Saturday, February 18, 2012

More insight on weapon vs armor combat mechanics in an RPG

Here's a little more insight on the combat mechanics in my search for the holy grail of roleplay damage calculation.  As posted previously I'm looking for a balanced system that creates an incentive for actual roleplay on the battle field rather than a stand and deliver  + cure light wounds mechanic.  All this around a game system based on Rifts and D&D.  Allowing for technology and magic, mechanics and supernatural beings to coexist at some time and thus do battle in real terms without instantly obliterating half the population with a blast.

In this post I'll review the basic combat between a dagger and leather armor.  We start off from the basics that the hit has been achieved and it is done by some d20 roll that has no armor modifier involved (as in classic D&D and AC/THACO).  It is a basic hit the object roll that includes skill, ability and some luck.

Now as you might recall a dagger does 1d4 and a leather armor protects with 2d4.  Running the numbers on a computer we get the table below.  Before you jump to it let me explain it a bit.

Each section is labeled for example  "Roll 1d4 * 1 + 0 vs 2d4 * 1 + 0".  This means a 1d4 with a identity (x1) multiplication modifier plus 0 bonus attacking a 2d4 defense also with a 1 multiplier (identity) plus cero bonus.  Below that are the probabilities of outcomes:

  • Full : means all attacking rolls breach defense rolls (aka max damage done)
  • Partial : means not all attacking rolls breach defense rolls (aka some damage done)
  • Blocked: means no attacking roll breaches defense rolls (aka no damage done)

The computer runs 100000 combat rounds and totals the outcome.  For the first entry (Roll 1d4 * 1 + 0 vs 2d4 * 1 + 0) 22.03% of all attacks breach the armor defense.  If the armor roll is deducted from the damager roll an average of 1.43 hit points of damage are delivered.  If we play by a passthrough all or nothing rule and no damage is deducted from the attack roll then an average of 3.57 hit points of damage are done.  To clarify:

Dagger roll : 4
Leather roll : 3, 2

The dagger overcomes the leather.  In a passthrough rule the dagger does the full 4 points to the character, otherwise the 3 is deducted for a 1 hp damage to the character.  This leads to the difference between 1.43 hp for blocked damage and 3.57 for full (passthrough) damage.

The next entry (Roll 1d4 * 1 + 0 vs 2d4 * 1 + 1), the armor is slightly better.  Maybe its magical or maybe its special dragon skin leather or just hardened futuristic stuff.  In this case each roll is benefited by an extra 1.  For example:


Dagger rolls: 3
Leather rolls: 2, 1 ( that become 3, 2 with the +1 bonus)

Leather then blocks the dagger's roll and the character receives no damage.  In this scenario the leather armor becomes more resistant and only 7.69 of all rolls breach the armor.  But when they do and you're playing with all or nothing then more damage (3.8 hp) is delivered on the average.  Further down you see +2 and +3 leather armor which become impenetrable to daggers (at least conventional ones).

Roll 1d4 * 1 + 0 vs 2d4 * 1 + 0





Stats: rounds % hits blocked damage
full damage
Full: 22029 22.03% 1.43 hp 3.57 hp
Partial: 0 0.00% ? hp ? hp
Blocked: 77971 77.97% 0 hp 0 hp
Roll 1d4 * 1 + 0 vs 2d4 * 1 + 1





Stats: rounds % hits blocked damage
full damage
Full: 7689 7.69% 1.2 hp 3.8 hp
Partial: 0 0.00% ? hp ? hp
Blocked: 92311 92.31% 0 hp 0 hp
Roll 1d4 * 1 + 0 vs 2d4 * 1 + 2





Stats: rounds % hits blocked damage
full damage
Full: 1538 1.54% 1 hp 4 hp
Partial: 0 0.00% ? hp ? hp
Blocked: 98462 98.46% 0 hp 0 hp
Roll 1d4 * 1 + 0 vs 2d4 * 1 + 3





Stats: rounds % hits blocked damage
full damage
Full: 0 0.00% ? hp ? hp
Partial: 0 0.00% ? hp ? hp
Blocked: 100000 100.00% 0 hp 0 hp



Now lets run a sword (1d8) against the same batch of armors.  A sword has a starting 60.61% chance of going through the armor.  As the armor is hardened magically it becomes harder 48.73%, 35.80% and 23.41% respectively.  And you notice how the damage increases when it actually does go through from roughly 6 to 7.3 (aprox 25% increase).  Which is also realistic in terms that the force delivered in such blows should be higher thus only high damage hits achieve any damage at al.



Roll 1d8 * 1 + 0 vs 2d4 * 1 + 0





Stats: rounds % hits blocked damage
full damage
Full: 60612 60.61% 3.03 hp 5.98 hp
Partial: 0 0.00% ? hp ? hp
Blocked: 39388 39.39% 0 hp 0 hp
Roll 1d8 * 1 + 0 vs 2d4 * 1 + 1





Stats: rounds % hits blocked damage
full damage
Full: 48726 48.73% 2.55 hp 6.45 hp
Partial: 0 0.00% ? hp ? hp
Blocked: 51274 51.27% 0 hp 0 hp
Roll 1d8 * 1 + 0 vs 2d4 * 1 + 2





Stats: rounds % hits blocked damage
full damage
Full: 35802 35.80% 2.08 hp 6.91 hp
Partial: 0 0.00% ? hp ? hp
Blocked: 64198 64.20% 0 hp 0 hp
Roll 1d8 * 1 + 0 vs 2d4 * 1 + 3





Stats: rounds % hits blocked damage
full damage
Full: 23413 23.41% 1.67 hp 7.32 hp
Partial: 0 0.00% ? hp ? hp
Blocked: 76587 76.59% 0 hp 0 hp



Now lets take a bastard sword 2d8 vs improving armors 1d6 for thick cloth armor, 2d6 for scale leather (bit better than 2d4 basic leather seen before), 3d6 for chain mail and 4d6 for scale mail armor.

As you can see basic cloth armor has no chance whatsoever at stopping a bastard sword.  The best it can do is a partial block (23.68% of the time) and stop one of the swords die.  Scale leather has a 25% chance of stopping all damage from the sword.  Chain mail aprox 35% and scale mail 40%.

Roll 2d8 * 1 + 0 vs 1d6 * 1 + 0





Stats:





Full: 76321 76.32% 6.91 hp 9.99 hp
Partial: 23679 23.68% 2.15 hp 2.15 hp
Blocked: 0 0.00% 0 hp 0 hp
Roll 2d8 * 1 + 0 vs 2d6 * 1 + 0





Stats:





Full: 41083 41.08% 5.68 hp 11.56 hp
Partial: 33878 33.88% 2.17 hp 5.82 hp
Blocked: 25039 25.04% 0 hp 0 hp
Roll 2d8 * 1 + 0 vs 3d6 * 1 + 0





Stats:





Full: 28846 28.85% 5.07 hp 12.31 hp
Partial: 36246 36.25% 2 hp 6.47 hp
Blocked: 34908 34.91% 0 hp 0 hp
Roll 2d8 * 1 + 0 vs 4d6 * 1 + 0





Stats:





Full: 22478 22.48% 4.58 hp 12.84 hp
Partial: 36731 36.73% 1.89 hp 6.82 hp
Blocked: 40791 40.79% 0 hp 0 hp


So how does all this fit into combat.  Well lets say you always work on a 10 to hit on a d20 for an unskilled character.  I roll and get a 6 then I miss, but if I roll a 16 I hit.  I then roll damage and let the defender's armor roll damage to stop the damage.

Of course there are skills and abilities to consider.  A proficient swordsmaster would get +4 to hit plus say -2 for the targets dexterity.  If so an 8 not a 10 would be needed to hit.  Yet once the hit to the target is achieved then the weapons and armors sort it out.  I think this gives out some very nice numbers as to the probability to do damage and the amount of damage delivered.  It also invites the character to actually try to dodge, parry and take cover not just stand and deliver.

What do you think? I'd love to hear feedback on this.

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