Sword of Spirit
Legend
Since I'm seeing more interest in monster design, I thought I'd share a tidbit of the official math I was able to derive during my attempts to reverse engineer it.
The rule of adjusting Defensive CR up/down by +1/-1 per each +2/-2 of AC difference from the 2014 DMG chart is a simplified approximation of the real math.
Here's what's actually going on.
1) The AC values in the chart are the values that will give a PC of Level equal to that CR, built in the assumed way, a 65% chance of hitting.
2) The assumed PC attack bonus is easy to determine. Start with a +3 in your attack stat, use your 4th level ASI to raise it +4, and your 8th level ASI to raise it to +5. Add the appropriate proficiency bonus.
3) This matches up exactly at every level, except level 9, where the hit chance is 70%. If you make a line graph of the values, that 1 AC shift at that level brings it closer to the trend line, which is almost certainly the reason for the discrepancy.
4) The reason AC stops increasing at 19 is because that's also when attack bonus stops increasing, maintaining that 65% hit chance.
What this means, is that you can precisely determine how AC and Hit Points interact to create Defensive CR. Divide the hit points by 0.65 to determine the expected PC damage potential over the course of 3 rounds. Then for every point by which the AC differs, adjust that 0.65 by +0.05 for lower AC or -0.05 for higher AC. Multiply the damage potential by that number to get the effective hit points, and the Defensive CR is whatever line that HP value gives you.
In the mid-ranges, +1/-1 for +2/-2 AC is accurate, but as you depart from the mid-ranges it becomes less and less accurate.
Hopefully that's useful!
(The Offensive CR adjustments almost certainly work in a similar manner, but deriving the actual math there is much more difficult due to various complications that I won't go into here unless there is real interest right now.)
The rule of adjusting Defensive CR up/down by +1/-1 per each +2/-2 of AC difference from the 2014 DMG chart is a simplified approximation of the real math.
Here's what's actually going on.
1) The AC values in the chart are the values that will give a PC of Level equal to that CR, built in the assumed way, a 65% chance of hitting.
2) The assumed PC attack bonus is easy to determine. Start with a +3 in your attack stat, use your 4th level ASI to raise it +4, and your 8th level ASI to raise it to +5. Add the appropriate proficiency bonus.
3) This matches up exactly at every level, except level 9, where the hit chance is 70%. If you make a line graph of the values, that 1 AC shift at that level brings it closer to the trend line, which is almost certainly the reason for the discrepancy.
4) The reason AC stops increasing at 19 is because that's also when attack bonus stops increasing, maintaining that 65% hit chance.
What this means, is that you can precisely determine how AC and Hit Points interact to create Defensive CR. Divide the hit points by 0.65 to determine the expected PC damage potential over the course of 3 rounds. Then for every point by which the AC differs, adjust that 0.65 by +0.05 for lower AC or -0.05 for higher AC. Multiply the damage potential by that number to get the effective hit points, and the Defensive CR is whatever line that HP value gives you.
In the mid-ranges, +1/-1 for +2/-2 AC is accurate, but as you depart from the mid-ranges it becomes less and less accurate.
Hopefully that's useful!
(The Offensive CR adjustments almost certainly work in a similar manner, but deriving the actual math there is much more difficult due to various complications that I won't go into here unless there is real interest right now.)
