AC/DC and Ability Scores (Or, Yet Another Post on d20 Mechanics)

 No... This has nothing to do with them.

Actually this post is about Math. One of the greatest foes to exist in the D&D universe, the unseen wizard behind the curtain, chaining the chaotic forces of "luck" within bounded walls of accuracy.

We may hate the guy, but he starts throwing fits if we ignore him.

This post is mainly about the math of how I got to my current standpoint, which isn't too off from "Standard". If you're looking for crazy ideas, see the next link. If you're interested in the math of d20 dice rolls, stick around!

I'm writing a GLOG, as inspired by Arnold K of Goblin Punch blog, and for some reason the issue of Ability Scores has become the snare on which I continually trip.

Actually, that reason is this post on Goblin Punch: Stat Squish and the Lawful Roll 

It confused me, and suddenly my understanding of Ability Scores was shattered.

The problem with not being sure about Ability Scores is that EVERYTHING is built on them, and if that foundation is rickety, the whole game starts shaking.

The basic function of my game, like basically all modern d20 TTRPGs, is roll a d20 and add your Ability Score (Ability Scores act AS the modifier in my game), then compare your total to the Difficulty Class (DC) of what you're attempting. If you're attacking a foe, the DC is their Armor Class (AC). If you meet or beat the DC, you succeed at the task you're attempting.

All this seems simple enough, but then you go and actually start trying to figure out what those scores should be, roughly, and how to generate them. Actually, to figure out what those scores should be, we want to start with DCs.

What's In a DC?

Since we're rolling a d20, each number represents a 5% chance of success. A DC of 10, without modifiers, will be achieved 55% of the time (because if you take ALL the successful options of 10-20 on the dice, and multiply the total number of options by 5, you get 55). That seems like a solid base, but let's say we want, as GMs, a variety of options to throw at our players. We consider the "Average Guy", and ask, "How hard would it be for THAT guy?" Note that we don't want to ask "How hard do I want this to be for the player's character?" as that robs the Ability Scores of their purpose. They differentiate who's going to be MORE likely to succeed at the task, they aren't there for us to calculate DCs from.

So let's break down some un-modded dice rolls against a handful of DCs and see the chance of success. I'm starting at a DC of 8 for trivial and going up by 4 for each level, because it gives a nice 20% difference between each level, which feels good. You can fiddle with DCs all day and night, like I have, but I like just a few reliable "levels" of difficulty.

• 8: Trivial. A child could accomplish this with effort. (65% Chance of success)
• 12: Easy. An adult can do this with effort. (45% Chance of success)
• 16: Hard. An adult would be challenged by this, but could do it. (25% Chance of success)
• 20: Very Hard. Most adults couldn't accomplish this. (5% Chance of success)
• 24: Legendary. Succeeding at this is worthy of song. (-20% Chance of success)

I think we will rarely use the extreme ends. Trivial tasks just aren't worth the roll unless the risk factor is high, and legendary tasks are only going to come up in "Hail Mary" situations.

So we're left with a DC range of 12-20, usually using the numbers 12, 16, and 20.

Criticals

Just as a note, we'll say that criticals (natural 1 or 20) always result in success or failure because it feels right. And that's a good enough reason. If you disagree let me know in the comments. 

Ability Scores

What an Ability Score does is adjust the odds of success. Each integer up or down is + or - 5% chance.  A +4 score makes an easy task trivial, and a Legendary Task only "Very Hard". Simultaneously, a -4 score (you poor creature) makes everything 20% less achievable.

So, if that's how hard everything is for my "Average Guy", what should our "Heroic" characters' Ability Scores look like?

Call me unfun, but I like the simplicity of Standard Arrays. They make everyone at the table roughly equal in power, and give them the ability to be good at what they want, rather than what the dice have told them.  So let's make someone a little "Above Average" and give them the following Standard Array.

-1, 0, 1, 1, 2, 3

We'll also let them add 1 to any score they want. This means they might take that juicy +4, or they might just bump up one of their lower numbers.

If you want to make players roll for these numbers, we can do some more math. Have you had enough yet?

We want slightly above 0 to be the average. 3d6 averages out to a score of 10, with a total range of 3-18. Let's make the formula (3d6-10)/2, which is going to average to 0. If you want them more heroic you could make it 4d6, drop the lowest.

Incidentally, we've now arrived almost precisely at 5e stats and math. But now I get it.

Armor Class

A note on AC now. We want ACs to look like DCs. The more elusive or armored something is, the harder it is to hit.

So we want our highest typical non-magical AC to be about 20. That's someone in Full Plate with a Helmet and Shield. Your average untrained peasant rushing them with a sword is going to have a bad time here.

So, let's see here.

• Unarmored = 10+DEX, It's fairly easy to smack the average person. Please don't try.
• Leather = 11+DEX, Cushions the blow, but isn't going to save your life all the time, best be light on your feet.
• Brigandine = 12+DEX, This is a more accurate name for studded leather.
• Chain Shirt = 13+DEX (Max 16), From this point on, wearing heavier armor limits your movement. This does mean that if your DEX is +4, you are better off sticking with Brigandine.
• Scale Mail = 14+DEX (Max 16), Again, not the best option for high DEX characters, as they're going to be paying more for it. Not bad either, I suppose.
• Half Plate = 16, This is going to be expensive, and heavy. No bonus from DEX, as we've gotten too heavy for that, and characters with +2 DEX or greater can stick with Scale Mail.
• Plate = 18, Best base AC from armor. Technically achievable in Brigandine if characters ever have the chance to increase their Ability Scores to 6+, but that's going to be very rare.
• Helmets = +1 AC. Everyone should wear a helmet. Seriously.
• Shields = +1 AC. Shields are also regularly used in combat to intercept attacks. I like to include this in games by giving them the "Sunder" feature. Essentially, a character can choose to use their reaction to break their shield and negate all the damage of 1 physical attack, or something similar.

Well, there it is, essentially the same numbers I've been using in 5e all this time. Turns out their math isn't too bad. Who knew?

Again, the purpose of this blog is to explain on "paper" how I came to my conclusions for my own GLOGhack. I also know I'll probably change my mind at some point, but I want to know how I got to those conclusions.

I hope it's been helpful, or at least interesting, to read through my musings.

If you think the math could be better, let me know in the comments.

My plan for this blog is to be a place for musings on all things TTRPG, and yep, it's starting with math and rules, but I hope to include work on a decent sized setting, dungeons, monsters, player classes, etc. Stay tuned if that sounds interesting.