Ground Unit Hit Mod is Pointless?

[Armand12 (OP)]

I need some verification on my math, I've been trying to make a spreadsheet to theorycraft some ground unit designs, but I've found something annoying/disturbing.    It's annoying if I've missed something, but it's disturbing if I haven't, probably a bug then I suppose. 

Edit 1:I failed to communicate my problem.    The actual value of "To Hit Chance" and "Final Chance To Hit" don't actually matter.    If "To Hit Chance" is less than "Final Chance To Hit" as far as I understand it, a hit is scored in ground combat.   

When a formation element is engaged in combat against a hostile formation element, supply is checked.   If supply is not available, the number of units firing will be 25% of normal.   Each attacking unit uses the following process:
The To Hit Chance is determined.   The base chance is 20% multiplied by the 'Dominant Terrain To Hit Modifier', the firing element morale / 100 and, if the target is not fortified, the base to hit chance for the target element unit class. 
The Fortification Modifier for the target element is determined, which is the current fortification level of the target multiplied by the 'Dominant Terrain Fortification Modifier'.   If the target is not fortified, the Fortification Modifier is 1. 
The Environment Modifier is calculated, taking into account gravity, pressure and temperature and whether the firing element has capabilities in those environments.   Each environment for which the element is not trained has a x2 modifier. 
The Terrain Capability Modifier is calculated.   If the element is trained to fight in the dominant terrain, the modifier is 0.  5. 
The Final Chance to Hit is calculated as To Hit Chance / (Fortification Modifier * Environment Modifier * Terrain Capability Modifier)

I've simplified the above into the following formulae:
To Hit Chance = (20%*Terrain Hit*Target Unit Hit Mod)
Final Chance to Hit = To Hit Chance / (Target Fort.  *Environment Mod*Terrain Capability Mod)

So let's assume the target unit is a light vehicle, and it's Forest terrain. 
Light Vehicle:  Max Self-Fort 3, Hit mod 0.  4
Forest Terrain:  Fort Multiplier 1.  25, To Hit 0.  5

Let's assume the unit has a fortification of 1, and the attacker has full environment & terrain capability for this exercise.    Thusly:
To Hit Chance = 20% * 0.  5 Terrain Hit * 0.  4 Unit Hit Mod = 0.  04 or 4%
Final Chance to Hit = 4% / ( 1 Target Fort * 1.  25 Terrain Fort * 1 Environment Mod * 0.  5 Terrain Capability Mod) = 4% / 0.  625 = 0.  064 or 6.  4%

So To Hit is 4% and Final Chance is 6.  4%, therefore the attack roll proceeds to the next step. 

Next let's look at a Heavy Vehicle
Heavy Vehicle:  Max Self-Fort 3, Hit mod 0.  8
Forest Terrain:  Fort Multiplier 1.  25, To Hit 0.  5
To Hit Chance = 20% * 0.  5 Terrain Hit * 0.  8 Unit Hit Mod = 0.  08 or 8%
Final Chance to Hit = 8% / ( 1 Target Fort * 1.  25 Terrain Fort * 1 Environment Mod * 0.  5 Terrain Capability Mod) = 4% / 0.  625 = 0.  128 or 12.  8%

So To Hit is 8% and Final Chance is 12%, therefore the.  .  .   wait.  .  . 
Why are they BOTH double? 

If you run the numbers based on the formulae I've cobbled together, you can check each unit type in any terrain, Ground Unit Hit Mod serves no purpose, it doesn't make a target any easier or more difficult to hit, since both formulae use it in the same way.    The only thing that matters is the amount of Fortification a Unit has managed to accrue as far as the Hit/Miss calculation is concerned. 

Fortification Side Note for Forest Terrain or similar with 1.  25 Fort Mod, without Commander Skills, 1.  7 Fort is all it takes to dodge all attacks, and with 50% Ground Offence Commander Skill it only takes 3.  3 Fortification, making infantry & static immortal with a minor investment in construction units.    1.  4 Fort on a Jungle Mountain world makes everything immortal, assuming I've read/calculated correctly. 

[Dawa1147]

To Hit modifier only works when you attack, Fortification only when you defend(/support/rear echelon)

[TheTalkingMeowth]

I don't see the problem. The light vehicle is twice as hard to hit as the heavy vehicle. This is what you would expect to see, no?

Also, as Dawa said, fortification only applies on defense/support/rear echelon, while to hit only applies to front line attack.

[Armand12 (OP)]

I failed to communicate my problem.   The actual value of "To Hit Chance" and "Final Chance To Hit" don't actually matter.   If "To Hit Chance" is less than "Final Chance To Hit" as far as I understand it, a hit is scored in ground combat.   

Therefore, if the only effect of changing the target is doubling both values, it has no actual effect on combat.   Nothing is harder or easier to hit than anything else excepting fortification, which is a whole other mess I don't want to deal with right now.

To Hit modifier only works when you attack, Fortification only when you defend(/support/rear echelon)

Okay, so what is "the base to hit chance for the target element unit class" if it is not the "hit mod" in the ground unit design window?
I'm using the rules above quoted from Steve's post about attacking, and the only thing I am changing is the stats for the target unit.

I don't see the problem.  The light vehicle is twice as hard to hit as the heavy vehicle.  This is what you would expect to see, no?

Also, as Dawa said, fortification only applies on defense/support/rear echelon, while to hit only applies to front line attack.

The light vehicle isn't twice as hard to hit as the heavy vehicle, it's hit in just the same way except the numbers are doubled pointlessly.

[xenoscepter]

 - Let's take a looksie shall we? I seem to vaguely recall something else along these lines, but only vaguely; at any rate, I suspect Steve has a penchant for using too many Capital Letters.

 - So let's take look at our contenders, yeah?

Light Vehicle, 0.4 Hit Mod

Heavy Vehicle 0.8 Hit Mod

 - Nice. So let's assume the defender will have 2 Fortification, for funzies and furthermore let's also assume that the terrain is Desert, because we can.

The To Hit Chance is determined. The base chance is 20% multiplied by the 'Dominant Terrain To Hit Modifier', the firing element morale / 100 and, if the target is not fortified, the base to hit chance for the target element unit class.

^ Let's start here then and see if we can't get to the bottom of it all.
 - We have a "Base Chance", and a "Base TO HIT Chance" which is a weird choice of words to say the least. We can tell from context that the Base To Hit Chance is related to unit class, thus it follows that it is, in fact, our "Hit Mod". Thusly:

The To Hit Chance is determined. The base chance is 20% multiplied by the 'Dominant Terrain To Hit Modifier', the firing element morale / 100 and, if the target is not fortified, the Hit Mod for the target element unit class.

^ Now we're getting somewhere! If we assume that the "Hit Mod" is a percentage given in decimal format, we can assume that a Hit Mod of 0.4 and 0.8 are 40% and 80% respectively. So following that logic our "Base Chance" becomes a 0.2 instead of a nasty 20%. Thusly:

The To Hit Chance is determined. The base chance is 0.2 multiplied by the 'Dominant Terrain To Hit Modifier', the firing element morale / 100 and, if the target is not fortified, the Hit Mod for the target element unit class.

^Alright, this gives us our first equation!

(Base Chance * Terrain Mod * Morale) / 100

OR, if the target is NOT fortified

(Base Chance * Terrain Mod * Morale) / (100 + Hit Mod)

 - Nice, now let's move on to the next statement!

The Fortification Modifier for the target element is determined, which is the current fortification level of the target multiplied by the 'Dominant Terrain Fortification Modifier'.   If the target is not fortified, the Fortification Modifier is 1.

^This is nice and simple, although I don't know what the "Dominant Terrain Fortification Modifier" for Desert, so let's change the parameters of our example to exclude any type of "Dominant Terrain" whatsoever, for simplicity's sake.

ONWARD!

The Environment Modifier is calculated, taking into account gravity, pressure and temperature and whether the firing element has capabilities in those environments. Each environment for which the element is not trained has a x2 modifier.
The Terrain Capability Modifier is calculated. If the element is trained to fight in the dominant terrain, the modifier is 0.5.

^Pretty straightforward as well, but since I've excluded terrain modifiers for the sake of expedience, this is a non-factor. I'll assume the forces are both fighting in a suitable gravity, pressure, temperature environment.

AND FINALLY!

The Final Chance to Hit is calculated as To Hit Chance / (Fortification Modifier * Environment Modifier * Terrain Capability Modifier)

^Yeah! That's the good stuff, right there, that's what were after innit? However, before we go any further, let's doll that up a smidge, eh?

The actual Chance to Hit is calculated as To Hit Chance / (Fortification Modifier * Environment Modifier * Terrain Capability Modifier)

- Much better. Now we can break it down to equation... oh wait. "To Hit Chance", the hell is that, eh? It's probably the results of our prior equation... so let's sus that out first.

Attacker:

(Base Chance * Terrain Mod * Morale) / (100 + Hit Mod)

Defender:

(Base Chance * Terrain Mod * Morale) / 100

For the sake of simplicity, I do so love her by the way , we are going to assume that the unit's Morale is "full", which I'm assuming means it is equal to 100, AKA 100%.

 - So, an the attack our Heavy Vehicle will have a "To Hit Chance" of 0.18518518518... sweet Christ on a stick that's hideous! Let's just round up then to 0.2 and call it a day. However, out Light Vehicle will have... 0.1923076923, or just 0.2, well now... ain't that a pickle, huh? Seems they both have an equal chance to get zapped while on the attack. How about defense then. We're assuming a fortification of 2, so both numbers are just doubled meaning Hit Mod is indeed useless... or is it?  We still don't have an actual To Hit Chance, just the "To Hit Chance" used to calculate it. Since Fortification Modifier is always 1 when attacking on account of an attacker having 0 Fortification, if we assume that we are defending, the Fortification doubles our chance to be hit.

 - However, this still results in out Light Vehicle and our Heavy Vehicle being equally easy to hit on the attack or defense... or does it? The defender doesn't take into account their Hit Mod, since they do possess fortification. Thus, while our vehicles are equally easy to hit on the attack, they are also just as easy to hit on the defense since Hit Mod is removed from the equation, and thus both have a 0.4 To Hit on the defense. Broken as hell it would seem... or is it? "To Hit Chance / (Fortification Modifier * Environment Modifier * Terrain Capability Modifier)", that's a forward slant, we gotta divide for our actual To Hit Chance calculation. However, that doesn't matter since the Hit Mod isn't part of the calculation when defending, and when attacking it's divided by 1 rendering the difference academic at best.

 - An interesting turn of events to be sure, but let's try a few more things before we call it borked. Let's try this:

(Base Chance * Terrain Mod * Morale / 100) / Hit Mod
^ This formula changes the order of operations to allow Hit Mod to modify the base equation as a whole.

 - Under this our Heavy Vehicle has a To Hit chance of 0.25 and our Light Vehicle has a To Hit Chance of 0.5, meaning the Heavy Vehicle is MORE evasive!? That can't be right... what if we made the equation as so:

(Base Chance * Terrain Mod * Morale / 100) * Hit Mod
^ This one uses multiplication of Hit Mod instead of division.

 - Under this equation our Light Vehicle has a meager 0.1, or 10% chance of being hit on the attack, while the Heavy Vehicle has a 0.2 or 20% chance... that's twice as easy to hit! That seems more in line with what we could expect, and of course it still doesn't alter the defense chances if the vehicle is fortified, since a stationary target is much easier to hit.

 --- In conclusion, we need a ruling from Steve to be sure, since his presentation of the rules are... vague, to say the least. I think it safe to assume that:

(Base Chance * Terrain Mod * Morale) / 100

OR, if the target is NOT fortified

(Base Chance * Terrain Mod * Morale / 100)*Hit Mod

^Determines the "To Hit Chance" for:

To Hit Chance / (Fortification Modifier * Environment Modifier * Terrain Capability Modifier)

^ Which is used to determine the actual To Hit Chance that the game then uses to determine whether or not your unit is hit...

Oh, and an important note, Aurora has a weird way of representing "chance"; in that a 10% chance means 10% and a 20% chance means 20%. That is, if you have 10 Light Vehicles on the attack, you will have one of them take a hit. Thus if you have 10 Heavy Vehicles on the attack, you will have two of them take a hit. But, hey, that's what Armor, Hit Points, Penetration, Damage, and Number of Shots is there for, innit?

[DIT_grue]

So To Hit is 4% and Final Chance is 6.  4%, therefore the attack roll proceeds to the next step. 

As best I can tell, your problem isn't in the maths you're checking so laboriously, you've just misunderstood the rules. You are comparing "To Hit Chance" with the "Final Chance to Hit" which is derived from it, but if you go back and look at Steve's rule post, what happens at this point is:

6. The unit fires each weapon it has (except for non-bombardment weapons on units bombarding from support and rear-echelon field positions). If the to-hit roll is equal or less than the final chance to hit, the weapon has struck the target.

(Underline mine.) This is the same method used for many parts of the game: a random number is generated and compared to some threshold to determine whether a thing happens. So the Heavy Vehicle is twice as likely to be hit as the Light Vehicle.

[xenoscepter]

 - I'm going to put a list of equations here so we can more easily figure this out going forward, same page and all that.

The To Hit Chance is determined.   The base chance is 20% multiplied by the 'Dominant Terrain To Hit Modifier', the firing element morale / 100 and, if the target is not fortified, the base to hit chance for the target element unit class.

Code: [Select]

(Base Chance * Terrain Mod * Morale) / 100 = To Hit Chance

OR, if the target is NOT fortified

(Base Chance * Terrain Mod * Morale / 100)*Hit Mod = To Hit Chance

The Fortification Modifier for the target element is determined, which is the current fortification level of the target multiplied by the 'Dominant Terrain Fortification Modifier'. If the target is not fortified, the Fortification Modifier is 1.

Code: [Select]

Fortification Modifier = Target's Current Level of Fortification

OR, if the target is not fortified

Fortification Modifier = 1

The Environment Modifier is calculated, taking into account gravity, pressure and temperature and whether the firing element has capabilities in those environments. Each environment for which the element is not trained has a x2 modifier. The Terrain Capability Modifier is calculated. If the element is trained to fight in the dominant terrain, the modifier is 0.5

Code: [Select]

Environment Modifier =

Planet's Gravity, Planet's Pressure, Planet's Temperature

Compared Against:

Species' Gravity Tolerance, Species' Pressure Tolerance, Species' Temperature Tolerance
 - The calculations are really, really straightforward on this. I'm making some pretty big assumptions on how this one works, so I may damn well be completely wrong here. Each, environment that unit isn't trained for applies a x2 modifier... and from the language used the penalty seems to be cumulative. If a unit has been specially trained to fight in the Dominant Terrain, then it gets a 0.5 modifier. I theorize the equation would look something like this:

Code: [Select]

X * 1

OR, if the target is trained for the Dominant Terrain
OR, if the planet has no Dominant Terrain

X * 0.5^ In this example, X is can be either 1, 2, 4, or 6 to account for the number of untrained Environments, where 1 would be all three environments are trained for or fell within the species' range of tolerance and 6 would be if all three environments were not trained for and fell outside the species' range of tolerance.

The Final Chance to Hit is calculated as To Hit Chance / (Fortification Modifier * Environment Modifier * Terrain Capability Modifier)

Code: [Select]

To Hit Chance / (Fortification Modifier * Environment Modifier * Terrain Capability Modifier = Final To Hit Chance

[xenoscepter]

6. The unit fires each weapon it has (except for non-bombardment weapons on units bombarding from support and rear-echelon field positions). If the to-hit roll is equal or less than the final chance to hit, the weapon has struck the target.

(Underline mine.) This is the same method used for many parts of the game: a random number is generated and compared to some threshold to determine whether a thing happens. So the Heavy Vehicle is twice as likely to be hit as the Light Vehicle.

 - This I did not know, that means the chances are non-deterministic for Ground Battles. I wonder if the space combat is the same now... that would change a lot of things. In VB6 this was not how the RNG worked and a 20% chance meant one in five... period. Dang it, where's Iceranger when you need him.