Arto Hietanen
Finland
Vantaa
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I have been recently playing the Tomb of Annihilation with Asharra the wizard. Even though the game is great and I enjoyed playing with the wizard, one of her Utility Powers seemed very unsatisfying, namely the Mage Armor (MA) spell.

This spell increases your (or someone elses) AC by one and it lasts until the monster hits you with a roll of 17-20. It feels like a really weak power and I wanted to see how it compared to older protection spells from this game series, Shield (S) spell from Castle Ravenloft and Mirror Image (MI) from Wrath of Ashardalon.

So when you have MA up and the monster tries to whack you, what happens? The spell protects you from the attack if it changes a hit into a miss, otherwise it does nothing. The only time the spell changes a hit into a miss is when the monster attack roll would otherwise just hit your AC, that is 5 % of the time. The spell gets discarded when the monster rolls 17-20, which is 20 % of the time. Due to the AC and attack roll values in the game, those rolls of 17-20 are also hits. So, for each attack the spell is four times as likely to end as it is to help. For one attack, it has a 5 % chance of protecting you, for the next attack it is the same 5 %, if the the spell was not previously discarded so 0.8*0.05 = 4 % chance and so on. For ten attacks, the cumulative protection is ~22 % and it pretty much settles into ~25 % after 18 attacks on the target. So for the price of the Utility Power, you have roughly a one in four chance of it changing a hit into a miss during the game. Not so great, especially in a game where a higher AC might cause you damage (Crushing Humidity encounter card).

Shield spell automatically changes a hit into a miss and after that gives you +2 AC until the end of your next turn. So even without benefiting from the increased AC, this spell starts from 100 % protection from one hit. And remember that you get to choose when the power activates, so that protection is most likely used when you are getting hit for multiple points of damage or a nasty condition. The +2 AC's worth is harder to estimate, as it depends on how many times you are attacked on that turn that the protection is up, but basically it adds a +10% protection for each attack. So here the protection value of the spell is something like 110% on average (causing 1.1 hits to miss) if you are attacked once on the following turn.

Mirror Image gives you three tokens, each giving you +2 to AC and each miss by a monster discards one of these tokens. This one is harder to calculate, as the monster's chance of missing plays into the calculation. I haven't gone through the monster cards to see what is the average attack modifier, but assuming that the monster hits the unprotected wizard on a roll of 8 on d20, we can calculate that the first miss by a monster is caused by the spell with a probability of 46 % (of those attacks that miss, attack rolls 1-7 are misses where the spell did not help, rolls 8-13 are caused by the MI). On the second miss attack the protection is only 36 % and on the third time 22 %. Summing these numbers we get that with those assumptions, the spell protection value is 105 % (causing 1.05 attacks to miss during the game). Pretty evenly matched with Shield. If the monsters have better attack rolls, the spell will help more and if the monsters have harder time hitting, the spell is a bit weaker on average.

All in all this math shows that the earlier protection spells are pretty much balanced versus each other but MA is an outlier. If the spell would give you +2 to AC and be removed on an attack roll of 20, then the spell would still be weaker than the earlier spells, but it would have some use (80% protection value at 10 attacks, 107% after 15 attacks).
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Fernando Amaral
France
Paris
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Nice analysis, I'm glad you did some quantitative comparison of the spells.

To aggravate MA's situation I believe reaching >12 attacks on the Wizard in a single game is unlikely.Hence the practical cap is much lower than 25%.
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Icarodx
Canada
Winnipeg
Manitoba
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Interesting. We usually overrate +1 in AC but it is not that powerful. This offers some perspective in comparing powers. Thank you!
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