Ever since we got the ability to get a second Protection of the Gods [PotG] materia for Minfilia from the Titan Raid, there's been the question about how it stacks (multiplicatively, additively, multi-processing) and how best it should be used, especially in a trial like Titan where many attacks are thrown at the party. I like to squeeze all the juice I can out of my party (especially since I'm still awaiting a killer 5* unit), so I sat down and did some testing and calculation to deduce how to get the most out of this handy ability.

The Short List of Results

A lot of people reading this aren't going to care about the numbers behind the scenes, so here is the skinny up front:

• A single Minfilia unit can process only a single PotG per attack received

• PotG stacks additively, so equipping two of them exactly doubles its chances of firing

• There is no processing benefit to using two Minfilias with one PotG each over a single Minfilia with two of them

Methodology

I don't have any data-mining capabilities, so I did this the hard way and took one of my Minfilias down to Earth shrine for what must have been the most frustrating day in that rat's life. I first equipped her with a single PotG. The reported processing rate for a single PotG is 20%. It's not that I don't trust the community, but I wanted to be relatively sure that was right, so I defended against 400 attacks from the rat, who only ever hits 1 time. This resulted in PotG processing 77 times, for a rate of 19.3%. This is close enough to 20% to say that our expected figure is probably right. I will say that running with a single PotG resulted in some unusual displays of RNG; I went 19 attacks in a row without it processing once, which was a highly unlikely occurrence.

With the base rate of a single PotG established, I wanted to know what would happen if two of them were equipped. So, after putting that rat out of its misery, I equipped Minfilia with two PotG and went back into the breach. This is a much more debated question, so I defended 500 attacks against the rat. I know that a higher sample pool, such as 5000 attacks would be better, but my sanity has a limit. The results were 207 instances of PotG processing, which is a 41.4% occurrence rate. That's only 7 instances away from being a perfect 40% (the result we would expect with an additive bonus for multiple equips), but 27 away from 36% (the result we would expect from a multiplicative bonus for multiple equips.)

With the result being significantly closer to 40% than 36% (and the result actually being slightly over 40%), I feel confident in saying that the bonus provided from multiple PotG materia is additive, which is a good thing. There are no diminishing returns from equipping multiples of them.

Double Processing of Protection of the Gods

In my 500 rounds of using two PotG, it never fired twice. With a base chance of 20% per materia, the odds of it firing twice from one attack is just 4%, which is not good. But the odds of it firing twice sometime in 500 rounds is 99.999999863%. That is, the odds of it being capable of double-processing and not doing so one time in 500 rounds is about one in seven billion.

So, we can safely say that the materia will only trigger once per attack received. So, the question becomes, are you losing out on the possibility of multiple PotG processes by putting them both on the same Minfilia versus, say, two Minfilias?

The answer is no. Because the materia has an additive benefit (no penalty for equipping multiples) and its base rate does not exceed 50%, you get exactly the same total healing from putting two of them on the same Minfilia and going out to fight then if you had two Minfilias.

In the one-Minfilia scenario, you have a 40% chance of processing a Single PotG for each attack received. Conversely, you have a 60% chance of no PotG for each attack. Thus, over the course of 100 attacks, you should see roughly 40 processes. If your Curaja heals for 1,500 hp, you're talking about 60,000 hp healed.

In the double-Minfilia scenario, you have two separate chances of 20% each to fire off PotG. This means that each Minfilia, when attacked, has a 20% chance to use PotG and an 80% not to. If an attack hits both Minfilias (which it would have to in order to have a chance to process both PotG materia), there is a 4% chance that both will process, a 32% chance that only one of them will process, and a 64% chance that neither of them will process. Thus, over the course of 100 dual attacks, you would see roughly 32 single-cast Curajas (1,500 hp each; 48,000 hp total) and 4 double-cast Curajas (3,000 hp each; 12,000 hp total), resulting in a total of 60,000 hp healed.

Separate units equipping the same materia for multi-processing is only a net benefit if the chance of the materia processing is over 50%. Once you exceed a 50% chance for the ability to process, then there is a clear advantage to having two units equip them separately--a single unit equipping both materia caps out at a 100% chance to use the ability once, while you get ever-increasing chances for multiple processes on more than one unit.

I'm not sure if we get a third PotG with the Garuda Raid, but the end result will be the same with three PotGs as it was with two. Whether or not you would want to expend three materia slots on Minfilia with PotG for that 60% chance is another matter entirely.