a step which does nothing to the formula as we already constructed in Part I, but I know for a fact that if I do not treat this subject now, people are bound to come asking for how Guardian buffs and Hero level factor in, as these will not be mentioned anymore beyond this point. I hope that you nonetheless found this interesting and don’t see this as a waste of time…I simply do not want to skip over things that will create problems later on.
So in this part we separated the buffs and saw why the other buffs from your city and Hero do not matter to your gear choices. But we still have to deal with an enemy army that also has buffs and debuffs that influence you and your gear choices…or do they? Stay tuned for an answer to this and why in Part III !