Game Mechanical Index [To be updated with new pictures etc. later]

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

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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

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...

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.

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 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 fourth thread I explained 'Dilution Theory', which is how merging two units can result in a lower condition and how to calculate it.

Today I would like to delve into how damage distribution work in this game. In the dilution theory thread I mentioned that this thread will base itself on the premise that if the dilution theory is true, then this theory will be true as well.

Simply put:

If dilution theory = true, then damage distribution theory = true.

Now that we have gotten that out of the way, let's begin.

As always I believe that the best way to explain things is by showing an example.

Suppose that you have say five infantry units and suppose that the HP of each unit is 100 for pedagogical purposes.

Example:

100, 100, 100, 100, 100 (HP)

Five units total

Cumulative HP value (500)

Average = 500/5 = 100

Now introduce e.g. 120 damage.

Since the damage exceeds the HP of 1 inf. it will destroy the first unit in line and then distribute the rest of the damage to the next unit, i.e. 20 damage distributed to the next inf. unit in the stack.

So we end up with this:

100, 100, 100, 80, X (HP)

X denotes a destroyed inf. unit in the stack.

We do however know that one inf. unit cannot have a different value in our stack since the dilution theory says that no unit in a stack can have a different value compared to another unit (provided they are not mechanical) of the same unit type in the same stack, therefore this means that the excess damage must be distributed evenly across all of the units in the stack.

So this means that we would end up with:

(Excess damage / number of surviving inf. units), or 20/4 = 5

100 - 5 = 95 HP

Cumulative HP value: 95 * 4 = 380

380/4 = 95

95, 95, 95, 95, X (HP)

As concluded every inf. unit will now have 95 HP or 95% condition.

* Note: The queue damage distribution theory has been confirmed by the company representatives, but it does not explain all there is to know about damage distribution and as such more research will have to be done in order to explain how damage distribution works if there are more than one unit type involved. Imagine a scenario in which you have e.g. 50 infantry and 50 cavalry. How will damage be allocated between these two unit types? Will it be 50/50? These are the questions that remain to be answered. Stay tuned for more information on how damage distribution work within Supremacy 1914.

** Note: Queue Damage Distribution Theory is only applicable on organic units. It is not applicable on mechanical units. Special thank you goes to Jkiller2911 for bringing this to my attention.

Greetings, everyone.

Today I would like to delve into how some of the game mechanics have incremental properties, including, but not limited to, the construction of buildings and production of units, as well as other mechanical features. The scope of this thread will be to thoroughly explain the incremental properties of building construction and a consequential impact that it can have on unit production, which may explain some oddities that I am fairly certain many of you have been wondering at some point about.

In order to explain mechanical incrementality we need to have the health point values of buildings – hereinafter referred to as “HP” – that you may find in the manual within section 4.4 ‘The Buildings’: Here

Please do take notice of the fact that every building has a HP value and for demonstration purposes we are going to take a look at the airfield, also known as the aerodrome within the game, in the aforementioned section of the manual. You will find something that looks like this:

I have taken the liberty to mark out the HP of the building and its construction time, which we are going to need for this relatively simple calculation. Suppose we want to find out the earliest point that we can start using the aerodrome. In order to find out we simply take the construction time and divide it by our HP value to end up with the threshold value. We will end up with the following: 24/4 = 6.

This tells us that we can start using the aerodrome six hours into its construction, because every building has something called a threshold of existence. Once it passes that threshold, in our case 1 HP that will occur after 6 hours of construction, the system will count this building as existing and hence operational. Now there are some exceptions to this, e.g. barracks, which if below level one requires full HP (4 HP) to be operational and hence can be said to not have any incrementality. Barracks, if below level one, do not function when they are only partially constructed as opposed to buildings with incrementality. If above level one barracks does have incremental properties.

The following buildings can be said to have incremental properties: Harbour, fortress, workshop level 1+, barrack level 1+, factory, aerodrome and railway. This leaves the barrack level one as the only significant building that does not have any incremental properties. The workshop level one does not have any incrementality either, but it takes just a few seconds to construct and hence are insignificant.

Buildings with incremental properties that provides protection or enhance your production, e.g. a fortress or a railway, do so gradually as they are constructed. Since they have incremental properties we know that they do not have to be fully constructed in order to be operational. The level of protection or the level of production enhancement the fortress or railway will provide is entirely dependent on the HP values or the so-called thresholds of each respective building.

For example, it takes 24 hours to construct a fortress and it has 2 HP per level according to the manual. Therefore, we simply take 24 and divide it by 2 to find out the threshold value, i.e. the number of hours it takes for the building to pass each threshold. We end up with 24/2 = 12, so after 12 hours the fortress will have 1 HP out of 2 and thus be halfway through its construction. At this threshold level the fortress will provide the local garrison with a damage mitigation of 50% against all incoming damage.

At threshold 2 some 12 hours later, the fortress is fully constructed at level 1 and will now provide a damage mitigation of 67% and on it goes… The point here is to show that a fortress does not have to be fully constructed to provide a defensive bonus, but rather just be 12 hours into its construction and I also wanted to show that as we pass threshold by threshold the significance of the protection the fortress provides will gradually increase.

Now there are strategies involving the incrementality and one of them is about railways. It was first publicly described in this guide here by Sebi Sterta [fetched 2018-04-10], but has been known within the veteran part of the community since the days of Java. A railroad, also known as railway within the game, have 6 HP according to the manual and it has a construction time of 3 days (72 hours). So, we do the same thing that we have done all throughout this entire thread and divide the construction time by the amount of HP. We end up with 72/6 = 12, so we have a threshold value of 12 hours and that means every 12 hours the building will gain 1 more HP and pass a threshold, because HP equals threshold.

We know that it is has incremental properties and as such we know that it does not have to be fully constructed to provide its benefits. The benefits as shown with the fortress example will come gradually with each threshold or HP to be clear. We can construct the railway to 5 HP out of 6, which will take place after some 12*5 = 60 hours into construction. We will then have + 28% enhanced resource production provided by the railway, however, we do not have any consumption until we hit the last threshold of 6 HP (fully constructed railway).

Therefore, we can simply cancel the construction after 60 hours and enjoy the + 28% without having to pay any upkeep for the railway. Granted, this strategy does have some drawdowns such as the fact that we miss out on the speed bonus that a fully constructed railway provides and in addition to this we sacrifice 5 percentage points that would be added to the + 28% at the last threshold.

I think that we have talked enough about the incrementality of buildings. Suppose we want to know the impact that incrementality has on unit production in factories… Now this in particular can cause headache, but it does help explaining some oddities that you might have been wondering about, such as… How on Earth did a player get an artillery piece at day 12.6 without spending goldmarks? Is that even possible? Yes, it is indeed possible and it is the earliest a player can roll out an artillery piece from his / her factories without spending precious premium currency. Allow me to show you the beautiful reason why this happen.

As you might have noticed, I have taken the liberty of marking the relevant information for our case. It seems a bit harder than the things we have been doing earlier in this thread and it is, but it relies on the same concepts except that we are now focusing on how production time is affected by incrementality.

As seen in the print screen, each level has four thresholds and we can say that each time you go over one of these thresholds the production time of any unit you have in production simultaneously will consequentially decrease. Since it takes two days to upgrade the factory it is reasonable that we divide 48 hours with four to find out when the thresholds will take place and so we end up with 12 hours. Artillery is the main unit for our case and it takes four days (96 hours) to produce one with a level one factory according to section 5.2 ‘The Units’: Here

Now it is extremely hard to structure this properly in a formula, but what we can do is to break the entire process down to its smallest parts as seen in table below:

Every threshold that you pass over will accelerate the unit production a little bit. If you let a factory level one handle the production of the artillery piece, then it would have taken you 4 days. However, it takes just 2.6 days to produce said artillery piece when you simultaneously upgrade the factory from the start. You may begin your construction of a factory level one at day 8 and it takes 2 days to finish the construction, so you will not have a factory level one until day 10 unless you spend premium currency.

As soon as day 10 comes you place an artillery piece in production and upgrade the factory and keep on doing it (with no time inefficiency, meaning you upgrade the factory again the very second it finishes upgrading at change of day) until the artillery rolls out of there 2.6 days later. So, 10 days + 2.6 days = 12.6 days. If they have artillery earlier than that, then they are either going through the tutorial or they spent premium currency. The point that I want to make is that incrementality does affect unit production and you can use it to your advantage.

Greetings, everyone.

In my fifth thread I explained 'Queue Damage Distribution Theory' – hereinafter referred to as “QDDT” – which is actually closely related to what I am going to go through in this thread about 'Sequential Damage Distribution Theory' – hereinafter referred to as “SDDT”.

QDDT and SDDT share some important similarities and differences:

• QDDT is for organic units whilst SDDT is for mechanical units.

• In QDDT any excessive damage that is not enough to take out a unit is distributed evenly across the remaining units in the stack of the same unit type.

• However, in SDDT any excessive damage is just distributed to the next unit in line of the same unit type within the stack.

As always it is best to pedagogically explain this by showing you an example of how SDDT works:

Suppose that we have 5 fighters with 100 HP each.

100 | 100 | 100 | 100 | 100

Now introduce 140 damage and we end up with this:

100 | 100 | 100 | 60 | X

The X denotes a destroyed fighter.

As you can see, we now have 3 fighters at full health plus 1 damaged fighter at 60 HP.

Therefore, our cumulative HP value is: 100+100+100+60 = 360 HP out of 400 possible since there are 4 units left in total and each is supposed to have 100 HP.

The condition of this unit therefore can be calculated by dividing 360 with 400, which will give you 0.9 or 90%, which is the condition of this stack and it is dragged down by that 1 damaged unit only.

Should that 1 damaged fighter unit be destroyed and there is no excessive damage to be distributed to the next one in line, then the condition of the fighters will go up to 100% again as there are no damaged fighters in the stack anymore.

* Note: SDDT does not explain all there is to know about damage distribution and as such more research will have to be done in order to explain how damage distribution works if there are more than one unit type involved. Imagine a scenario in which you have e.g. 50 tanks and 50 armoured cars. How will damage be allocated between these two unit types? Will it be 50/50? These are the questions that remain to be answered. Stay tuned for more information on how damage distribution work within Supremacy 1914.