Discussions here on armor use started me thinking. What follows is an analysis of the maximum protective benefits of mithral vs. adamantine full plate against normal weapon damage. The benefits/drawbacks of the other differences (run speed, touch AC, armor skill penalties) are highly situational and would require a case-by-case analysis of specific character builds (to include movement bonuses, energy resistances, grapple check modifiers, etc.) vs. specific challenges/opponents.
At the extremes, when both ACs are always hit except on 1 or always missed except on 20, adamantine is superior. For most of the other situations, the benefit can be calculated by using the average damage per hit (D) multiplied by the number of hits in 20 (H); the average damage per 20 attacks for mithral full plate is D x H and the average damage per 20 attacks for adamantine full plate is (D - 3) x (H + 2).
The break-even point for the protective values of the two armors can be determined as follows:
D x H = (D - 3) x (H +2)
DH = DH + 2D - 3H - 6
0 = 2D - 3H - 6
2D = 3H +6
D = 1.5H +3
Therefore, at the following hit probabilities, if the average damage per attack is less than the break-even point, adamantine is the better choice; if the average damage per attack is greater than the break-even point, then mithral is the better choice.
mithral hit %/adamantine hit % - avg. dam. per attack
5%/10%* - 6
5%/15% - 4.5
10%/20% - 6
15%/25% - 7.5
20%/30% - 9
25%/35% - 10.5
30%/40% - 12
35%/45% - 13.5
40%/50% - 15
45%/55% - 16.5
50%/60% - 18
55%/65% - 19.5
60%/70% - 21
65%/75% - 22.5
70%/80% - 24
75%/85% - 25.5
80%/90% - 27
85%/95% - 28.5
90%/95%* - 57
*- Because of the auto-hit/-miss feature of d20 combat, the break-even point for these is calculated using the following equation: D x H = (D - 3) x (H + 1), which reduces to D = 3H + 3.
Because of the differences between light and medium armor, comparing mithral vs. adamantine breastplates is like comparing apples to oranges. Comparing mithral vs. adamantine chain shirts reveals that the break-even point is so low (D = .5H + 1) adamantine is not worth it in most circumstances.