ulmont said:
On the other hand:
Code:
1 Inf '41 + 4 Mil '36: 30 MP, 1500 IC-days, 1.8 TC
2 Inf '41 + 2 Mil '36: 30 MP, 1700 IC-days, 2.4 TCulmont said:
The key is to take mixing into account.
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On the other hand:
The key is to take mixing into account.
Two excellent posts, and a good breakdown of the numbers for dummies ulmont - appreciated.
One question on this though:
One question on this though:
ulmont said:
First I though it was contradictory, but am I correct in my interpretation that while MIL are never MP-efficient as replacement for INF, they are indeed MP-efficient as casualtyabsorbers (bodies for the grinder) while mixed with INF? So BWA be damned, will I suffer less casualties in the campaign if I trot around 2 INF + 1 MIL?theokrat said:
And neither of those two is as good on attack as either 3 Inf '41 or 13 Mil '36 is, and neither of those two is as good on defense as either 3 Inf '41 or 8 Mil '36 is.theokrat said:
When you take mixing into account, if you keep combat effectiveness steady, you will find that you can't do any better on manpower efficiency as the full Inf build, or any better on TC than the full Mil build. Your mixed examples are both sacrificing combat efficiency over either of my pure options.theokrat said:
Dakk said:First I though it was contradictory, but am I correct in my interpretation that while MIL are never MP-efficient as replacement for INF, they are indeed MP-efficient as casualtyabsorbers (bodies for the grinder) while mixed with INF? So BWA be damned, will I suffer less casualties in the campaign if I trot around 2 INF + 1 MIL?
I should rephrase my post:
If you have a given amount of Manpower X and wnat to transform it into units in order to win a battle, then you should use INF.
If, during an attack one of you militas get targeted by an enemy then you will always suffer less manpowerloos than if the enemy targeted an INF.
The difference is that ulmont compared the costs to build something, while my point was only refering to the "running" costs that happen during a series of battles.
ulmont said:
How did you calculate? I went for BWA:
2 INF and 2 MIL: Softattack 2*(14+2)=32. For BWA *4 (#units)=128.
thats the same as 8^2*2=128 or 3^2*14=126.
That's the theory. I am unconvinced. If you lower the efficiency of your stacks in winning battles, then they will have to fight longer and will take more casualties. I suspect the increased casualties as a result of decreased efficiency will outweigh the benefit of reinforcing Mil for half the manpower of Inf.Dakk said:
Taking 2 Inf '41 + 1 Mil '36 versus the now-standard 1 Inf '41:
2 Inf '41 + 1 Mil '36 v. 1 Inf '41 will generate 30 shots, 6 will be doubled, for an effective 36.
2 Inf '41 + 1 Mil '36 v. 1 Inf '41 will receive 14 shots. Either 0 (Inf target) or 13 of these will be doubled (Mil target). On average, this will result in (14 + 14 + 27) / 3 or 18.33 effective shots, or 6.11 per target.
Dealing 36 shots and receiving 6.11 shots / target yields a ratio of 5.89:1. This is abysmal compared to the 12.85:1 ratio that 3 Inf '41 get.
In fact, this means that the stack of 2 Inf '41 + 1 Mil '36 will receive over double the hits in overcoming 1 Inf '41 that a stack of 3 Inf '41 would, meaning that even if the whole stack was Mil it would be more expensive to replace casualties compared to the 3 Inf '41.
So, in conclusion, I say thee nay.
On attack, I modeled the stack's shots dealt:shots received ratio per target against 1 Inf '41 (simulating the 3:1 odds I aim for on attack).theokrat said:
On attack:
3 Inf '41 will generate 60 effective shots against 1 Inf '41 (60 / target) and will receive 14 effective shots (4.67 / target), for a ratio of 12.85:1.
13 Mil '36 will generate 28 effective shots against 1 Inf '41 (28 / target) and will receive 27 effective shots (2.08 / target), for a ratio of 13.46:1.
On defense, I modeled the stack's shots dealt:shots received ratio per target against 3 Inf '41 (since I was thinking about beach attacks, I'm not expecting much more than that).
On defense:
3 Inf '41 will receive 42 effective shots from 3 Inf '41 (14 / target), and will deal 42 effective shots (14 / target), for a ratio of 1:1.
9 Mil '36 will receive 60 effective shots (each Mil has 8 def) from 3 Inf '41 (6.67 / target) and will deal 18 effective shots (6 / target), for a ratio of 1.11:1. 10 Mil reverse the ratio to 1:1.11. This is adjusted up 1-2 Mil; the original calculations had ignored the exceeded defensiveness.
I don't think that's the right metric.theokrat said:
ulmont said:
In your terms:
8 Milita generate 16 shots. Their Defensiveness will be exceeded. We assume each Milita is only targeted by one attacking INF. 14 + (14-8)=20. Attackers generate 3*20=60 shots, for an avarage of 7.5 shots per defender. Thats an 5.33 : 7.5 = 0.71 ratio.
One INF and 4 MIL generate 14+8=24 shots. With a propability of 80% an attacker will shot at an Milita and exeed its DEF, with 20% prop he will target the INF and not exceed its DEF leaces us with 14 + 0.8 * (14-8) = 18.8. So the attakers in total: 18.8*3= 56.4 shots or 11.3 per defender. Thats a 8 : 11.3 = 0.71 ratio. That is exactly the same! And 25% cheaper in manpower, 6% cheaper in IC.
Lets assume we fight at 99% instead of 100% combat eff.:
8 Militas now generate only 8 shots, 1INF+4 Mil generate 13+4=17. So the only milita stack suddenly lost 50% of its fighting power, while even one INF will reduce that to 30%. The difference is 40% more fighint power for the mixed stack.
Yes, I need to increase the defender equivalent to 9 or 10 Mil '36 to equal 3 Inf '41 on defense (player's choice: the ratio is slightly in favor of infantry at 9 or militia at 10 by the same amount). I did the recalculation above.theokrat said:
[1 Inf '41 + 4 Mil '36 defend as well as 8 Mil '36 against 3 Inf '41]
I completely agree. I have agreed that Inf are cheaper in MP than Mil when considering equal defensive effectiveness. I have disagreed that 1 Inf + 2 Mil or 2 Inf + 1 Mil is a useful stack.theokrat said:
Yes, Mil should go home rather than fight with reduced combat efficiency. This leads to a "only use Mil on defense" conclusion.theokrat said:
ulmont said:
I still think it is. Lets compare it to unmixed stacks:
5 * (1INF + 2 MIL) = 5325 IC*d = 8 INF.
Mixed generate 70+20=90 shots, vanilla generates 8*14=112 shots.
Each units in the mixed stack gets hit by 1/15 of the attackers shots, but for the 2 thirds of milita they get exceeded: 1/15 * (1 + 2/3 * 6/14 )= 0.086.
Each unit from the vanilla stack will get hit by 1/8 = 0.125 of the attackers shots.
So the mixed stack can deal only 20% the damage of the vanilla stack, but receives 30% less hits per unit. Favours the mixed stack.
Comparing to Milita:
3* (INF + 2 MIL) = 3200 IC*d = 16 Militia
mixed generate 54 shots, compared to 32 of the militas.
The militas receive 1/16 * (1+6/14)=0.09 of the attackers shots, since they are all exceed. Mixed stack gets 1/9 * (1 + 2/3 * 6/14)=0.14 of the attackers shots.
Leaves us with the mixed stack receiving 60% more shots per unit than the militas, but still having 70% more attack themselves.
So the stack propsed by Dakk is better than any "pure" militia or INF stack. I dont know if its better than another mixed composition tough.
Im using Militias as a replacement for Gar. Just added ability to attach MP. Much better value for money...err IC than Gars.
Couldn't we test this by going into multiplayer and staging battles with fixed test forces?
Testing empirically is alot more effort for less accuracy than the power of math. Especially when thrown around by theokrat. Makes me all giddy.Viz said:
More math to follow much later tonight, after work, but I would like to note the following caveats of your analysis of the mixed stack:theokrat said:
You tested it 1) on defense only and 2) using constant IC-day values.
For constant manpower, pure infantry would be superior. For constant TC, pure militia would be superior.
IC-days are rarely the main limiting factor for a nations ground army, as compared to TC or MP limits (and the closer IC-days are to a limiting factor, the worse the TC problems usually are). Accordingly, I think you have chosen the worst possible option.
ulmont said:I'm hurt.
I can't believe I was so callous.. of course I get giddy when you chuck out the powermath too!EDIT: I'm following this intently - first I was going to try my next GC (with a ((somewhat)) MP-rich, IC-poor nation) with mixed INF+MIL, then I wasn't, and now I'm inclined to to again.. oh the agony of min/maxing!
ulmont said:
Well, thats kind of what i said in the very first post of this thread. I do not claim IC is the limit for most nations- i know it is not. But then again, some nations are, at least over a period limited by this. I dont attempt to see which unit is best, but to find out which might be of use and in what kind of situations...
Besides i think the biggest flaw in these calculations is neither of us included ane MTE (see my sig).
If not even taking Def into account then, even for manpower reasons a mixture of 2 INF + 1 MIL would be best on the defence in 41.
MTE would only favor the Militia, I think, considering they were already taking a large number of double-shots and have the most opportunities to avoid MTE (more targets).theokrat said:
When you say Def, do you mean the concept you define in your thread, or the Defensiveness stat?theokrat said:
Assuming you meant your MTE-thread-Def concept, and ignoring MTE for a moment: 2 * (2 Inf + 1 Mil) = 50 MP.
50 MP = 5 Inf, 4 Inf + 2 Mil, 2 Inf + 4 Mil, 3 Inf + 6 Mil, 2 Inf + 8 Mil, or 10 Mil.
On defense, against 5 Inf '41, assuming unit-level targeting and no MTE:
5 Inf generate 70 shots, which don't overcome toughness, or 14 effective shots per target.
5 Inf generate 70 shots, which don't overcome defensiveness, or 14 effective shots per target.
Ratio of 14:14 or 1:1.
4 Inf + 2 Mil generate 60 shots, which don't overcome toughness, or 12 effective shots per target.
5 Inf generate 70 shots. 4/6 target infantry, 2/6 target mil. Effective shots of 5 * (2/3 * 14 + 1/3 * (14 + (14 - 8))) = 5 * (2/3 * 14 + 1/3 * 20) = 5 * 16 = 80 effective shots, or 13.33 per target.
Ratio of 12:13.33 or 1:1.11.
3 Inf + 4 Mil generate 50 shots, or 10 effective shots per target.
5 Inf generate 70 shots. 3/7 target infantry, 4/7 target mil. Effective shots of 5 * (3/7 * 14 + 4/7 * 20) = 5 * (122 / 7) = 87.14 effective shots, or 12.45 shots per target.
Ratio of 10:12.45 or 1:1.25.
2 Inf + 6 Mil generate 40 shots, or 8 effective shots per target.
5 Inf generate 70 shots. 2/8 target infantry, 6/8 target mil. Effective shots of 5 * (2/8 * 14 + 6/8 * 20) = 5 * (148 / 8) = 92.5 effective shots, or 11.56 shots per target.
Ratio of 8:11.56 or 1:1.45.
1 Inf + 8 Mil generates 30 shots, or 6 effective shots per target.
5 Inf generate 70 shots. 1/9 target infantry, 8/9 target mil. Effective shots of 5 * (1/9 * 14 + 8/9 * 20) = 5 * (174 / 9) = 96.67 effective shots, or 10.74 shots per target.
Ratio of 6:10.74 or 1:1.79.
10 Mil generate 20 shots, or 4 effective shots per target.
5 Inf generate 70 shots. 1/1 target mil. Effective shots of 5 * 20 = 100 effective shots, or 10 shots per target.
Ratio of 4:10 or 1:2.5.
So, if we keep manpower constant, defense capacity drops steadily as 1 Inf is replaced with 2 Mil...
Why most comparisons in this thread are of 36 mil and 41 inf? I understand this is the case for the beginning of barbarossa, but 41 period is very unfair towards militia. Comparing 36 mil to inf 36 & 39 and inf 43 to mil 43 gives much different results, and is viable in game i.e. first comparison would be for China theater, second for Europe were one side (either Germany or SU) should be losing by then.
ulmont said:
This is not so obvious. On the one hand Militas due to their large number make MTE much less likely to happen to us. However their Def is already exceeded. One problem is that MTE will hardly do any harm to the enemy. An example form above was 9 militias or 3 Inf defending against 3 incoming Infs. Each militia generates only 2 shots, so we do not have any chance to get double shots. For the INFs on the other hand we only need two to pick the same target to get double shots - thats already happening in 25% of all cases.
ulmont said:
That is the same. In the other thread i defined a parameter "Def" (i admit i called it sub-optimal) as the stat Defensiveness, just i took it in units of the enemies attack for convenience. But its really the same, just makes it easier to compare different years.
ulmont said:
My first calcuation was without taking Defensiveness into account. However i recalculated and you are right, even in this case it does not make much difference.
Borsook said:
In the first post i choose this setup because it was bad for Militas and showed that even in this "worst case" scenario they had a shot. However i was wrong about the targeting alogarythm at the time as i assumed targeting would happen per shot. I will have to rework it but its not trivial to take MTE into account for a mixed stack. Or at least the results are not as vivid anymore