Monday, November 12, 2012

Weapon & Damage Modelling in Era

Era uses a damage roll and soak roll for weapon and armour respectively.  The concept of damage and soak roll is not novel and has been around for a while.  Yet the mechanisms commonly in use add the die rolls to arrive at a value for damage and a value for soak.  Era on the other hand compares the rolls die to die and in doing so exploits some of the value of the roll that is lost in adding them up.

When dice are compared one to one some nice tricks can be made and some really interesting patterns emerge.  First of all lets look at an example.  Lets imagine a sword rolls 2d8 for damage and a chain mail armour rolls 2d8 for soak.  The rolls could be 6 and 4 for the sword and 5 and 4 for the armour.  Comparing the dice from highest to lowest we get:

6 vs 5 - the sword roll beats the armour roll
4 vs 4 - the sword roll ties the armour roll

Only the succeeding are added to total damage.  These rolls are called penetrating rolls.  In this case the 6 is the only penetrating roll and 6 is the total damage done.  The sword's 4 is stopped by the armours 4.  If the second armour roll had been lower, the second damage roll would have gone through and added 4 more points for a grand total of 10.

This creates an interesting dynamic because each die can represent a certain effectiveness for the weapon to penetrate the armour.  Bigger dice mean more AP (armour piercing) punch.  For example a weapon that rolls with d8 is inherently more effective against armours rolling with d6.  There is no way the armour can roll a 7 or 8 to soak the weapon's high rolls.  Adding more dice to the roll makes it more effective as well.  If the weapon has more dice than the armour there are dice the armour simply can not stop (6d4 vs 2d6, the six attacking are no match for the two defending).  Fortunately these would be the lower valued ones.  This comes in really handy when you want to simulate engulfing attacks like fire.  A blast of fire can be said to do 6d4.  All low dice, but lots of them to represent the engulfing nature of the attack.  Armour will stop the highest rolls, but be ineffective against the lower ones.

Too put this a bit more down to earth lets see how much damage a weapon of varying kind does to a 2d8 armour.  We'll graph 1d8, 2d8, 3d8, 4d8 and an amazing 5d8 weapon against the armour.

Putting it all together, calculated and graphed we get the following graph. 

Lets look at how this behaves.  The blue line shows how a 1d8 weapon fares against a 2d8 armour.  Most of the time (72%) the blade does no damage, but when it does it tends to do so at higher than normal values.  Damage above 4 and up to 8 takes up about 25% of the values.  Think of this as a dagger which is not very effective in general, but when it is it is quite good at doing damage.  It represents the ability to find critical holes in the armour quite well.

Compare this with the curve of the result when the dice are added.  Below is a graph that shows a 2d8 armour vs a 1d8 dagger (red line).  About 90% of the time the dagger does no damage and when it does it rises very gradually.

A strange behaviour happens when the armour matches the weapon (both 2d8).  Observe the red 2d8 line on the first graph.  It starts to rise quickly, then there's a small spike and then the slope diminishes.  So a quick rise to mid point value and then a slower slope toward the higher values.  Compare that to the blue 2d8 line above when dice are added.  The slope when the dice are added is very gradual and 55% of the time it causes no damage at all.

Finally when the weapon has more dice than the armour as is the case of the yellow, green and purple lines on the first graphs, there is always a minimum amount of damage done and the slope becomes more gradual.

Now lets compare the 2d8 armour against weapons with different dice (better amrour piercing properties).  On the following graph we see the armour going against d8 weapons and d10 weapons.  When facing d10 weapons the armour can't roll higher than 8 and the weapon is clearly in advantage.  Take a look at how the blue 1d10 curve behaves compared to the 1d8 curve.  It is considerably more effective against the armour.  The red 2d10 curve (on the graph below) is very close to the cyan 3d8 curve.  This is a good representation of technological advancements in weapon design.  The 2d10 could be seen as maybe lighter than the 3d8 (less dice), but it is almost as effective given its penetrating power (given the large die, d10 vs d8).  It becomes pretty easy for a game designer or game master to represent technological advantages this way.

One final graph I want to show is the effect of modifiers to the roll.  A typical example of this is magic weapons in the game.  In those cases the weapons get a plus that is added to each die rolled.  The following graph shows the d8 weapon (our dagger) against the same 2d8 armour.  Notice how the red curve of a +1 turns the simple dagger into something similar to a 1d10.  Additional modifiers create an ever increasing slope and lower odds for zero or low value damages.  Compare these two graphs with the first one at the top and compare the effects of a bonus vs adding extra dice to the roll.

As you can see by moving away from adding the dice to comparing them one on one a new way of representing the weapon's and armour's effectiveness is created.  One that gives a totally different and much more effective (greater damage) than the classic adding of the values.

A drawback is that comparing one on one may be a little more work.  But one that could be worth paying for the added benefit of the behaviour shown on the graphs and the ease in which the technological edge of a weapon or armour can be represented.
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