Author Topic: C# Ground Forces Composition  (Read 14293 times)

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Offline Jorgen_CAB

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Re: C# Ground Forces Composition
« Reply #60 on: September 25, 2018, 07:03:45 PM »
You also have a few other important thing that size provide which is the rate at which the enemy will engage them or something else. Such as a Vehicles with one medium gun being better then vehicle with two guns, that only holds true when compared with each other. When you mix troops together you will then see that the smaller size of the the vehicles with two guns meas they will use their firepower more effectively when they have other units shielding them, having less size for more guns will give them far more time to use them effectively.

You basically always want glass-cannons being as small as possible so they are not hit as often while you want something heavily armoured and beefy OR cheap to soak enemy shots.

This is only the case with bombardment weapons where the infantry are more likely to be targeted than the artillery; when both the tanks and infantry are front line units, having infantry to "soak" the hits doesn't change the equation any.

Let's consider a hypothetical tank with 2 weapons that's size 75, and a tank with 1 weapon that's size 50.

If we assume 750 size of tanks on both sides, those 2 weapon tanks fire 20 times (10*2), and the 1 weapon tanks fire 15 times. The 2 weapon tanks are inflicting 33% more damage, but have two thirds the health - they'll lose.

Then give both sides 750 size in tanks and 3000 size in infantry. The 2 weapon tanks fire 20 (10*2) shots, 4 hit enemy tanks, and 16 hit enemy infantry (are ignored for this scenario). The single weapon tanks fire 15 shots, 3 hit enemy tanks, and 12 hit enemy infantry. The 2 weapon tanks are still inflicting 33% more damage, but still have two thirds the health. The existence of the infantry might make the battle last longer, but it doesn't change the ratio of losses - the 2 weapon tanks still lose.

You could argue that the 2 weapon tanks are inflicting more losses to the infantry, but the inverse is also true - those 3000 size worth of infantry will sometimes hit and kill tanks instead of infantry, and each 2 weapon tank they kill is a much bigger loss than every 1 weapon tank they kill.

That is not really how the economy work... I would look at the amount of GUNS you bring not tanks. The purpose of the dual Anti-Tank guns is to kill tanks and the number of guns is what matter to its general size.

The dual wielding tanks cost LESS per gun you bring and has a smaller footprint, thus you can bring a greater padding of other stuff to protect it. A hypothetical example would be that I bring 10 tanks with 20 guns and you bring 20 tanks with one gun... which mean we will kill an equal number of tanks. But 10 tanks with two guns are both smaller in size and cheaper in cost for what it is suppose to be doing thus you can bring more infantry to protect it which means they are even LESS likely to get hit and will destroy more tanks.

There is also the way you deploy the formations. I think that you would more likely deploy dual wielding anti-tank tanks in the defensive, that will make them survive even longer since they will be harder to hit. You would deploy your infantry killing tanks in the offence since you usually want them to manage good breakthroughs.

To be honest I don't think any tank is very effective in the soaking area in comparison to infantry cost wise. Size wise yes... but not per cost.
 

Offline Jorgen_CAB

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Re: C# Ground Forces Composition
« Reply #61 on: September 25, 2018, 07:15:24 PM »

IIRC the size of the frontline is defined by the size of the troops you place there. If your enemy frontline is sufficiently larger than your own he will gain a greater chance of Breakthrough attacks, modeling your positions getting overrun in tides of steel and men.


Yes... but that was not what I meant. What I meant was that advantage in number should only take you so far in general. A smaller force you likely be defending a smaller area and you can't really attack with all your your forces at once. Having infinitely long front lines able to all attack at the same time make no real sense. I just meant there should be some rules to limit the amount of size that can attack a smaller size in the front line.

This would mean that you would always take at least some losses and even a smaller force could hold out for some time even if it is doomed to succumb.

« Last Edit: September 29, 2018, 12:19:21 PM by Jorgen_CAB »
 

Offline Bremen

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Re: C# Ground Forces Composition
« Reply #62 on: September 25, 2018, 08:45:17 PM »
This is true until the 1 weapon tank is replaced by a tank with both an anti vehicle and a crew served anti personnel weapon. It will still be notably smaller than the 2 main weapon tank, if by a small margin, but it's murdering the enemy infantry in droves. The ability to take more actions, more shots, per turn is a major advantage in any turn based system, and Aurora C# ground combat rules are definitely very turn based combat like. The only exception would be if the actions taken are sufficiently without effectiveness, but with size 750 tanks and size 3000 infantry 80% of the shots would hit infantry, so with the standard 6 shot firing rate of crew served anti personnel weapons you can expect 4.8 shots per round per tank to successfully threaten to kill an enemy infantry unit.

I never said that having both anti-infantry and anti-tank weapons were bad, just provided a formula that showed when two weapons were worse than one. And it still applies here; if the formula says a tank with a CAP and MAV is worse, then you can just have half the vehicles with MAV and half the vehicles with CAP.
 

Offline Bremen

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Re: C# Ground Forces Composition
« Reply #63 on: September 25, 2018, 09:38:43 PM »
Moving on, we can do some math with the formula.

Take the new HCAP. How good is it? It's easy to compare to CAP because it's only different in one aspect.

An infantry unit with CAP is size 12, AP 1, damage 1, shots 6. An infantry unit with HCAP is size 20, AP 1.6, damage 1, shots 6. This means that it inflicts 2.56 as much damage to anything with (adjusted) armor of 16 or higher. Plug that into the formula and we get:

(20/12)^2 = 2.78

2.78 is more than 2.56, so this means that CAP infantry will win in a straight fight against HCAP infantry, even if they both have armor 20. This isn't the same thing as saying HCAP is useless - it may perform better on vehicles than infantry, for instance - but it does mean that HCAP infantry could be categorized as a "glass cannon", which is to say the increased firepower is overshadowed by the increased fragility. And of course the comparison goes even better for CAP against anything with an armor of 10 or even 15. I wont go as far as to say never use HCAP infantry, but I will say that CAP infantry are going to generally be better, even if your opponent never uses a unit with armor <2.

The numbers are different on a light vehicle, since a CAP light vehicle is 24 and an HCAP is 32:

(32/24)^2 = 1.78

1.78 is much lower than 2.56, so HCAP light vehicles definitely outperform the CAP version against targets with armor of 16 or more. Since light vehicles always have a base armor multiplier of 2, this means that HCAP light vehicles will definitely be at an advantage in a fight with CAP light vehicles, though the latter would still outperform them when fighting very low armor opponents, like a mass of light infantry.


How about CAP vs personal weapons for infantry? CAP has the same stats as personal weapons but gets 6 shots, so it's straight up 6 times better. They both have the same AP, so armor doesn't matter. CAP infantry is size 12 and normal infantry is size 5.

(12/5)^2 = 5.76

5.76 is slightly less than 6, so we would expect a formation of nothing but CAP infantry to (barely) beat the same size of infantry with personal weapons. This is probably a good balance point, since personal weapon infantry works better at absorbing damage and garrisoning, and therefor CAP infantry performing better in a straight fight doesn't obsolete personal weapon infantry.



Other than that, after playing around with the numbers I do want to say that I think autocannons need a buff (unless I'm missing something crucial about them). The light autocannon is still straight up worse than even the nerfed HCAP, since it's heavier, has less AP, and 3 20 damage shots are statistically worse than 6 1 damage in every situation. I'd suggest either making it AP 20, putting it in the HCAP's old role but heavier and half as effective against infantry, or possibly upping the damage to 30 and making the autocannon line specialized against high health, low armor targets (the LAC would still be weaker than the HCAP against anything with armor 16 or higher with this change, but it would be closer).
« Last Edit: September 26, 2018, 12:52:47 AM by Bremen »
 

Offline Jorgen_CAB

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Re: C# Ground Forces Composition
« Reply #64 on: September 28, 2018, 03:55:18 PM »
One other thing that I realized is how expensive combat supply is and this totally change the way we need to look at high quality infantry as a viable component in our war plans.

Since supply is based on your weapon and don't consider armour, mostly reflecting ammunition it means that a Power Armoured infantry draw as much supply as a regular infantry when using the same weapon.

A single vehicle with 500GSP has a cost of roughly 2.5 and will be enough to sustain about 500 infantry (power armoured or regulars) for 30 hours or ten combat rounds.

500 light armoured infantry will cost you 5 so you pay their entire build cost in just 60 hours of combat while a Power Armoured Infantry get about 120 hours of combat to cover their production cost.

This means that Powered Armoured infantry are quite likely allot cheaper in combat cost-wise as well as size-wise. I assume that combat can easily drag on for several months if the fights are relatively even.
« Last Edit: September 28, 2018, 04:31:57 PM by Jorgen_CAB »
 

Offline Hazard

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Re: C# Ground Forces Composition
« Reply #65 on: September 28, 2018, 05:06:01 PM »
Looking at the Pacific theater of WW2, most island battles seem to last either less than a week, or the better part of a month, depending.There were exceptions, but they were uncommon.

Now, it's kind of unrealistic to compare these battles directly with the planet wide battles you are likely to see in Aurora, which would most likely take a good deal longer, especially as the size of the garrison that needs to be engaged increases. But several months is probably a fair estimation, or at least until the attacker manages to bring in a wave of fresh troops. Having the ability to reinforce will likely decide a lot of planetary battles.

That does mean you need a lot of supplies. And I do mean a lot. And everybody's logistics arm hates battles fought on planets with the Rifts, Forest, Mountain or Jungle dominant terrain. And gods help you if it's Mountain Jungle terrain against entrenched infantry and static units. You need massive numerical advantages on the offense just to break even in trading troops, and it'll eat through your supplies like you wouldn't believe because of the fortification stacking for the defense.
 

Offline Jorgen_CAB

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Re: C# Ground Forces Composition
« Reply #66 on: September 28, 2018, 05:22:06 PM »
Looking at the Pacific theater of WW2, most island battles seem to last either less than a week, or the better part of a month, depending.There were exceptions, but they were uncommon.

Now, it's kind of unrealistic to compare these battles directly with the planet wide battles you are likely to see in Aurora, which would most likely take a good deal longer, especially as the size of the garrison that needs to be engaged increases. But several months is probably a fair estimation, or at least until the attacker manages to bring in a wave of fresh troops. Having the ability to reinforce will likely decide a lot of planetary battles.

That does mean you need a lot of supplies. And I do mean a lot. And everybody's logistics arm hates battles fought on planets with the Rifts, Forest, Mountain or Jungle dominant terrain. And gods help you if it's Mountain Jungle terrain against entrenched infantry and static units. You need massive numerical advantages on the offense just to break even in trading troops, and it'll eat through your supplies like you wouldn't believe because of the fortification stacking for the defense.

Combat the likes of tiny island are probably being something like attacking a military base or something like that. Invading a planet with millions if not billions of people should take way longer to conclude and eat tremendous amount of troops. Smaller bases are much more likely to be severely outnumbered where large populated worlds won't as easily.

You will of course try to find really easily defend-able military bases where your troops get allot of benefits from fortifying their units. So they might still be able to hold out long enough for some relief force our counter strike being mustered to thwart that invasion attempt.

Experience will tell... one thing is at least clear... attacking will cost you lot's and lots of expenditure of resources.

At least that is the way I see it for the most part.
 

Offline Jorgen_CAB

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Re: C# Ground Forces Composition
« Reply #67 on: September 29, 2018, 12:38:52 PM »
Moving on, we can do some math with the formula.

Take the new HCAP. How good is it? It's easy to compare to CAP because it's only different in one aspect.

An infantry unit with CAP is size 12, AP 1, damage 1, shots 6. An infantry unit with HCAP is size 20, AP 1.6, damage 1, shots 6. This means that it inflicts 2.56 as much damage to anything with (adjusted) armor of 16 or higher. Plug that into the formula and we get:

(20/12)^2 = 2.78

2.78 is more than 2.56, so this means that CAP infantry will win in a straight fight against HCAP infantry, even if they both have armor 20. This isn't the same thing as saying HCAP is useless - it may perform better on vehicles than infantry, for instance - but it does mean that HCAP infantry could be categorized as a "glass cannon", which is to say the increased firepower is overshadowed by the increased fragility. And of course the comparison goes even better for CAP against anything with an armor of 10 or even 15. I wont go as far as to say never use HCAP infantry, but I will say that CAP infantry are going to generally be better, even if your opponent never uses a unit with armor <2.

The numbers are different on a light vehicle, since a CAP light vehicle is 24 and an HCAP is 32:

(32/24)^2 = 1.78

1.78 is much lower than 2.56, so HCAP light vehicles definitely outperform the CAP version against targets with armor of 16 or more. Since light vehicles always have a base armor multiplier of 2, this means that HCAP light vehicles will definitely be at an advantage in a fight with CAP light vehicles, though the latter would still outperform them when fighting very low armor opponents, like a mass of light infantry.


How about CAP vs personal weapons for infantry? CAP has the same stats as personal weapons but gets 6 shots, so it's straight up 6 times better. They both have the same AP, so armor doesn't matter. CAP infantry is size 12 and normal infantry is size 5.

(12/5)^2 = 5.76

5.76 is slightly less than 6, so we would expect a formation of nothing but CAP infantry to (barely) beat the same size of infantry with personal weapons. This is probably a good balance point, since personal weapon infantry works better at absorbing damage and garrisoning, and therefor CAP infantry performing better in a straight fight doesn't obsolete personal weapon infantry.



Other than that, after playing around with the numbers I do want to say that I think autocannons need a buff (unless I'm missing something crucial about them). The light autocannon is still straight up worse than even the nerfed HCAP, since it's heavier, has less AP, and 3 20 damage shots are statistically worse than 6 1 damage in every situation. I'd suggest either making it AP 20, putting it in the HCAP's old role but heavier and half as effective against infantry, or possibly upping the damage to 30 and making the autocannon line specialized against high health, low armor targets (the LAC would still be weaker than the HCAP against anything with armor 16 or higher with this change, but it would be closer).

I think HCAP seem to be in a good place right now.

The fact that it is suppose to be good against high armoured units is quite clear to me.

A few very important things that you miss is the amount of space the HCAP take up in the defensive line versus an equal amount of CAP for engaging high armour target. Since these units are glass cannons it is quite important they are not hit in the first place.

The second thing is how effective they are per supply point used which as I have noticed are going to be more important than the units initial construction cost.

An HCAP will spend 6*1*1.6=9,6 SPP and do 6 damage against 1.6 armoured infantry, that is 1.6 SPP per damage.
AN CAP will spend 6*1*1=6 SPP and do 2.34 damage against 1.6 armoured infantry, that is 2.56 SPP per damage.

An HCAP will spend 6*1*1.6=9,6 SPP and do 5.20 damage against 2.0 armoured infantry, that is 1.85 SPP per damage.
AN CAP will spend 6*1*1=6 SPP and do 1.5 damage against 1.6 armoured infantry, that is 4 SPP per damage.

That supply will mount up quite allot over time in cost as will the increased chance (on equal cost) of the CAP unit to get hit as well.

So... you need to factor in more than just build cost and the units fighting in isolation not in a combined arms force.

The same goes for calculating cost of vehicles and their use of them in an army as a whole. Artillery for example will burn huge amounts of supplies as will vehicles armed with anti-vehicle cannons. A single medium artillery cannon will burn 13.5 SPP... which are the same amount of supplies as almost 14 infantry with personal weapons.

The only thing I don't fully understand with the combat model so far is if there are some limitation of how many units can be at the front and how many front units that can fight each other every turn. Can an unlimited amount of front units fight a very small enemy front line and force. Given the cost in supply and build of artillery I might sort of question their worth if there are no restriction on front units engaging each other. It might just be me that don't fully understand the combat model. But in reality artillery is a strength multiplier and there is a limitation for how much force you can bring in the front lines and pit against the enemy front lines at any given time. More is not always better, especially when there are enemy area effect weapons in play. WW2 was the first real war where formations needed to become dispersed and fight over vast areas as a result. Artillery was extremely dangerous as was tank weapons.

I think that adding some sort of bonus to front line units from bombardment units could be important. Just adding firepower will likely see them either not used or used too much based on their strength versus cost. Say that having support artillery of air cover make your attacking/defending front units harder to hit, based on the abstraction of supporting front line operation. Or something like it.

There also is the issue of hit point versus damage being a linear relationship... this makes high damage weapons just bad from a supply perspective since many targets will be extremely expensive to kill over other where a low damage weapon will never be. Sure... there are not that many high AP low damage weapons around... but that is what I would look for from a cost AND size perspective.

Perhaps a SPP formula of something like AP*Shots*((Damage+10)/2). This would not make the damage trait so overwhelmingly expensive and unbalanced for what it actually does in combat.
« Last Edit: September 29, 2018, 01:40:15 PM by Jorgen_CAB »
 

Offline Whitecold

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Re: C# Ground Forces Composition
« Reply #68 on: September 29, 2018, 06:09:42 PM »
The only thing I don't fully understand with the combat model so far is if there are some limitation of how many units can be at the front and how many front units that can fight each other every turn. Can an unlimited amount of front units fight a very small enemy front line and force. Given the cost in supply and build of artillery I might sort of question their worth if there are no restriction on front units engaging each other. It might just be me that don't fully understand the combat model. But in reality artillery is a strength multiplier and there is a limitation for how much force you can bring in the front lines and pit against the enemy front lines at any given time. More is not always better, especially when there are enemy area effect weapons in play. WW2 was the first real war where formations needed to become dispersed and fight over vast areas as a result. Artillery was extremely dangerous as was tank weapons.

I think that adding some sort of bonus to front line units from bombardment units could be important. Just adding firepower will likely see them either not used or used too much based on their strength versus cost. Say that having support artillery of air cover make your attacking/defending front units harder to hit, based on the abstraction of supporting front line operation. Or something like it.

There also is the issue of hit point versus damage being a linear relationship... this makes high damage weapons just bad from a supply perspective since many targets will be extremely expensive to kill over other where a low damage weapon will never be. Sure... there are not that many high AP low damage weapons around... but that is what I would look for from a cost AND size perspective.

I think the main intention of artillery is that they make quite good glass cannons. They do all have multiple shots, which otherwise only CAP and the autocannon line has, with reasonable AP to be suitable against all kinds of targets. Having these units in the backline where they cannot be engaged should be quite useful, and artillery does have the capability of engaging the enemy artillery to negate exactly that advantage.

As far as high AP low damage weapons go, they simply should not be a thing, and currently there don't seem to be any. The compromise autocannon currently does not look too good, so I would not be worried too much.
 

Offline Father Tim

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Re: C# Ground Forces Composition
« Reply #69 on: September 29, 2018, 07:08:03 PM »
I don't mind if it looks like combat effectiveness is going to vary wildly by Supply usage.  I think about WWI and the Shell Crisis and how over 90% of wounds/deaths were caused by artillery -- despite the fame of 'marching into machine guns' -- and I am okay with four hundred eighty power-armoured Elementals burning through supplies as fast as a million cloth-wearing riflebeings.

And I have complete confidence that if supply costs/usage truly become a problem, Steve will fix it in C# Aurora 1.01.
 

Offline Jorgen_CAB

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Re: C# Ground Forces Composition
« Reply #70 on: September 30, 2018, 06:23:23 AM »
Why not fix it before release if possible... ;)

Anyhow... I agree with the notion of having artillery in the back but it is quite inefficient for what it does in comparison with say an HCAP in the frontlines. The fact that artillery is less attacked I think is not weighed up versus the firepower and lower supply usage of CAP/HCAP for example.

The problem with the current model is that either you bring only Artillery as support or CAP/HCAP. Game mechanic wise there are no difference but the damage they do and receive versus the total cost of building and supplying them. That is what I think can be a mechanical problem.

Supply is also something you will need to fit into your transports... so bringing CAP/HCAP will in general give you both more firepower and take less space through less supply usage.

I have no problem with supply being a huge consideration... but if Artillery/Tanks and that stuff are going to spend more realistic supply versus infantry these assets also need to be more important or right out mandatory for success.

I would like to see artillery be more of a force multiplier rather than doing massive damage on its own. Such as if you don't have artillery on your own to suppress enemy artillery then enemy forces will become way stronger and harder to kill. Air-force and bombardment should work in the same way. This is basically the function of support weapon in real life as well. Support weapon allow infantry and tanks to operate unhindered more or less which is what is important. The actual damage these weapons do to enemy infantry and tanks should be more of a secondary effect.

« Last Edit: September 30, 2018, 06:39:43 AM by Jorgen_CAB »
 

Offline sloanjh

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Re: C# Ground Forces Composition
« Reply #71 on: September 30, 2018, 10:10:15 AM »
Why not fix it before release if possible... ;)

Because a fundamental Agile principle is to deliver a working vertical slice as quickly as possible and worry about fine-tuning the details in later iterations because you're almost certain to get them (the details) wrong if you try to plan them up-front :)

Note that the above should not be construed to be a criticism of the thought experiments being performed in this thread - it was simply that I saw a straight line that was too good to pass up :)  I think the thought experiments/discussions are fine as long as they don't jam up the main threads (and kudos to the OP who pulled a topic that would get lots of discussion into a separate thread from the start), and if they turn up an egregious problem then it gives Steve an opportunity to fix it before release.  But in terms of figuring out how the complex systems of rules will behave with one another, nothing beats actual experiments where a functioning game is in the hands of users who are trying to maximize their outcomes.  So having Steve spend a lot of time trying to get the "20" (in the sense of 80/20) right upfront risks actually delaying getting to the end goal of having a good working game.  From comments Steve has posted in the past I'm sure he understands this, so I'm confident that he'll fix whatever he thinks is sure to be a big enough problem to justify the schedule delay and defer the rest of it to Father Tim's 1.0.1

John
 

Offline TMaekler

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Re: C# Ground Forces Composition
« Reply #72 on: September 30, 2018, 10:57:31 AM »
I am not that familiar with the new ground system yet. But was wondering if units like artillery in the background can be attacked by air wings? At least that is what they are supposed to do, when not directly supporting the front lines.
 

Offline Jorgen_CAB

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Re: C# Ground Forces Composition
« Reply #73 on: September 30, 2018, 11:17:51 AM »
Why not fix it before release if possible... ;)

Because a fundamental Agile principle is to deliver a working vertical slice as quickly as possible and worry about fine-tuning the details in later iterations because you're almost certain to get them (the details) wrong if you try to plan them up-front :)

Note that the above should not be construed to be a criticism of the thought experiments being performed in this thread - it was simply that I saw a straight line that was too good to pass up :)  I think the thought experiments/discussions are fine as long as they don't jam up the main threads (and kudos to the OP who pulled a topic that would get lots of discussion into a separate thread from the start), and if they turn up an egregious problem then it gives Steve an opportunity to fix it before release.  But in terms of figuring out how the complex systems of rules will behave with one another, nothing beats actual experiments where a functioning game is in the hands of users who are trying to maximize their outcomes.  So having Steve spend a lot of time trying to get the "20" (in the sense of 80/20) right upfront risks actually delaying getting to the end goal of having a good working game.  From comments Steve has posted in the past I'm sure he understands this, so I'm confident that he'll fix whatever he thinks is sure to be a big enough problem to justify the schedule delay and defer the rest of it to Father Tim's 1.0.1

John

Yes... I don't think delaying the release of the game for this should be a priority.

I also agree that practical experience will quickly see any glaring imbalances.

Though... I think that things such as Artillery, Tanks, Air-force and Anti-Air should not just be a function of hits and kills. When you have it like that you will quite fast find the best solution to most problems (disregarding the rock/paper/scissor style of AP versus Armour).

Air bombardment and artillery should instead enable/disable attacks, tanks and infantry should have some impact on each others abilities other than pure combat hit/kills and Anti-air should mainly suppress enemy air-attacks rather then kill the air-craft as its main job. Bombardment from space should act like artillery but be suppressed by OTS weapons in the same way anti-air suppress air-force attacks.

If there is sort of a logarithmic effect of these weapon types you will have huge advantages with your air-force if there are no Anti-air as one example. The same with Artillery and Orbital bombardment... this is basically how things work in real life.

As is, the benefit of most support are basically just a shift to the left or right (and linear) and I guess there is very little difference from deploying just infantry in defence or back them up with some artillery and slightly less infantry.

If those support elements can give you huge benefits if unopposed it will be very hard to argue against a high supply draw even if it has a marginal effect since the enemy brought enough artillery and air-force to suppress it effectively and you the same. But if they did not have a counter to your artillery you would be almost unstoppable (given roughly equal ground forces).

This is of course just my opinion....  :)
« Last Edit: September 30, 2018, 11:21:50 AM by Jorgen_CAB »
 

Offline Jorgen_CAB

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Re: C# Ground Forces Composition
« Reply #74 on: September 30, 2018, 11:19:15 AM »
I am not that familiar with the new ground system yet. But was wondering if units like artillery in the background can be attacked by air wings? At least that is what they are supposed to do, when not directly supporting the front lines.

I'm pretty sure air-force will be able to hit support elements, but they are perhaps less likely to hit the rear part rather than the front lines in the same way attacking units in the front line are.