Good to know. You are always busyI'm working on that, they are not that 'invisible' early on, nor are they that over-effective anymore
Maybe you should implement my idea:
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Maybe you should implement my idea:
I have yet to see where in 1942 or later that the German subs strangle the UK. Either it has already happned or it never happens. And when I play as UK I start to find subs fairly soon after getting all the 1942 and 1943 techs in this area.
This is a mod issue and Slan is working on it or has worked on it. but don't confuse it with the vanilla game. So either your problems are with the mod in which case you shouldn't try to confuse it with vanilla, or just show issues where HOI3, SF 2.03c vanilla starves UK AI.
As stated earlier in playing as Germany VH mode it's May 1941 and I am no where close to starving UK. Maybe if I devoted lots more IC to subs and more research to subs I could but then my air/land forces would have suffered. All about tradeoffs.
Who said vanilla was balanced? In vanilla it's often better to invest the IC and MP in land units, aircraft or ships for Sea Lion, because UK will have 159051801706 stockpiles by 1939.
Spamming has always been a problem in HOI games. Can't say I like this "all or nothing" strategy. Germany had no chance of starving UK during late-war period, but subs were still being produced. It's because of the fact that they force the enemy to use inadequately large resources to counter the sub threat. Unfortunately, in HOI3 AI always puts its units on patrol orders even when the threat is non-existent (just look at Japan wasting all its fuel during war with China...).
In HOI games units such as submarines or STRATs aren't terribly effective when used in small numbers. They become extremely powerful when used in large numbers - in HOI3 it's especially true because of very powerful practical effect. So either go all for it or don't bother at all (many GER players ignore the navy). Strats can actually become overpowered.
Spamming has always been a problem in HOI games. Can't say I like this "all or nothing" strategy. Germany had no chance of starving UK during late-war period, but subs were still being produced. It's because of the fact that they force the enemy to use inadequately large resources to counter the sub threat. Unfortunately, in HOI3 AI always puts its units on patrol orders even when the threat is non-existent (just look at Japan wasting all its fuel during war with China...).
Now, this thread seems to have moved on to discuss something completely different than air stacking penalties. However, I thought about how one could get an optimum number. It seems that this is possible if the multiplicative penalty is applied incorrectly. In the discussion below, I assumed that the penalty was applied to each plane. The total strength would thus be the sum over planes:
s(x) = a^0 + a^1 + a^2 + ... + a^x,
where, using the notation below, a = 1 - SP. However, if the penatly is somewhat incorrectly applied directly to the entire strength, which I did not think of before, then things look a little bit different. The total strength is then
s(x) = x a^x
The derivative is
d/dx s(x) = a^x + x ln (a) a^x = (1 + x ln (a)) a^x.
This is zero for
x = -1 / ln (a) = -1 / ln (0.9) = 9.491
which is the optimum value. To illustrate:
s(8) = 8 * 0.9^8 = 3.4437
s(9) = 9 * 0.9^9 = 3.4878 (optimum)
s(10) = 10 * 0.9^10 = 3.4867
s(11) = 11 * 0.9^11 = 3.4519
If this somewhat incorrect way of calculating the penalty is applied the peak strength would occur for 9 aircraft, although this stack would be only 3.5 times stronger than a single one.
s(x) = a^0 + a^1 + a^2 + ... + a^x,
where, using the notation below, a = 1 - SP. However, if the penatly is somewhat incorrectly applied directly to the entire strength, which I did not think of before, then things look a little bit different. The total strength is then
s(x) = x a^x
The derivative is
d/dx s(x) = a^x + x ln (a) a^x = (1 + x ln (a)) a^x.
This is zero for
x = -1 / ln (a) = -1 / ln (0.9) = 9.491
which is the optimum value. To illustrate:
s(8) = 8 * 0.9^8 = 3.4437
s(9) = 9 * 0.9^9 = 3.4878 (optimum)
s(10) = 10 * 0.9^10 = 3.4867
s(11) = 11 * 0.9^11 = 3.4519
If this somewhat incorrect way of calculating the penalty is applied the peak strength would occur for 9 aircraft, although this stack would be only 3.5 times stronger than a single one.
I am not sure I understand the calculation above. If you stacking penalty is called SP, then your strength function is
(1-SP)^x
If we call (1-SP) = a, which numerically is 0.9, then we have that the derivative is
d/dx a^x = ln(a) a^x,
where ln (0.9) = -0.105. This derivative is not zero for any positive x. Thus, no optimum exits. You always gain strength by adding planes, but your attack per plane is largest for the first one, and drops as you add them.
This is the entire point! I think originally there was a bug in this calculation (which I hope has been fixed now), where the strength was calculated as
(1 - SP * x) instead of (1 - SP)^x, which clearly leads to some mathematical issues.
I am not sure I understand the calculation above. If you stacking penalty is called SP, then your strength function is
(1-SP)^x
If we call (1-SP) = a, which numerically is 0.9, then we have that the derivative is
d/dx a^x = ln(a) a^x,
where ln (0.9) = -0.105. This derivative is not zero for any positive x. Thus, no optimum exits. You always gain strength by adding planes, but your attack per plane is largest for the first one, and drops as you add them.
This is the entire point! I think originally there was a bug in this calculation (which I hope has been fixed now), where the strength was calculated as
(1 - SP * x) instead of (1 - SP)^x, which clearly leads to some mathematical issues.
How does your math differ from the math at this page:
http://www.paradoxian.org/hoi3wiki/Air_combat_reference
I do notice you come to a different conclusion.
I really don't want to go off topic but where are your actual complaints comming form? Are they related to:
a) An AI UK vs. a human Germany
b) An AI Germany vs a human UK
c) AI UK vs AI Germany
d) Multiplay human Uk vs human Germany
If (a) then as Germany don't build 1000000 subs. You are gamming it if you do. And if you don't the AI UK doesn't starve. In fact Sealion is a bigger issue then sub warfare.
If (b) then show me where the AI Germany builds this many subs. Never saw it. And as human UK you should be able to deal with it easily enough.
If (c) this usually isn't an issue because AI Germany doens't build that many subs.
If (d) then have your human SU kick Germany's butt since they ignored their land forces.
Please be specific in how you are playing where this is a big issue?
Can't say much about d).
AI Germany doesn't build many subs, because it's not told to do so in LUA files. It has nothing to do with subs effectiveness.
Besides, "starving" UK is not really possible in Vanilla, because of huge stockpiles. It will hurt UK's overseas actions.
I don't play Vanilla anymore because it's neither balanced nor realistic (or challenging), I'm just commenting.
AI Germany doesn't build many subs, because it's not told to do so in LUA files. It has nothing to do with subs effectiveness.
What? By investing in subs I'm gaming the system? If it can handle it, then it's just terribly balanced.
Besides, "starving" UK is not really possible in Vanilla, because of huge stockpiles. It will hurt UK's overseas actions.
I don't play Vanilla anymore because it's neither balanced nor realistic (or challenging), I'm just commenting.
No you want to change it. I'm asking why you want it changed. If it's because you find it too easy then play at a harder level. If you don't like what the default penalties are then change them to what you do like.
You keep saying its unbalanced. In an AI vs AI it's not. So if it's unbalanced because you build 10000 subs then stop doing it. This is like the guy who goes to the doctor and says "Everyting I hit myself in the hand with this hammer my hand hurts". The doctor replies: "Then stop hitting yourself".
In the game HOI3 SF 2.03c vanilla version subs are not found that often till after all the spotting and other anti-sub techs are researched to 1942/1943 levels. Newer subs require even better anti-sub research. To me that is WAD.
I can game the system by building tons of paratroops and knocking out all enemy forces. Why don't I do that? Because the game would be boring that way. There is nothing stopping me from doing this and it would work cause the AI can't deal with every single possible action a human can think of.
Well, the difference is in the assumption as to how the penalty is implemented. There are basically three ways of doing it, and the one shown on the wiki is the worst - although it may actually be the way it is done in the game.
The wiki assumes that the bonus is applied to all the planes equally, and that it is done additively. The form of the strength function is then, with p being the penalty,
1)
s(x) = x (1 - p x) = x - p x^2
The optimum here, found from
d/dx s(x) = 1 - 2 p x = 0,
is at x = 1 / 2 p = 5
The way I described above uses the expression
2)
s(x) = x (1 - p)^x,
which has an optimum at x = -1 / ln (1 - p) = -1 / ln (0.9) = 9.49.
This is better than the one above, but neither method gives the desired result, which is that a higher penalty is successively added to each plane without creating an artificial optimum.
3)
The best expression is
s(x) = (1 - p) + (1 - p)^1 + ... + (1 - p)^(x - 1)
The for large x, the contribution from the last plane will go to zero, but does not affect the previous ones. This is how diminishing returns normally is implemented.
I understand that your equation might be better, but to be honest as a player I'm really only interested in the equation that they actually use.
The wikki claims that the equation used there closely matches actual in-game results. Have you checked your equation to in-game results yet? If so how did they turn out?
Like most others it would be nice to know if 5 bombers are really the best number or is it 9. Thanks.
I know that it used to be as it is on the wiki. It was then posted as a bug report, but have no idea if they actually did something about it. There are many areas of the game where one can make significant improvements to the game mechanics by changing only a few lines of code - if one understands the underlying math.
The expression for diminishing returns in the form of a series
s(x) = x ((1 - p)^0 + (1 - p)^1 + ... + (1 - p)^(x-1))
could, of course, be applied to any stack, not only for planes.
The expression for diminishing returns in the form of a series
s(x) = x ((1 - p)^0 + (1 - p)^1 + ... + (1 - p)^(x-1))
could, of course, be applied to any stack, not only for planes.
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Hey, diminish return this!
I've been playing around a bit with Air Wing stacks and checking their total modifier effects in game, 1.4 vanilla.
IME, I recognise 3 squadron Wings as the most effectively efficient as far as my poor maths works it. However I find 4 squadron Wings achieve a fairly reasonable return in terms of gaining effectiveness for the most limited reduction of cost effectiveness.
For instance, given a ground bombardment target consisting of 12 Brigades and said mission ought to last 4 turn hours, I figure that I get 1 attack on each Brigade with the 3, but 3.25 with 4, or that 8 of the Brigades get attacked 3 times while 4 of them are attacked 4 times. Importantly the return fire is diminished because each squadron of the triangle Wing is shot at with the flak of the Brigades 4 times, those in the Square Wing are shot at 3 times although I do realise there is a minor stacking penalty reduction for the 4 in the square formation so that each of their defensiveness efficiency actually reduces by about 15% because of the extra 10% stacking penalty. But that still works out as a practical improvement because of the reduction of the number of chances of suffering hits.
Now I figure that the 4 squadron Wing costs an extra 33% build IC/MP, Officers required and Supply & Fuel consumption but increases the attack strength by about 21%, although its attachment reduces defensiveness by about 15% for each bomber squadron in the Wing. OTOH each squadron now gets targeted (AA shot at) 33% less often, so that works out to be about a 28% improvement in the Wings durability/survivability.
So for the extra 33% outlay/costs the gain as I see it are 21% for attack and 28% for defence, for bombers. (Non-Intercept)
Again for Intercepting the improvement provided by the addition of a 4th squadron into the Wing is similar.
IMHO I find that adding a 5th (or a 6th INT which improves nothing!) squadron not to be worthwild, there is an improvement of the Wings effectiveness, but the return has diminished to half that of adding the 4th and there for not worthwild, since the increase is less than half the performance value of the extra 5th squadron. What surprised me was that as TECH and experience gains improved the amount of percentage of bonuses that the squadrons in the Wings gained for combat modification, it didn't change the point that 3 squadrons in a Wing is the most effectively efficient, that 4 squadron Wings still had a reasonable though limited improvement to consider, but that 5 squadron Wings didn't become any more effective and thereby still remained an unworthy formation IMHO, while 6 squadron Wings never budged from providing no improvement over 5 for Interception and still remained a negative retardation for the total effectiveness of bombers!
I would definitely advise that both single and twin or pair Wings are not as effective as 3 squadron Wings, while they have higher individual efficiency the total air-to-air or air-to-ground firepower doesn't make up for the lack of the third squadron.
Personally I recommend 3 squadron Wings early War, but after a few TECH advances of Radio, Mission Efficiency and gaining of experience and with good skilled Leaders, 4 squadrons isn't too bad for air Wing formation set ups for both Interceptors and all other kinds of air-to-ground aircraft, although myself I'll start using 4 by about 1940!
(I also noticed during my testing that most Air Leader Traits don't seem to work at all, not just Superior Air Tactician, but also Tank Buster, Carpet Bomber and may be the Fleet Destroyer & Spotter?)
I've been playing around a bit with Air Wing stacks and checking their total modifier effects in game, 1.4 vanilla.
IME, I recognise 3 squadron Wings as the most effectively efficient as far as my poor maths works it. However I find 4 squadron Wings achieve a fairly reasonable return in terms of gaining effectiveness for the most limited reduction of cost effectiveness.
For instance, given a ground bombardment target consisting of 12 Brigades and said mission ought to last 4 turn hours, I figure that I get 1 attack on each Brigade with the 3, but 3.25 with 4, or that 8 of the Brigades get attacked 3 times while 4 of them are attacked 4 times. Importantly the return fire is diminished because each squadron of the triangle Wing is shot at with the flak of the Brigades 4 times, those in the Square Wing are shot at 3 times although I do realise there is a minor stacking penalty reduction for the 4 in the square formation so that each of their defensiveness efficiency actually reduces by about 15% because of the extra 10% stacking penalty. But that still works out as a practical improvement because of the reduction of the number of chances of suffering hits.
Now I figure that the 4 squadron Wing costs an extra 33% build IC/MP, Officers required and Supply & Fuel consumption but increases the attack strength by about 21%, although its attachment reduces defensiveness by about 15% for each bomber squadron in the Wing. OTOH each squadron now gets targeted (AA shot at) 33% less often, so that works out to be about a 28% improvement in the Wings durability/survivability.
So for the extra 33% outlay/costs the gain as I see it are 21% for attack and 28% for defence, for bombers. (Non-Intercept)
Again for Intercepting the improvement provided by the addition of a 4th squadron into the Wing is similar.
IMHO I find that adding a 5th (or a 6th INT which improves nothing!) squadron not to be worthwild, there is an improvement of the Wings effectiveness, but the return has diminished to half that of adding the 4th and there for not worthwild, since the increase is less than half the performance value of the extra 5th squadron. What surprised me was that as TECH and experience gains improved the amount of percentage of bonuses that the squadrons in the Wings gained for combat modification, it didn't change the point that 3 squadrons in a Wing is the most effectively efficient, that 4 squadron Wings still had a reasonable though limited improvement to consider, but that 5 squadron Wings didn't become any more effective and thereby still remained an unworthy formation IMHO, while 6 squadron Wings never budged from providing no improvement over 5 for Interception and still remained a negative retardation for the total effectiveness of bombers!
I would definitely advise that both single and twin or pair Wings are not as effective as 3 squadron Wings, while they have higher individual efficiency the total air-to-air or air-to-ground firepower doesn't make up for the lack of the third squadron.
Personally I recommend 3 squadron Wings early War, but after a few TECH advances of Radio, Mission Efficiency and gaining of experience and with good skilled Leaders, 4 squadrons isn't too bad for air Wing formation set ups for both Interceptors and all other kinds of air-to-ground aircraft, although myself I'll start using 4 by about 1940!
(I also noticed during my testing that most Air Leader Traits don't seem to work at all, not just Superior Air Tactician, but also Tank Buster, Carpet Bomber and may be the Fleet Destroyer & Spotter?
)
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Calculations like this just make me shake my head. The Allies routinely conducted 1,000-bomber raids during the war, and they were devastating. So were the massive "fighter sweeps" which regularly accompanied the bombing.
But they didn't crush the German land forces nor destroyed they industry. They hindered them and made the task easier for Allied land forces...
Which is why I think the HOI3 Air Stacking Penalty is unbalanced in the long term duration of the game play. It doesn't help that the Air Leader Traits don't seem to be working, or at least applied in a way that players can see the effects of in the tool tip if they somehow are applied behind the scene. Also I would like to see a TECH that works to reduce the Air stacking penalty, even if incrementally by 1% per TECH advance or some such, since I think that long term it would be worthwild.
One more question I have is about the Air TECH type "Reduce Organisation Damage" ones, I think it is the 4th one under Fighters, CAS, NAV & STR and the last Tech under the TAC group on the Air Warfare Theories page of Techs, does anybody know if these actually work, because I still see my Air Squadrons de-organise too quickly no matter what?
Hm, I think you guys are partly on the right track, but partly missing the point. The reason for the current problems is that diminishing returns is not implemented correctly. It is just a matter of simple math. As i pointed out above, if your strength was given by
s(x) = x ((1 - p)^0 + (1 - p)^1 + ... + (1 - p)^(x-1))
then you would not need to bother about finding an optimum. Adding planes, up to the ability of your commander to handle them, would always add some strength.
Now, a different question is if you would benefit from concentrating all your planes in one stack. Having several smaller stacks gives you a higher combined strength, and if you are either able to attack multiple targets or have to defend from multiple attacks, it thus makes more sense to split them up.
s(x) = x ((1 - p)^0 + (1 - p)^1 + ... + (1 - p)^(x-1))
then you would not need to bother about finding an optimum. Adding planes, up to the ability of your commander to handle them, would always add some strength.
Now, a different question is if you would benefit from concentrating all your planes in one stack. Having several smaller stacks gives you a higher combined strength, and if you are either able to attack multiple targets or have to defend from multiple attacks, it thus makes more sense to split them up.
(I also noticed during my testing that most Air Leader Traits don't seem to work at all, not just Superior Air Tactician, but also Tank Buster, Carpet Bomber and may be the Fleet Destroyer & Spotter?
I know the S-A-T has been theorized to death, but how would you go about checking if the Tank Buster actually works?
The effect that it has (via the tooltip) wouldn't be one that displays anywhere in the combat screen; since a target's softness rating isn't displayed, it can't be "modified" visually.
Have you done statistical analysis on the effects of it vs armored targets? If so, do you have some charts I can peruse?
True, IME it does makes sense to split up from one big stack to form multiple smaller stacks, however the question remains for me what size ought I be making those smaller stacks and what is the cost benefit/diminishing return issue between triangles and squares?
I know the S-A-T has been theorized to death, but how would you go about checking if the Tank Buster actually works?
The effect that it has (via the tooltip) wouldn't be one that displays anywhere in the combat screen; since a target's softness rating isn't displayed, it can't be "modified" visually.
Have you done statistical analysis on the effects of it vs armored targets? If so, do you have some charts I can peruse?
Hmmm, testing the Tank Busting trait could be checked by Ground Attacking/Interdicting multiple times variously Hard ground units and checking that against not employing a TB trait Leader, different skilled Leaders and no Leader Wings of CAS only, mixed and TAC only Wings and also checking against 100% soft units as well. Re-do until you have a good sample and analyse the result, I guess. Lengthy but not absolutely the most scientific way unless someone has a better idea!
Have I done that yet? No. Am I going to, may be if I have to unless someone more wiser who has already done it provides that kind of statistical data and analysed it already. Could I be wrong, well yes. I did mean it in the context of modifying the air attack efficiency, but I am very willing and interested in ascertaining as the whether Tank Busting actually improves the air attacks effectiveness against hard targets. Very interested, but if this has already been done to death or I test it and find out that it does I won't be disappointed, but I concede that I made an uninformed blanket statement in the above post you quoted.
It's hard to peruse everything one writes on a game forum!
oWell, there is at least a simple answer to this problem!
For attack, you want to use as small stacks as you can get away with. No matter what stacking penalty is applied, your total attack is always largest for single planes going to different targets (since the penalty is applied at the target, not the starting point).
For defense, you want to put in as many planes against each target as you can, as long as it does not exceed the point of peak strength (if one exist). However, in reality the number of fighters you have at your disposal is probably comparable to the number of bombers your opponent has. Thus, the optimum would be to use stacks of similar size to those of the attacker in order to meet all the threats.