The math

On Tuesday I suggested a model for monsters in Heroes By Trade that removed their damage rolls and allowed them to deal fixed damage.  Normally monsters roll 1d10 and add their damage bonus to it but with the new system they would, for example, deal 11 damage instead of 1d10+5.  This is generally a raw damage increase because 1d10+5 averages to 10.5.  A couple people talked about how this was potentially an issue because if a player managed to get their Armour value to 10 they could become nearly invincible to the monster hitting for fixed damage.  This is a valid concern so I decided to crunch some numbers and see how it actually shakes out.

This chart shows the average damage dealt given the Armour values on the left.

Armour value	Fixed Damage (11)	Random Damage (1d10+5)
5	6	5.5
6	5	4.6
7	4	3.8
8	3	3.1
9	2	2.5
10	1	2
11	1	1.6
12	1	1.3
13	1	1.1
14+	1	1

What we see here is that fixed damage actually does more damage right up until Armour reduces the damage to 3 and isn't a big deal until Armour gets the damage taken down to 1.  This looks like a bit of a problem in theory but I am not sure in practice that it matters.  Here is the critical thing - any player with enough Armour to be taking 1 damage from attacks is basically invincible in any case.  Upping the average damage / round from 1 to 1.6 is hardly relevant to the outcome of the battle since when you account for hit chance the character can almost certainly stand there and just heal through 8 enemies beating on them constantly in either case.  Heroes By Trade is not designed for solo battles to the death so presumably those 8 enemies will eventually realize the futility of their efforts and go bash on somebody a lot squishier, disarm the character, or run away.  Characters with that much Armour tend to be very slow and clumsy so they are vulnerable to such tactics.

Also there is the consideration that if the battle includes multiple enemies with different attacks things will likely balance out.  If a character with 11 Armour is being attacked by 1 enemy that deals 11 damage and 1 enemy that deals 17 damage they take 7 damage per round.  If the same character is attacked by enemies that roll for damage instead they take 7.1 damage per round.  The only time the high Armour character is really out of line is when they are exclusively being attacked by enemies that fit in a very tight damage band and if those are the only enemies the character is going to mop them up no matter what system is being used.

There is an argument that carries much more weight though - if the system feels bad and players don't like it then the numerical benefits aren't particularly relevant.  Personally I have no issue with monsters dealing fixed damage because an ogre that hits for 23 does not feel in any way more realistic or immersive than an ogre that has precisely a 10% chance to hit for any value from 18 to 27.  What does get me going is that the fixed damage ogre gets its turn done faster so we can get back to doing cool stuff to blow said ogre up.

It is pretty clear to me that the combat math works just fine with fixed damage or rolled damage.  The only question is whether or not everyone has more fun.