another soft cap question

[hugh2711]

I am trying to get my head around the soft cap - i am just going through the grand campaign again but this time with all my SE units being tanks and hence not included in the calculations. I have tried to read some threads about the soft cap but they seem confusing (or i am just a bit thick

Is there clear/EASY and definitive explanation of how the soft cap is calculated in VERSION 1.25? Is there a clear/easy thread?

How does overstrengthening affect the calculation?

Thanks for info

[ThvN]

Hello hugh2711, I'm a bit late with replying but I have info. There is information scattered about, but a recent post by the lead developer has given some extra insight.

OK, you already know the softcap is meant to gradually lower your income as your fielded units start to get more expensive. SE units are excluded, so this means their cost is not used to limit your income. Auxiliary units & reserve are excluded as well, only the core units that are one the map are used for the calculation.

Every scenario, you are allowed to deploy a certain number of units: these are your core slots. Let's say you are allowed to field 20 units. If these 20 units have an average cost of more than 400 prestige (pr) than the game will start lowering any prestige income (from capturing objectives, scenario bonuses, etc.) by a certain amount. Normally you would get 100pr for a Victory Hex (VH), but if your fielded units have an average cost of more than 400pr you will receive less. This lowering cannot go lower than 20%, so you will always receive 20% of the normal income regardless of how expensive your units are.

Each time you receive prestige, the game calculates the exact cost of the core units on the map, and adjusts the prestige. So if you lose units during a scenario the average cost of all your units will change, and so will your income. So it is important to realize what this average cost is and what counts towards it.


Unit cost/core slots
what you pay for a new unit is the baseline cost. An Elefant costs 600pr, well above the 400pr mark. So if you have 20 core slots and field only Elefants, average unit cost is 600pr: ((20 x 600)=12000)/20= 600.
Way above the 400pr mark and you will see your income lowered considerably.

But if you have 20 core slots and field an army of just 13 Elefants and nothing else (or SE units), the average unit cost will be ((13 x 600)= 7800)/20 = 390pr. So your income would not be lowered, but you'd have less units deployed.


Current strength
When units take losses they lose strength points. This is taken into account. A 10-str Elefant is 600pr, so an 8-str is worth 480pr. a 3-str = 180pr. If you have a lot of badly damaged units you will see your income increasing as you play.


Overstrength
Overstrengthing a unit makes it more expensive, so it counts towards the softcap. Let's take another Elefant.

At 10-str, it costs 600pr. Suppose it is a 5-star unit, and you purchase all 5 steps of overstrength, making it 15-str. You might think each step is worth 60pr, but just like when you purchase overstrength each extra step of overstrength is progressively more expensive. The game calculates the value of each point of overstrength like this:

First point (11-str): 100% of 60pr, then multiplied by 2: (1x60)x2=120.
Total value of an 11-str Elefant: 600+120 = 720pr

Second point (12-str): 150% of 60pr, then multiplied by 2: (1.5x60)x2=180.
Total value of an 12-str Elefant: 600+120+180 = 900pr

Third point (13-str): 200% of 60pr, then multiplied by 2: (2x60)x2=240.
Total value of an 13-str Elefant: 600+120+180+240 = 1140pr

Fourth point (14-str): 250% of 60pr, then multiplied by 2: (2.5x60)x2=300.
Total value of an 13-str Elefant: 600+120+180+240+300 = 1440pr

Fifth point (15-str): 300% of 60pr, then multiplied by 2: (3x60)x2=360.
Total value of an 13-str Elefant: 600+120+180+240+300+360 = 1800pr

So this adds up really quickly...


Than there is another important factor to consider:

Cost of transports
If a unit has an organic transport (truck, halftrack) this cost is added to the value of the unit, and when overstrengthing the same cost mulitplier applies for both the parent unit and its transport. So those 200pr halftracks will drive up the average unit cost a lot. A couple of examples:

'43 Grenadier (227pr) + Opel Blitz (50pr) at 11-str: 332pr total value.
'43 Grenadier (227pr) + SdKfz 251 (100pr) at 11-str: 392pr total value.
'43 Grenadier (227pr) + SdKfz 250 (200pr) at 11-str: 512pr total value.


Here's an interesting comparison: both these guns have a rate of fire of 80%, so for an extra shot you need them at 12-str, 11 is just a waste of prestige:
15cm sFH (271pr) + SdKfz 251 (100pr) at 12-str: 556pr
17cm K18 (310pr) + SdKfz 7 (70pr) at 12-str: 570pr

So the heavier gun is actually pretty cheap if you want a halftrack as transport. For this reason I use either sFH's with trucks or K18's.

As for the exact income penalty, I had long assumed that this would be linear, and that there was a bug in the calculation as the values I observed did not seem to match my calculations. What was certain is that the softcap seemed to hit that 20% minimum at around 625pr average unit cost. Well, I was wrong, it isn't linear... Here I've pasted the math for the softcap as given by Rudankort:

There are several values governing the work of soft cap. First, we have Normal Prestige and Max Prestige, per unit slot in the core. As these names imply:
- To have Normal Prestige amount of prestige is, well, perfectly normal, so no adjustment of income is necessary. The player gets full income from whatever action he performs.
- Max Prestige is, well, the maximum amount the player is allowed to have. So, once the player reaches this amount, he must be getting zero.

This means that between Normal Prestige and Max Prestige player's income must gradually change from 100% to 0%. How exactly? Well, various approaches are possible, but the game uses parabolic function. In other words, between normal and max values of prestige, the following coefficient is applied to income:

(MaxPrestige - ActualPrestige)^2 / (MaxPrestige - NormalPrestige)^2

This is the basic mechanic. But if player's income ever dropping to zero sounds too severe, there is an additional parameter in place, called MinKoff. If it is not zero, income coefficient is never allowed to drop below this value.

The bottom line is, there is no bug in soft cap implementation, but there has been a misunderstanding how exactly this feature works.

If current values set in gamerules are too severe and break balance in some scenarios, this might be a balance issue which needs fixing, but a fix would be related to adjusting values in gamerules, not in the algorithm itself. My approach to this has been as follows. 800 is a lot of prestige per unit (somewhere between Tiger I and Tiger II cost), so getting to this value should take a lot of time. On the other hand, half of this value (400), which is about average unit cost, should be easy to have.

[hugh2711]

Many thanks for that excellent explanation.

It certainly puts an interesting slant on overstrengthening.I am just going through the grand campaign again but keeping all my SE slots as tanks which will eventually end up as king tigers prestige permitting. I have always used the cheapest infantry transport. So far by this method I have managed to accumulate more prestige than before which i will need in the later DLC's .I think in future I will now be reluctant to overstrength the few heroed up non-SE tanks I have. (I tend to disband most of the capturable stuff for prestige).

This also makes me reluctant to overstrength wulfrahmen as the cost is already way over the 400 mark (510).
This makes all the artillery very expensive but the problem is it is so neccessary!
so the question now is what is the most cost effective artillery in the later years given the light stuff just doesnt cut it later on.
I think i will also save my overstrengthening for the air force.

[captainjack]

An unfortunate side effect of the soft cap appears to be to make SE infantry (and tac bombers) effectively useless - mainly because they are cheaper than tanks and fighters. Any fix to simplify or clarify the soft cap would also need to eliminate this effect.

[peterw]

I really dislike the fact that SE units don't count for soft cap.
One idea is you don't play with SE and use higher values for the soft cap parameters for compensation.

Or you do it like me and just disable soft cap at all.

[Magic1111]

Or you do it like me and just disable soft cap at all.

That´s exatly that was I did since "Soft cap" came out...

[hugh2711]

Yet another reason for the information about rate of fire to be easily available or preferably visible!

[captainjack]

<br abp="742">Or you do it like me and just disable soft cap at all.

<br abp="743"><br abp="744">That´s exatly that was I did since "Soft cap" came out...

Me too (once I found out how).
I like having an SE division with infantry and tanks (and in some games SE fighters and Tac bombers).

[hugh2711]

ThvN wrote "
"Here's an interesting comparison: both these guns have a rate of fire of 80%, so for an extra shot you need them at 12-str, 11 is just a waste of prestige:"

But 12 x 80% =9.6, 13 x 80% = 10.4 Does it definately round them UP (not down)?

Thanks

[ThvN]

Sorry I'm bit late, holidays etc.

But 12 x 80% =9.6, 13 x 80% = 10.4 Does it definately round them UP (not down)?

It always rounds down to the nearest integer. To be more clear, when I said an extra shot, I ment compared to the 10-str original unit:

10str x 80% (=8.0 ) = 8 shots

11str x 80% (=8.8 ) = 8 shots (so 11-str does not get you another shot, waste of prestige)

12str x 80% (=9.6 ) = 9 shots (first 'extra' shot requires 12-str)