Damage Formulae

Day 2,698, 15:06 • Published in Japan Japan • by Eikyuu

The material of this article is partly outdated and I decided to publish it while it might still be of some use. Sadly, the degradation of the battle-page is in progress, and there is no telling for how long it will be useful. Rest assured, this is not going to be a rant article, just statement of facts, some of which will show you that the disconnect between the support and/or developers and what we encounter on the real battlefield. Make of it what you will.

It seems best to proceed chronologically, showing you what changed and how we are losing information. It might be that the problems will be fixed at some point in the future, and what I present will once again become practical.

Stage 1 – a couple months ago.

The old battle-page was fully functional and it allowed for a very exact analysis. As most of you know, there are two types of damage: one that determines the influence, and the other which is subtracted from your opponent's energy to determine when they are defeated.

The first counts for Battle Hero medals, True Patriot, Epic Battles and so on. It is easy to check its value in both the old and new battle-pages – it is displayed by the button for changing the weapon type. It is modified by the weapon type, damage boosters, Natural Enemy and determination bonuses, which are always shown and can be taken into account easily.

The hidden part is: how to calculate the base damage? Fortunately, we do not have to look far, there is an official article on wiki called Military formulas, and the first formula there shows how the influence is calculated. Let us quote it here

I = 10 × (1 + S/400) × (1 + R/5) × (1 + FP/100),

where S is your strength, R is the military rank expressed as a number according to the table of ranks, and FP is the weapon firepower which is 0 for no weapon, and then 20, 40, 60, 80, 100, 120, 200 for qualities Q1 through Q7.

Pretty straightforward, so you can determine in advance how much more damage you will deal with a better weapon or more strength. The various bonuses are applied multiplicatively, so a damage booster is an additional factor of 1.5 in the above. Note also, that your level has no impact on this quantity and that bazookas have fixed damage of 10000 (before bonuses). I think this part is widely known, and many people, including me, checked that it works.

What about the other type of damage? The formula for hits, given in wiki is wrong. It is neither the number of hits required to defeat an opponent, nor is it the amount of energy taken with one hit. This could have been easily checked as follows: fight with just 10 (or 20) energy of your own, so that you do not kill the enemy immediately, and check how much damage is displayed on their energy bar. Check both strengths and weapons and analyze.

Immediately one runs into inconsistencies here. The damage displayed for a brief moment after each hit was not equal to the difference in energy. E.g. the enemy had 83 energy, your hit showed 21, and checking their energy afterwards shows 61. I suspect it is a simple matter of rounding, just as strength is displayed rounded, so is probably the damage. Fortunately, this error was small anyway, so it did not matter too much.

The next step was to realize that it was the difference between your and the enemy's strength that mattered. You have probably noticed that it is almost never higher nor lower than 200. Similarly for the weapons – when attacking the same opponent with different weapons one notices that each quality "step" changes the damage by 2 per 20 points of firepower.

So we can make a pretty informed guess as to the basic components of the equation, but in the end it has to be confirmed experimentally. The formula for the (energy) damage I found was the following:

D = 30 + (S1 - S2)/20 + (FP1 - FP2)/10,

with the symbols as above and subscript 1 denoting your quantities and 2 your enemy's. As you can see this is considerably different from the formula on wiki. How do I know this is correct? Let us look at the data. The graph below shows reduced damage D as a function of the strength difference 𝛥. By reduced I mean that I added/subtracted the firepower part, knowing both weapons used, here is the result:



Remembering the rounding error (±1) issue mentioned above, there is almost exact agreement between the red data points and the blue line given by D = 30 + 𝛥/20. An interesting finding is that for the defending side, a bazooka counts as a Q5 weapon – if its real damage was used it would take ages to defeat such enemy, while as you probably noticed, it is easier to kill them than one with a Q7 weapon.

Sadly, the usefulness of this result was short lived, so I will spare you a more detailed analysis of goodness of fit etc. If anyone is interested I am open to discussion of course.

Stage 2 – a couple weeks ago.

I think this happened when the Damage Accelerator was introduced. I know several people had similar problems, but I am not sure how exactly it affected everyone – I would definitely like to hear your thoughts on this.

The big change was that ever since, all opponents have been displayed with Q7 weapons. In fact it was impossible to tell whether the opponents were just displayed wrong or whether their damage was also calculated wrong. Since then I have not encountered a single enemy with any other type of weapon.

I thought for some time that it might have something to do with my transition to the second division, but I still use bazookas, or no weapons from time to time. I find it impossible to believe that among thousands of my opponents around the eWorld, not even one used other weapons. I wonder if citizens of other divisions can confirm this – so far I only heard from some D1 people, who share my version.

The second bug that appeared back then was that sometimes fighting with 20 energy made you deal 3 times the damage (and similarly with 30 or 40). The influence and prestige points were higher, but also additional weapons got consumed. It was thus both costly, but at the same time abusable.

I reported both issues, which immediately got dismissed. The support also pointed to the wiki page as a source of information about the calculation of damage. By this time I knew the formula therein was wrong, which shows how well they know the game. They claimed no changes were made, despite the new accelerator having been introduced, which made me realize they do not even bother to test. Eventually I made screenshots of the abusable bug and finally it appears to have been fixed.

At this stage it seemed that even though the weapon was not displayed, the above formula could still be used to some degree. Taking Q7 as the safe guess, or treating it as a random variable for example. However, the mechanism of matching opponents was also broken. Before, defeating an enemy caused a new one to be chosen, and remain the same even after refreshing the page.

Afterwards, each refresh changed the enemy, and only after the first hit were they actually decided (stopped changing with each refresh). The first hit itself seemed to deal a completely random amount of damage, sometimes, this is not a joke, even negative. So you could not make use of any formula at all, unless you had time to fight with 10 or 20 energy every 6 minutes. No one does that ordinarily of course.

My inquires about the refresh and weapon display bug remained without any action, in particular I was told that the old battle-page would be soon removed anyway. I also asked whether its functionalities, like displaying the weapon type, would be coded into the new page, to which the answer was: not in any foreseeable future.

Stage 3 - a few days ago.

The button switching between the old and new battle-pages was removed, as was planned. We are now left with rudimentary information on the battlefield. No exact energy values, no weapon type. Determining the number of hits has become a guessing game. Also the enemy refresh bug is still in place. In theory, one could still estimate the length of the energy bar, assume that most people are using Q7 weapons. I am not sure it is worth it, though, seeing the steady degradation.

Sadly, some citizens to whom I spoke about this did not even consider it worth reporting. I believe that the support and developers are under the impression all is well partly because of lack of feedback. Screenshots work, but how could we take thousands of them to prove the display bug? Additionally, the diffusion of responsibility is not acting in our favour, so I would also like to ask you all to consider the whole matter seriously.

As always, I am counting on you to comment and discussion, especially since this seems to be an ongoing process with fundamental problems in communication. Not to end up on a gloomy note: if the new battle-page ever gets properly upgraded, we will easily recover the correct formulae again.