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                The difference in penalties in AD&D1 and D&D5

Sunday was our gaming group “Hallowe'en One Shot” (which is now at least a
“duo shot” as we didn't finish) and for some reason, I got to thinking about
the penalty differences between AD&D (Advanced Dungeons and Dragons) and D&D5
(Dungeon and Dragons 5th Edition).

Everyone in our group started out playing AD&D (or the original Dungeons and
Dragons) and in that system, if you are trying to hit something you can't
see, you subtract 4 from your (20-sided) die roll (d20) when trying to hit
it. But in D&D5, you roll two 20-sided dice (2d20) and take the lower value
(called “disadvantage”). I was curious as to the actual difference between
the two. I did a bit of programming and I got the following graph:

[A graph of AC (x-axis) and chance of hitting (y-axis) with various
penalties, bonuses, and just plain hits] [1]

Along the X-axis is AC (Armor Class). In AD&D goes from 10 (basically,
nothing) to -10 (nigh impossible to hit) while in D&D5, it goes from 10
(basicaly nothing) to 30 (nigh impossible to hit), so the range is the same.
So the X-axis is AC, going from 2 to 20. In both systems, rolling a 1 is an
automatic miss, so I'm not bothering with even listing an AC of 1. The Y-axis
is the probability of hitting said AC, from 1 (always a hit) to 0 (always
amiss).

The red line (the one cutting diagonally across the middle) is just the
result of rolling a d20 and is prety much what one would expect, a straight
line. The light-green line (the lower diagonal line) is the AD&D penalty of
subtracting four from a d20 (d20-4). Again, it's a straight line but giving a
lower chance of hitting.

What I find fascinating is the blue line (the lower curved line). This is the
D&D5 “disadvantage” roll. What's interesting about this is that at lower and
higher ACs, it's better than a -4 penalty, but between ACs of 7 to 15, it's
worse!

When I saw that, I just had to do the plot with a bonus. The purple line (the
upper diagonal line) represents a d20+4, and the curved dark green line (the
upper curved line) is the D&D5 “advantage” roll—where you roll 2d20 and take
the higher. It's the opposite of “disadvantage”—you do worse at lower and
higher ACs, but better between ACs of 7 and 15.

Wierd!

[1] gopher://gopher.conman.org/IPhlog:2023/10/31/hits.png
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Lazy Reading for 2023/11/05 – DragonFly BSD Digest
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