Posts by Alexiel Lucien

Greetings, everyone.

In my first thread I explained why comparing strength is not a reliable way to determine advantage, and I concluded that it is better to compare attack damages instead.

In my second thread I explained how to calculate the attack damage of enemy units and how to see the own attack damage.

In my third thread I explained how to calculate damage efficiency along with what it is and what it does.

In this thread I would like to present something which I call the dilution theory. The veterans of this community are likely familiar with this since they have probably experienced and reflected over it at some point. Allow me to explain what it is and how it impacts your troops.

Suppose you have 9 fighters á 100 condition each.

That is a cumulative condition of 900, because 9 times 100 equals 900.

Suppose that you decide to merge these 9 fighters with another 9 fighters; however, these new 9 fighters have all 98 condition each and thus their cumulative condition is 9 times 98 which equals 882.

Let's add the cumulative values together: 900 + 882 = 1782

Now let's divide it by the total amount of units involved in the merger: 1782/18 = 99, where 18 denotes the amount of units involved in the merger. We had 9 fighters and decided to merge them with another 9 fighters and so we get 9 + 9 = 18.

Once the two stacks have finalised their merger you will therefore notice that the condition of the new stack is 99.

If you now select this 18 fighter stack and split it apart one by one, then you will find that every fighter have a condition of 99 even though half of them had a condition of 100 before the merger.

The reason for this is because the system averages out the condition of the units in the stack. Therefore, you have effectively diluted the condition of your units.

Furthermore, once you have diluted the condition of your units the process cannot be reversed. It is like mixing two glasses of water. Once it has been done, good luck separating them from one another.

That concludes the lesson about dilution theory, which will later serve as the bedrock of what I call the queue damage distribution theory that will soon enough receive a thread of its own.

Greetings, everyone.

In my first thread I explained why comparing strength is not a reliable way to determine advantage, and I concluded that it is better to compare attack damages instead.

In my second thread I explained how to calculate the attack damage of enemy units and how to see the own attack damage. I used a formula and in this formula something called 'damage efficiency' made an appearance.

I showed you where to find it and you can find it in the same place for enemy units, meaning that this is something that you do not really have to calculate. However, there are misconceptions still about what damage efficiency is and what it does, which is what I intend to go through with all of you today.

Let's first have a look at the intimidating formula in all its glory:

Link to formula: Here

This is how it would look if we write it in a linear formatting, i.e. plain text style:

Code:

Now this looks overwhelming at first; but let's break it down, shall we?

The best way to break this down from a pedagogical point of view is to demonstrate it with an example.

Imagine that you have an infantry stack with 63 infantry units. Its morale is 100% and its mobilization is 100%.

This printscreen will demonstrate the value that we are after, i.e. 17%:

Let's have a look at our formula again, and this time I will bold the part that we are breaking down:

Code:

The bold part of the formula basically is telling us to summarise the size factors for the unit type (in our case "infantry").

The size factors can be found in the manual, within section 5.2 'The Units': Here

You should now have the following highlighted size factors:

These size factors are telling us that the first 5 infantry units will contribute with 100% of their attack damage to the stack, meaning there has been no loss of attack damage that they contribute with to the stack.

However, they are also telling us that from unit nr. 6 to nr. 15 each additional infantry unit will only contribute with 0.3 or 30% of their attack damage to the stack. In other words, there has been a loss of damage that they can contribute with to the stack and this tells us that not all units are operating at maximum efficiency.

So we can see that 5 units will operate at 1 or 100% efficiency, 10 units will be able to operate at 0.3 or 30% efficiency and finally we can also see that 25 units will be able to operate at 0.1 or 10% efficiency. Now let's throw them together like this as we are summarising them:

Code:

Okay, we have now broken down the bold part of the formula.

Let's take a look at what's left to do:

Code:

Okay, we need to multiply 10.5 with our mobilisation and morale, which we said was both 100%.

Code:

Now the only thing left to do is to plug in the size of our unit which we said was 63 infantry units.

Code:

You should end up with a value that says 0.16666666666, which we can round up to 0.17 or 17%, which is the value that we were after.

Okay, we now know how to calculate damage efficiency, but what is it?

Well, it is a variable in attack damage calculation (see corresponding thread) and if it is lower than 100%, then we know that not all units in the stack are contributing with 100% of their attack damage towards the accumulated attack damage of the stack.

The accumulated attack damage of the stack is called 'total strength' and it shows us how much attack damage a stack would have if every unit contributed with 100% of their attack damage, but due to size factors this is rarely ever the case.

So what damage efficiency is telling us is that it is a measurement between what could have been and what we actually have.

To provide one last example: Our stack with 63 infantry units have a total strength of 63*1.2 = 75.6. Our actual attack damage is 12.6 and what we can do in order to find our damage efficiency is to divide 12.6 with 75.6, i.e. divide our actual attack damage with the theoretical maximum attack damage that we could have had, if every unit had contributed will all of their attack damage.

We end up with this:

12.6/75.6 = 0.16666666666, which can be rounded up to 17% and that is the damage efficiency of this stack as we have established earlier.

I hope this helps a little bit and whilst I do realise that I might not have been as pedagogical as I could have been, at least these final sentences ought to have conveyed the message of the thread and taught you what damage efficiency is and what it does.

I wish everyone a continued pleasant gaming experience.

Greetings, everyone.

In the last thread I explained why comparing strength is not a reliable way of determining advantage, and I also said that comparing attack damage is better. There is only one problem with that... You need to calculate the enemy unit attack damage.

You cannot straight up reveal it by hovering with your mouse above their total strength at the bottom bar. What we are going to do in this thread is to calculate the attack damage of enemy units.

The formula for calculating attack damage is as follows:

Code:

Here is a visual of the three variables that we are going to look at:

Let's proceed to calculate attack damage of two enemy units.

Army A: 100 infantry units

Code:

So let's take a look at how it compares to reality:

There appear to be a 0.6 difference between our calculation and what the game displays. The reason why there is a difference is because the game never gave us the decimal values for the damage efficiency. The game only ever showed us 10% in damage efficiency as seen in the first printscreen, but in truth the actual non-rounded damage efficiency value is 10.4999999999....%.

If you put 10.4999999999....% into the formula rather than the 10% that the game told us, then you will end up with 12.6 in attack damage, which is exactly the attack damage that our 100 infantry stack have. The attack damage formula is not wrong, but it is the game that omit information by providing us with a rounded number.

Now, there are ways to get a hold of the decimal values, but that involves technical expertise. For the sake of convenience we will settle with using the rounded numbers that the game provides us. This means that the attack damage values that we end up with in this thread might not necessarily be 100% accurate, but they are accurate enough to base fair decisions on.

Let's calculate the attack damage of our second enemy army:

Army B: 50 infantry units + 10 heavy tanks

Code:

So let's take a look at how our calculation compares to reality:

A perfect match.

Please take note that there was more than one unit type. You must calculate the attack damage of each unit type separately and then add it on to the other, hence why I calculated the infantry unit and the heavy tank unit separately even though they are in the same stack.

Comparing attack damages between two units is more reliable than comparing strength, because we concluded in our previous thread here that when people compare strength to strength, they are really just comparing theoretical values and not the actual values. When you compare attack damage values, then you are comparing actual values and this is why it is far more reliable to compare attack damages.

Lastly, heed my word - exercise caution. Attack damage is not everything when you compare advantage. It would be wise to also consider the health pools of the armies that you are comparing.

My dear fellow community participants,

I have noticed a recurring pattern for years now within this community. People are providing one another with false information and then base their decisions on this faulty information. I am talking about the common misconception that Total Strength (hereinafter referred to as "Strength") is a value that should be used as an indication of advantage.

People tell one another to compare the strength values of armies to determine whether they hold the advantage. It is not unusual to hear that you should win if you have three times the strength of the enemy unit, but what exactly is strength and why can it be so misleading?

Suppose that you have an infantry stack with 100 infantry units. We know from the manual and the ingame data that the strength of 1 infantry unit is 1.2. We can therefore conclude that our strength must be 100 * 1.2 = 120.

- Great, right?

- Well, not so fast...

This strength value ("120") postulates that there is no loss in damage efficiency, i.e. that every single infantry unit will continue to contribute with 1.2 attack damage to the stack.

This is not the case within the game as there is something called 'size factors', which in our case says that at a certain amount of infantry units in the stack, each additional infantry unit will contribute less attack damage to the stack.

If we look within the manual in section 5.2 'The Units' we can conclude by looking at the size factor for infantry that e.g. the 6th infantry unit will contribute with only 0.4 attack damage and after the 15th infantry unit in the stack each additional infantry unit will only contribute with 0.1 in attack damage to the stack and so on. Here you have a visual of what I am talking about:

The size factor just slashed our strength value ("120") down to 12.6, which is our attack damage for this stack of 100 infantry units as after 40 infantry units in a stack each additional infantry unit will contribute with no attack damage to the stack as seen above and if you still do not believe me, then here:

So we can conclude based on this that strength only shows you the attack damage that your unit could have had, if only there had not been any decrease in damage efficiency. However, due to the size factor there has been a decrease in damage efficiency and hence we end up with 12.6 attack damage rather than 120 as seen in the picture above.

When people compare strength to strength, they are really just comparing theoretical values and not the actual values, and this can have devastating consequences for the outcome of the battle, which is why strength should not be used as an indicator of advantage.

Suppose we have two armies:

Army A: 100 infantry [Strength: 120]

Army B: 80 infantry + 4 tanks [Strength: 112]

In this scenario comparing strength would have you believe that Army A hold the advantage, however let's take a look at the actual values:

Army A: 100 infantry [Attack damage: 12.6]

Army B: 80 infantry + 4 tanks [Attack damage: 28.6]

Now it all of a sudden does not look so bright for Army A as the strength comparison would have us believe.

Note: This was just an example of a scenario showing how strength can be misleading and why it is better to compare the actual values instead to avoid 'minor inconveniences' at the battlefield. I could have provided more extreme examples, but I think this will do just fine to prove my point.

I hope this thread will serve as a proper warning to all of you who compare strength or tell other people to do it, because as shown it is not reliable and mark my word when I say that one day it could be the end of you...

Game Mechanical Index

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To make it easier for people to find their way on the forum and to make sure these posts are not lost in the sea of threads, we have decided to create an index page where we will gather all information about the mechanics of Supremacy pertaining to features such as attack damage and damage distribution.

— NarmerTheLion

1. On the Calculation & Use of Strength
2. On the Calculation & Use of Attack Damage
3. On the Calculation & Use of Damage Efficiency
4. On the Calculation & Use of the Dilution Theory
5. On the Calculation & Use of the Queue Damage Distribution Theory
6. On the Calculation & Use of Mechanical Incrementality
7. On the Calculation & Use of Sequential Damage Distribution Theory

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AI Trade Offers: We will remove the automated Goldmark trades issued by AI players in certain intervals. We felt that they were too much of a distraction in the Diplomacy section which should be focused on player-to-player communication.

In times of hardship we endure through the exercise of commendable perseverance that can be solely attributed with great certitude to the perpetuality of our commitment to progress. Gentlemen, before you lies the future. No more shall we lie awake late at night pondering over how much the artificial intelligence will be spamming our ingame diplomacy inbox with mostly useless offers.