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A&A Attack Matrix

I've been tinkering with different options for adjudicating combat in Archons & Armigers, my OD&D hack. OD&D famously doesn't have a fully-developed combat system, and I'm taking that license to tinker and running with it. I've been particularly inspired by several posts on Traverse Fantasy.

Starting point & goals

(Very picky, I know)

With all that in mind, I considered and rejected the following:

The Damage Die Matrix

I was perusing the LBBs, saw the to-hit matrices and thought, 'what if I made a matrix to scale damage by AC?'. So I came up with this:

HD\AC 9 8 7 6 5 4 3 2
0.5 d5 d4 d3 d2 d2 d3-1 d2-1 -
1 d6 d5 d4 d3 d3 d2 d3-1 d2-1
2 d6 d5 d5 d4 d4 d3 d2 d3-1
3 d8 d6 d6 d5 d5 d4 d3 d2
4 d8 d8 d6 d6 d5 d4 d4 d3
5 d8 d8 d8 d6 d6 d5 d5 d4
6 d10 d10 d8 d8 d8 d6 d6 d5
7 d10 d10 d10 d8 d8 d8 d6 d6
8 d12 d12 d10 d10 d10 d8 d8 d6
9 d12 d12 d12 d10 d10 d10 d8 d8
10 d14 d12 d12 d12 d10 d10 d10 d8
11 d14 d14 d12 d12 d12 d10 d10 d10
12 d20 d14 d14 d14 d12 d12 d12 d10

The idea here is to use this instead of a to-hit roll; so if a 3 HD bandit chief is attacking a figure in chain+shield, she'd consult the HD 3 row and Armor 4 column and roll a d4, subtracting the result directly from the target's HP.

The assignment of the specific die sizes was a vibes-based undertaking, though I took some initial cues from here and generally tried to think in terms of how quickly a roll would kill a figure of HD 1, 2, and 3. Furthermore:

Here's the matrix of average damage/round:

Hd 9 8 7 6 5 4 3 2
0.5 3 2.5 2 1.5 1.5 1 0.5 0
1 3.5 3 2.5 2 2 1.5 1 0.5
2 3.5 3.5 3 2.5 2.5 2 1.5 1
3 4.5 3.5 3.5 3 3 2.5 2 1.5
4 4.5 4.5 3.5 3.5 3 2.5 2.5 2
5 4.5 4.5 4.5 3.5 3.5 3 3 2.5
6 5.5 5.5 4.5 4.5 4.5 3.5 3.5 3
7 5.5 5.5 5.5 4.5 4.5 4.5 3.5 3.5
8 6.5 6.5 5.5 5.5 5.5 4.5 4.5 3.5
9 6.5 6.5 6.5 5.5 5.5 5.5 4.5 4.5
10 7.5 6.5 6.5 6.5 5.5 5.5 5.5 4.5
11 7.5 7.5 6.5 6.5 6.5 5.5 5.5 5.5
12 10.5 7.5 7.5 7.5 6.5 6.5 6.5 5.5

And here's ODD damage/round for comparison (using the Delving Deeper attack matrix and assuming all attacks do a d6):

Hd 9 8 7 6 5 4 3 2
0.5 1.925 1.75 1.575 1.4 1.225 1.05 0.875 0.7
1 2.1 1.925 1.75 1.575 1.4 1.225 1.05 0.875
2 2.275 2.1 1.925 1.75 1.575 1.4 1.225 1.05
3 2.45 2.275 2.1 1.925 1.75 1.575 1.4 1.225
4 2.625 2.45 2.275 2.1 1.925 1.75 1.575 1.4
5 2.625 2.45 2.275 2.1 1.925 1.75 1.575 1.4
6 2.8 2.625 2.45 2.275 2.1 1.925 1.75 1.575
7 2.8 2.625 2.45 2.275 2.1 1.925 1.75 1.575
8 2.975 2.8 2.625 2.45 2.275 2.1 1.925 1.75
9 3.15 2.975 2.8 2.625 2.45 2.275 2.1 1.925
10 3.325 3.15 2.975 2.8 2.625 2.45 2.275 2.1
11 3.325 3.325 3.15 2.975 2.8 2.625 2.45 2.275
12 3.325 3.325 3.325 3.15 2.975 2.8 2.625 2.45

And here's the damage/round difference between the two methods. My approach advantages heavily armored figures fighting low-HD figures, and makes high-HD figures substantially scarier (excepting OD&D combat systems granting extra attacks with HD).

Hd 9 8 7 6 5 4 3 2
0.5 1.08 0.75 0.43 0.10 0.28 -0.05 -0.38 -0.70
1 1.40 1.08 0.75 0.43 0.60 0.28 -0.05 -0.38
2 1.23 1.40 1.08 0.75 0.93 0.60 0.28 -0.05
3 2.05 1.23 1.40 1.08 1.25 0.93 0.60 0.28
4 1.88 2.05 1.23 1.40 1.08 0.75 0.93 0.60
5 1.88 2.05 2.23 1.40 1.58 1.25 1.43 1.10
6 2.70 2.88 2.05 2.23 2.40 1.58 1.75 1.43
7 2.70 2.88 3.05 2.23 2.40 2.58 1.75 1.93
8 3.53 3.70 2.88 3.05 3.23 2.40 2.58 1.75
9 3.35 3.53 3.70 2.88 3.05 3.23 2.40 2.58
10 4.18 3.35 3.53 3.70 2.88 3.05 3.23 2.40
11 4.18 4.18 3.35 3.53 3.70 2.88 3.05 3.23
12 7.18 4.18 4.18 4.35 3.53 3.70 3.88 3.05

I think the mechanics-to-fiction interpretation would have to take abstraction cues from Into The Odd and Muster:

And to flesh out the system a bit more:

Clunkiness aside, I feel like there has to be at least one glaring issue with this, but for now it seems like it checks most of my boxes. Only playtesting will tell for sure.

Addendum

As I was about to publish this Marcia B analyzed an ultra-simple combat system proposed by Reddit user Kubular. Just for kicks, I decided to compare it to my system.

Average damage:

HD\AC 9 8 7 6 5 4 3 2
0.5 2.25 1.8 1.4 1.05 0.75 0.5 0.3 0.15
1 2.75 2.25 1.8 1.4 1.05 0.75 0.5 0.3
2 3.3 2.75 2.25 1.8 1.4 1.05 0.75 0.5
3 3.9 3.3 2.75 2.25 1.8 1.4 1.05 0.75
4 4.55 3.9 3.3 2.75 2.25 1.8 1.4 1.05
5 5.25 4.55 3.9 3.3 2.75 2.25 1.8 1.4
6 6 5.25 4.55 3.9 3.3 2.75 2.25 1.8
7 6.8 6 5.25 4.55 3.9 3.3 2.75 2.25
8 7.65 6.8 6 5.25 4.55 3.9 3.3 2.75
9 8.55 7.65 6.8 6 5.25 4.55 3.9 3.3
10 9.5 8.55 7.65 6.8 6 5.25 4.55 3.9
11 10.5 9.5 8.55 7.65 6.8 6 5.25 4.55
12 11.55 10.5 9.5 8.55 7.65 6.8 6 5.25

Compared to my matrix:

HD\AC 9 8 7 6 5 4 3 2
0.5 0.75 0.70 0.60 0.45 0.75 0.50 0.20 -0.15
1 0.75 0.75 0.70 0.60 0.95 0.75 0.50 0.20
2 0.20 0.75 0.75 0.70 1.10 0.95 0.75 0.50
3 0.60 0.20 0.75 0.75 1.20 1.10 0.95 0.75
4 -0.05 0.60 0.20 0.75 0.75 0.70 1.10 0.95
5 -0.75 -0.05 0.60 0.20 0.75 0.75 1.20 1.10
6 -0.50 0.25 -0.05 0.60 1.20 0.75 1.25 1.20
7 -1.30 -0.50 0.25 -0.05 0.60 1.20 0.75 1.25
8 -1.15 -0.30 -0.50 0.25 0.95 0.60 1.20 0.75
9 -2.05 -1.15 -0.30 -0.50 0.25 0.95 0.60 1.20
10 -2.00 -2.05 -1.15 -0.30 -0.50 0.25 0.95 0.60
11 -3.00 -2.00 -2.05 -1.15 -0.30 -0.50 0.25 0.95
12 -1.05 -3.00 -2.00 -1.05 -1.15 -0.30 0.50 0.25

It's... almost identical (if I did my math right), rarely off by more than a point save for edge cases where a high HD figure is attacking someone with low armor. This threw me for a bit of a loop as Kubular's system is way, way simpler. Were I writing Archons & Armigers to adhere to principles like 'good game design' and 'appeal to a wide audience' I would almost certainly just snag Kubular's system. But I'm not, so I think I'll stick to the system that allows more granular tinkering and incorporates more funky polehedra.


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