Join the new world

Hey everyone,

Note: To be able to fully comprehend this article, you have to be familiar with this update.

So… How are you all doing? I’m actually doing fine, not that bad… I’ve recently decided to write an article that should explain all the details about how the total damage per hit is calculated. The reason why I’m writing this article is because I believe that the Administrators haven’t explained enough about this and because I don’t feel like their sense of mathematics is that good. Look at this pic:



Notice anything wrong?



What about now? Here it is clearly stated that there is a 5% increase to your hit once you obtain a new rank. This is not true or even close to being accurate. There is a formula that determines your damage per hit, and when you earn a new rank, your new damage is recalculated using that formula, so the increase in damage has nothing to do with 5%. Naturally when I saw that this wasn’t true (and I noticed this more than two years ago, but didn’t bother to do anything about it), I asked myself if anything else they said about the damage increase was true. What if the 10% bonus you get isn’t really a 10% bonus, but something like a “double rank increase” (two times 5😵? Or maybe it really is a 10% increase? This was my main incentive in doing a short analysis to determine the real damage per hit formula. And of course, this article will show the results that I got through trial and error.

Before we start, I’d like to clarify that I’m not insulting the Administrators in any way, I’m merely trying to elaborate on what they said in a mathematically clear way, because I consider their explanation confusing. So I’m actually helping both them and the players. I’m not against anyone.

So, now I’ll publish my analysis results. The damage formula is based on 7 coefficients. It’s pretty much based on these coefficients being multiplied together, and all of that multiplied by 10. Mathematically speaking, this is our formula:



S, R, W, B, E, L and NE represent 7 coefficients that are mostly independent with one another. Now I’ll show you how all of them are defined/calculated. Firstly, the S coefficient:



Strength represents the amount of strength points you have. You can view that on your profile. For example, at this very moment I have 100842.76 strength points, so my S coefficient can be calculated like this:



Now, the R coefficient:



You can’t find the “Rank” value on your profile, but you can find it here. The Rank values for the Legends of the New World go on forever. For example, for Legend I, the Rank value is equal to 70, for Legend II it’s 71, then for Legend III it’s 72, etc. Every time a citizen ranks up, his Rank Value grows exactly by 1. Now we’ll calculate my R coefficient by replacing the “Rank” from the formula with 68 (because I’m a Titan*😉:



And when I rank up and become a Titan***, my new R coefficient will be:



We see that when that happens, my damage per hit will become 14.8 / 14.6 = 1.01369863 times bigger, so it will actually grow by 1.369863%, not 5%... These two coefficients (S and R) are actually the most important ones. All the others are pretty “fixed”.



The W coefficient depends on the quality of the weapon that you use. If you use a Q7 tank, its value is 3, so unless you switch between different weapon types, the W coefficient is fixed. Here you can see how big the W coefficient is for all the tanks:



The B coefficient is modified by using different damage boosters. Its initial value is 1. When you activate a 50% damage booster, B becomes 1.5, and when you activate a 100% damage booster, its value becomes 2. Its value gets back to 1 once the booster expires. However, it is possible that the Admins temporarily change the initial value from 1 to something else where there is a special eRepublik event, like the 7th Anniversary, when the Admins added a special +70% damage bonus. During that event, the initial B coefficient value was 1.7, but when you used a 50% damage booster, B was equal to 2.2 (obviously, when you used a 100% damage booster, it was equal to 2.7). If we don’t take into consideration special promotions like this, then we have:



The E coefficient depends on whether the player in question is an Elite Citizen or not. If he isn’t, then E equals 1, and if he is, then E is 1.1 (10% bigger, which also makes the damage itself 10% bigger).



The L coefficient is the most complicated one, both for explaining and understanding how it functions. Basically, it depends on the country, i.e. the number of “times” the player in question has ranked up to get a Legendary rank in that country.



If someone is a Legend IV, that doesn’t necessarily mean that T equals 4 when he fights for his citizenship country. There is a different T value for each country and they are all equal to 0 before the fighter reaches the Legend I rank. When somebody ranks up to get a new Legend rank (Legend I, Legend II, Legend III, etc.), the T value for his citizenship country (at that time) grows by 1.

For example, if player X gets his Legend I rank in country A, then his Legend II rank in country B, then the Legend III rank in country A again, then changes his citizenship to country C, his T value for country A will be 2, while for country B it will be 1. Note that his T value for country C will still be 0, even though that’s his citizenship country, because he never got any Legendary rank while having that citizenship. It only counts if you rank up while having the citizenship. His T value for all the other countries will still be 0, of course. We get that his L coefficient will be 1.2 for country A, 1.1 for country B, and 1 for all the other countries. Note that if player X subsequently gets the Legend IV rank while still having country C’s citizenship, his L coefficient will become 1.1 for country C.

The final coefficient present in the damage per hit formula is NE, which is affected by the Natural Enemy bonus. This coefficient is equal to 1.1 when the player in question fights for his citizenship country against his country’s Natural Enemy, in a direct battle (not a Resistance War), and 1 otherwise.



We see that 3 conditions have to be satisfied so that a fighter can obtain the Natural Enemy bonus (get a 1.1 NE coefficient): (1) he has to fight for his citizenship country, (2) against his country’s Natural Enemy (if he fights for his country against some other country that’s not his Natural Enemy, the NE coefficient will still be 1), and (3) he must fight in a direct battle (a battle which is not a Resistance War).

So this is how the damage formula functions. It all sounds pretty complex, while in reality it’s pretty simple, because a lot of these coefficients are mostly fixed, like W, if we always use Q7 tanks. Before we go on, I’ll only write down the formula that calculates how many Rank Points we gain per hit.



The formula is pretty similar to the damage per hit formula, the only difference being that the NE coefficient is replaced with the new WS coefficient and all the coefficients are not multiplied by 10. We can even write it like this:



The WS coefficient is influenced by the special War Stash Rank Points bonus. It’s equal to 1 when the fighter doesn’t have an activated War Stash bonus, and if he has, then it’s 1.1 (remember that the War Stash gives us 10% more rank points while it’s activated).



Note: This only applies to the War Stash, not the Combat Stash (the War Stash is the only stash that gives you a Rank Points bonus).

If you happen to be using bazookas while fighting, and not normal weapons (tanks), then the damage and Rank Points formulas function a bit differently:



The S, R and W coefficients get replaced with a single base value that’s always equal to 1000, unless you use Bazooka Boosters, in which case its value depends on the Division you’re in (it’s equal to 2000 if you’re Division 1, 3000 if you’re Division 2, 4000 if you’re Division 3, and 5000 if you’re Division 4).



And last, but not least, if you don’t use tanks or bazookas, but fight using bombs or rockets, the damage you make is usually displayed when you use your mouse to hover over the bombs or rockets on the Storage page. You can also go here to see how much damage each bomb/rocket makes.



So now you know how to calculate the amount of damage you make no matter which weapon you use. That’s why I believe it’s time for me to show you this interesting graph:



You might ask yourself what exactly this is? This is a graph which I made on my own and it shows how much damage you make with respect to your Rank. There are 5 different functions, and they represent how much damage you make when you have a certain amount of Strength. The graph takes into consideration only the values for the S, R and L coefficients, while the other coefficients are fixed, so I picked these values for them (by default):

W = 3 (the citizen is using a Q7 tank)
B = 1 (the citizen isn’t using any damage booster)
E = 1.1 (the citizen is an Elite citizen)
NE = 1 (there is no Natural Enemy bonus)

It’s obvious that if you use a 50% damage booster, you will make 50% more damage, and the graph will still look pretty much the same… The only thing that will change are the numbers, but their ratio will be the same, and that’s all that matters.

As you can clearly see, the graph looks pretty normal until the Rank value becomes 70. It’s linear. But it’s quite obvious that it doesn’t stay linear after the Rank has surpassed the value of 70. Keep in mind that the 70th Rank is actually Legend I. So, what’s up with that? And what do those dotted lines represent? The dotted lines represent the potential damage a fighter can have, provided he gets all of his Legendary ranks in one country and he fights for that country. For example:

When Rank = 70 (which is Legend I), we have L = 1.1;
when Rank = 71 (which is Legend II), we have L = 1.2;
when Rank = 72 (which is Legend III), we have L = 1.3;
when Rank = 73 (which is Legend IV), we have L = 1.4;
etc.

Of course, if someone gets two Legendary ranks in two different countries, then he will not be able to reach his potential damage, but we will assume that the citizen in question always ranks up in one country on purpose, in order to maximize his top hit.

So, from this graph we can clearly see that when someone has a Legendary rank and fights for a country where he has never ranked up to get a Legendary rank, his hit stays pretty normal. But, when he does fight for “his” country, his hit is insane… And the more he ranks up, the crazier his hit gets. It’s also possible that his hit becomes better than many other players’, even if they might have a lot more Strength. Remember that those other players might not be from the same country, so they probably won’t have a hit bonus like the player in question.

I don’t believe that most players are well aware of how big of an impact these Ranks will actually make. That is why I would like to make a small analysis via this article and talk about it, tell everyone about my personal opinion, make some predictions, etc. I’ll start off with the obvious thing: the effect that these Ranks have in the present. At the moment, there aren’t many players with a Legendary rank. Maybe 15 or so. And there are even less countries that actually have someone with a Legendary rank (less than 10). Most of these players who are Legends also have a good Strength, so we have two direct consequences:

1) Players who “tank” (inflict a lot of damage regularly) are now able to tank even more.

In my educated opinion this is exactly what the Administrators want. The players with the Top Ranks can now have extra fun by competing with each other to see who gets the next rank first, because the first person to do that in each country gets the rank named after him. Their hit is also a lot bigger, so they can gain rank points faster than before. Basically, if you have a lot of rank points, it’s easier for you to get even more rank points, and if you don’t, well… Too bad.

2) The players who are Legends at the moment totally dominate the battlefield when they fight for their country.

Especially the Legend II dudes. For example, look at this:



This pic explains everything: it’s pretty clear that when you have a Legendary Rank (and a decent Strength) that you have a huge advantage when fighting for your country. The only other players who could have the same advantage are your country’s other Legends. Imagine going for a Battle Hero medal against a Legend while fighting for his country? It’s almost a guaranteed loss.

But the questions is, will these new ranks bring us something new in the future? I think that this is possible but we shall see. My predictions are that gaining rank points will become a lot more important than ever before, because there is no final rank anymore. After each rank there comes a stronger one, and the sooner you get it, the better. This also makes it possible to “make up” for not having enough strength by having an insane amount of rank points, which now have the potential to give you a lot more damage per hit.

This might not be obvious, but if you get all your Legendary ranks in one country, then each new Legendary rank is similar to a 10% strength increase, which is insane! Having 100k strength and 110k strength is not the same, the difference is big. With the help of these new ranks, one single rank up has the power to fill that gap. Of course, getting 10 billion rank points isn’t easy, it requires a lot of fighting, but I think it’s safe to say that some players (the top tankers) will always have at least 10 billion rank points more than the others (the moderate tankers and non-tankers). So now, that is kind of like permanently having 10% more strength. Who’s in charge now? The dudes with the Top Strength or the dudes with the Top Rank? The answer is obvious.

I can’t be 100% sure about what will happen in the future. The Admins might make gaining rank points easier or harder, depends on what suits them better. But one thing is for certain, when the majority of the stronger players actually get the Legend Rank (and this will happen sooner or later), Strength will drastically lose its importance. All that will matter will be how Legendary you are, i.e. whether you’re a Legend I, Legend II, Legend III or whatever… I hope I’m wrong, but we shall see, as I’ve already said.

To me, this isn’t really shocking: once again the Admins have decided to give more benefits to those who spend a lot of time and/or money on this game, and that is how it must be. I personally don’t think this game change had any bad intentions (the Admins probably only wanted the top tankers to have more fun and not get bored), but it might create some bad results in the future, if not today. Time will tell.

That’s all from me… I hope you like this article.

Also, thanks a lot to SerbianLegenda, kamysje, blackpanther76, 1224333 and Mithrantir for helping me crack the formula by telling me how big their hits are with and without the Legendary bonus.

I-G-D