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You're missing that the scales reset each day. It's unlikely that you ever reach 8 scales on a regular adventuring day.
When in doubt, go for the highest AC. No damage reduction in the game is high enough to be worth the loss of AC.
Gut instinct is that the higher AC and better flat check for avoiding crits is going to significantly outperform an 'up to 8 points' damage reduction.
I'll have to do a more thorough math analysis later though. Will take too much time for right now.
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Some assumptions, design, and example values used:
* Assuming that the enemy needs to roll an 8 to hit you on its first attack. So it needs an 18 to crit. I'm not going to be looking at additional attacks each round because that makes things much more confusing.
* Assuming that there are no additional effects for a crit other than doubling the damage dealt.
* Since these armor options are available at about level 18, I am using a typical damage amount of a level 16 creature: 35 points of damage per hit.
* Creating a baseline of an armor with the same AC as the Impenetrable Scale armor, but no Fortification runes or damage reduction.
* Splint Mail has one point higher item bonus to AC and has the greater fortification rune.
* Impenetrable Scale armor has regular fortification rune and possible damage reduction. I am only calculating for DR 0, DR 2, DR 5, and DR 8.
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First, like Blave mentioned, the DR of the Impenetrable Scale armor has to be charged up each day - by being hit.
So needing an 18 to crit, that means a 15% chance. With a flat check of DC 17, that is a 20% chance to reduce it to a standard hit and charge the DR of the armor. So having both happen is (0.15 * 0.20) = 0.03 or 3% chance. So about once every 33 first-action attacks that are pointed at you.
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With the baseline armor, the expected value of damage per first-action attack is 28: miss 35% of the time, hit 50% of the time for 35 points of damage, and crit 15% of the time for 70 points of damage. So (0.50 * 35) + (0.15 * 70) = 28.
The +1 AC by itself will drop the expected value of damage down to 24.5 per attack.
The Greater Fortification rune drops the expected value of a crit from 70 down to 57.75. Combining that with the +1 AC gives a total expected value of 23.275.
The regular Fortification rune only drops the expected value of a crit down to 63 damage. So the baseline AC and regular Fortification rune - the initial values for the Impenetrable Scale armor - has an expected value for damage of 26.95. Which is actually quite a bit worse than the 24.5 from just the +1 AC. Never mind the improvement from the Greater Fortification rune.
With DR 2 on the Impenetrable Scale it has expected damage per hit of 25.41.
With DR 5 it has expected damage per hit of 23.1.
With DR 8 it has expected damage per hit of 20.79.
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So after taking about (33 * 5) = 165 first-action attacks in a day the Impenetrable Scale armor will finally pull even to the Greater Fortification Splint Mail.
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Tinkering with the input values on my spreadsheet here:
If the enemies have a higher chance of hitting you - only needing a 4 to hit and a 14 to crit while you are in baseline armor - then the conclusions still hold. The Impenetrable Scale armor is only better than the Greater Fortification Splint Mail at DR 5 or higher.
At lower chances of hitting you, the difference between the various DR levels becomes a lot lower. Somewhere between DR 3 and DR 4 the two armor options become practically identical. But the Splint Mail is still better than the base form of Impenetrable Scale armor - and at low chance of hitting you, there is nearly zero chance of critting you to charge the DR of the Impenetrable Scale. (0.05 * 0.20) = 0.01 or 1% per attack, or once every 100 attacks.
Thanks for the analysis.
No problem.
I swear it didn't seem that bad at the beginning...
Yeah. Complicated probabilities are one of those things in math that it is actually rather hard to have a good instinctive understanding of.
And I am still wondering what "significant foe" Means...
It is actually a term better defined and used more often in Starfinder since one of the core classes has their main class feature trigger off of it.
The closest I have seen in PF2 is here. Probably somewhere between low-threat and moderate-threat.
Low-threat encounters present a veneer of difficulty and typically use some of the party’s resources. However, it would be rare or the result of very poor tactics for the entire party to be seriously threatened.
Moderate-threat encounters are a serious challenge to the characters, though unlikely to overpower them completely. Characters usually need to use sound tactics and manage their resources wisely to come out of a moderate-threat encounter ready to continue on and face a harder challenge without resting.