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The Miniatures War College
Advenio paratus. Egressus melior paratus.
D&D Miniatures strategy and analysis.

February 15, 2005

Basic Functional Damage

The basic measure of the offensive capabilities of a Skirmish figure will be what I call "Functional Damage." In other words, averaged over the long run how much damage will my figure be dishing out? For melee and ranged attacks, there are some metrics that can be derived immediately.

Ignoring critical hits and critical misses, the long run damage is the damage per hit times the odds you will actually hit. This is where basing things off of a single d20 makes the math easier than 2d6 or other dice. (d% makes it very easy, but still requires 2 dice). For every number that you can roll to make the hit you have a 5% chance or a probability of 0.05 to connect. From this we can derive an equation based on AC for the amount of damage we can deal...

AttackBonus - AC + 21* Damage

The magic number 21 is added so that a +0 will have one chance to hit an AC of 20. For full attacks, it is merely the sum of all of the functional damage for each of the bonuses.

This equation isn't perfect. It starts to break down when the bonus and AC difference approaches 20 and does weird things after then. However, we cannot calculate 17 odd values for each different figure, and we really want one or two numbers (full and single) for each figure. So for simplicity we should pick a reference AC to measure all other attacks against. What number should that be? Well, a nice round number like 21 would make the equation very easy to handle, canceling out the AC and the magic constant.

Now if we pick 21, the actual effective AC will be 20. Why? Well, now we bring in critical hits. When you have only one chance to hit a target it is always going to be a critical and (ignoring immunity to critical hits) is in effect a second chance to hit. So a +0 person swinging at an AC of 20 will do twice it's damage on a 20, and none otherwise. Also, we can conclude that immunity to critical hits is worth about 1 point of Armor Class (ignoring the sneak/death attack benefits).

By picking a reference AC of 20 this breaks down completely below +1 and above +39 to attack. But since ultra-extreme figures do not exist (Regdar, Epic OozeMaster anyone?) and making out of command MongrelFolk the main melee threat will have a predictable outcome the choice will be sufficient.

Next week I will apply the smell test and run this formula through all of the creatures legal in 200 point play: all 314 of them. I won't post all of the results but I will pull out some very interesting observations that have been all but confirmed in the field.


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