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 and D&D5.
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:
Along the X-axis is AC. 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.