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:

- Damage Efficiency = ((Σ_(ⅈ=0)^size Sizefactors[i])*Mobilisation*(Morale*0.45+0.55))/size

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:

- Damage Efficiency = ((Σ_(ⅈ=0)^size Sizefactors[i])*Mobilisation*(Morale*0.45+0.55))/size

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:

- ((5*1)+(10*0.3)+(25*0.1)) = 10.5

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

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

Code:

- Damage Efficiency = (10.5*Mobilisation*(Morale*0.45+0.55))/size

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

Code:

- Damage Efficiency = (10.5*1*(1*0.45+0.55))/size

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

Code:

- Damage Efficiency = (10.5*1*(1*0.45+0.55))/63

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.