Statistical Combat Analysis

[crzyrndm]

Sorry one more question. What is your unit size setting? I am trying to see how well a anydice model (ie. http://anydice.com/program/2ac6 - "At Least" view is the most useful) compares to your test. It would help to see percentage of casualties compare to total unit size.

Given that casualties wasn't 100%, would that mean range units aim for the first few ranks of the unit? That would makes sense if they are trying to maximize casualties instead of damage.

Largest unmodded unit size, so 120 for archers and 160 for melee units.

100% casualties (120 kills) would assume that every projectile hit a different target, all hits were fatal (100 damage/low armour achieves this), no missed targets (even with 3000 accuracy, projectiles aimed at the edge of a unit could miss because an earlier projectile made a gap), etc, etc.

[memteh]

How works damage calculation - we know. So statistics based on different damage and armour values - not so interesting now. But how calculated hit chance - very interesting. This calculation using melee_hit_chance_min, melee_hit_chance_max, melee_hit_chance_base, melee_defence, melee_attack, may be something else. I am sure, that best melee system is based on 1 hit point per man. In my own tests i can't uderstand how calculated hit chance. Have you any ideas about this?

I saw your answer in this topic, but your formula is too abstract.

P.S. Sorry for my English, it's not my native language. I hope you can understand me

[rrgg]

Have you considered looking into the effects of formations? Stats are one thing, but I've always wondered about how different things like unit spacing and guard actually impact combat.

[crzyrndm]

Have you any ideas about this?

My abstract answer was as much as I know at this point in time. It's also a very simplified version as terrain, formations, and possibly animations could also impact on it.

Have you considered looking into the effects of formations? Stats are one thing, but I've always wondered about how different things like unit spacing and guard actually impact combat.

I'll get attack/defence done before I consider further. I just don't have the time atm to sit down for 3-4 hours and get this done.

[crzyrndm]

Melee Attack vs. Melee Defence

Testing Conditions:

Units: Royal Peltasts vs. Royal Thorax Swordsmen (ie. near identical sword units with formation attack)
Testing Regime: One unit is defined as the attack unit, has its defence set to zero. One unit defined as defensive unit, has its attack set to zero. Testing values of attack and defence are given to the corresponding unit. Thus the two melee attack/defence pairs should be: (0, 0) and (test_attack, test_defence).

Extraneous stats (armour/charge/morale/damage/health/fatigue/experience) are set to values at which they will not interfere.

In a set custom battle map with the AI as the attacker controlling the defending unit, human controlling the attack unit gives no input. Remaining number of men from the victorious unit is recorded, with AI unit being recorded as a negative value (if melee defence wins, the value will be negative). Results are averaged over 5 battles.

Results

Averaged data

Graphical representation

Notes

• Melee defence is noticably less important than melee attack under the test conditions.
• It is very apparent that reaching the 95% hit limit doesn't take a very high attack value.
• 40 attack/80 defence appears to be an outlier

[stratigo]

If melee attack is so much more important then melee defense, why do oathsworn so decisively beat royal peltasts?

[crzyrndm]

A) No formation attack attribute. While it looks better than the blob, it's actually detrimental to combat ability due to the inability to spread out and envelop
B) Wider default formation. Two equal units 1v1, the wider formation will be the victor in every TW game I have tested. Because they don't have formation attack, Oathsworn make a lot of use of this to envelop the peltasts fairly decisively
C) Abilities and stat distribution. Oathsworn have a better charge, so they get their nose infront right from the start, and then the second stage of headhunt gives them more melee attack than the peltasts. By the time headhunt wears off and they're exhausted, they already have a commanding lead giving them stat bonuses through numerical advantage.

tl;dr
A whole bunch of reasons that I removed from testing. I used two units that were exactly equal other than attack/defence, but combat isn't just on those stats

[stratigo]

So, formation fighting is detrimental to your units? XD

[rrgg]

I just realized something. If what Jack said is correct then the effect of normal damage against armor is exponential. If you take, for example normal bows vs composite bows (25 damage vs 30, no AP) then against no armor that's obviously just a 20% increase in damage output, but against targets with 30 or more armor then it turns out closer to a 44% percent average damage increase for the composite bow.

Yet another reason why this game is so tricky to balance.

[JaM]

which makes sense, as arrows would have relatively similar effects on unarmored men, yet if he has some armor, increased speed thanks to better bow, and higher arrow weight will play more significant role in defeating that armor and causing the damage.

[crzyrndm]

This is what I think the theoretical plot of damage vs. armour should look like (%Damage on the vertical, Armour/Damage on the horizontal).

While armour <= to damage (x<=1 on chart), it's a linear function: (Damage - Armour/2)
When armour > damage (x>1 on the chart), it's a 1/x decay function: ((Damage²)/2) * (1/Armour)

Points of note:
50% damage: Damage = Armour
25% damage: Damage = Armour / 2
16.7% damage: Damage = Armour / 3
12.5% damage: Damage = Armour / 4

[rrgg]

That's essentially the equation I got. Although you need to differentiate between AP and normal damage. After messing around a bit I've concluded that ranged weapons are actually much better balanced than I originally gave them credit for.

Here's a graph I posted on the sling thread of normal arrow ammo vs normal sling ammo. Slings only deal more damage if the target has more than 120 armor.

[crzyrndm]

That's essentially the equation I got. Although you need to differentiate between AP and normal damage.

I ignore ap damage because it's purely an offset, which among other things, makes adding it to a generalised plot a little difficult. It's also not a particularly interesting factor as it ignores everything else

RE: slings vs. bows
The actual effective point is a lot less once you consider ammo (+2/3rds) and RoF (+1/6), but it's really not as bad as people make it out to be.

[Downtown1]

So armor doesn't matter for melee 1v1? Only melee attack/defence?

[Roach]

Exactly.. attack/defense affect the outcome of the melee. If the attack is successful, then the guy gets stabbed and the weapon damage is modified by armour and subtracted from HP and the fight continues until someone runs out of HP.

[Downtown1]

Exactly.. attack/defense affect the outcome of the melee. If the attack is successful, then the guy gets stabbed and the weapon damage is modified by armour and subtracted from HP and the fight continues until someone runs out of HP.

Is there equation for this? It seems a lot like missile damage (step 1: determine if any damage was made at all, step 2: determine actual damage based on dice roll) but I'm not sure. Equations for either of the steps would be good (preferably both)?

[crzyrndm]

Is there equation for this? It seems a lot like missile damage (step 1: determine if any damage was made at all, step 2: determine actual damage based on dice roll) but I'm not sure. Equations for either of the steps would be good (preferably both)?

Chance to hit we don't really have any specifics on (it's all done within the code, which we have no access to), but in essence:

Hit_Chance_pct = 50 + Fn(Melee_Attack, Charge) - Fn(Melee_Defence) +/- Fn(Situation, Environment)
if(Hit_Chance_pct > 95) {Hit_Chance_pct = 95}
if(Hit_Chance_pct < 20) {Hit_Chance_pct = 20}

You could use the data I collected for the OP to formulate something a little more specific, but the amount of randomness involved here is substantial, nevermind how much the caps are interfering.

The armour/damage/health system is much simpler (and exposed due to developer comments).

Damage_dealt = Weapon_Damage - Armour*Rand()
Current_health = Current_health - Damage_dealt

[hispanicpanic]

Great work, i applaud you. It has come to my attention that different shields have different missile block chances associated with it. Is this true? Can you comment on this at all? Does missile block chance act just like melee defense during missile fire? Perhaps it is something worthy of some experimentation.

[crzyrndm]

Great work, i applaud you. It has come to my attention that different shields have different missile block chances associated with it. Is this true? Can you comment on this at all? Does missile block chance act just like melee defense during missile fire? Perhaps it is something worthy of some experimentation.

Yes, missile block chance is effectively a version of melee defence for projectiles. Any projectiles from the front or left of a soldier have a chance ranging from 5% (small cavalry shield) to 55% (tower shield) to be entirely blocked. Formations such as attacking testudo raise the scutum from 50% to 85%.

The issue I have with it is that there is no counterbalancing stat (the melee attack if you will). Javelins are blocked the same amount of times as a slingstone or arrow which doesn't make any sense to me.

[La Tene]

I want to spend more time reading through this thread but I have a couple quick questions:

• 40 attack/80 defence appears to be an outlier

Does this mean that one would need 80 defense or greater to achieve a proper defense against 40 attack?

So far, simply out of instinct, I have been turning formation attack off when I have the advantage, thinking that I would rather my tough melee troops to get in and get dirty as opposed to keeping form which seems like a defensive tactic to me. I wonder if I'm understanding this correctly.

Also, when against a tough barbarian unit such as oathsworn I wouldn't want to be surrounded but would want disciplined formation set to on, am I right?

I was thinking also, that if the animation of the formed attack side shuffle were to be depicted in a slower, more weighty kind of way, that it would feel much less awkward. In fact the lack of weightiness has been my major complaint since R2 launch, though, it is indeed getting better.