Level 50 Squadron Scroll Missions: An Analysis

Let me start this by breaking down the mathematics of these missions.
Once you have finished leveling your squadron, the optimal use of your weekly priority mission is one of the priority missions that rewards 10 buff items.

There are 9 level-50 priority missions.

Each of these missions has a set of required attributes, pulled from what I will call a "profile index". This profile index is set weekly, affects all missions simultaneously.
There are 6 possible profile indices. It is unclear how this index is chosen, or whether it is distributed among the 3 grand companies (e.g. 2 per GC), so we will assume it is random and that all profiles are available to all GCs (side note, I would appreciate some data gathering to prove this true or false).

Additionally, each mission has either 1, 2, or 3 "Mission Affinities", each of which can a race or class.
For squadrons, there are 9 classes and 6 races.

This comes out to num_missions * num_profiles * (affinities + affinities^2 + affinities^3)
= 9 * 6 * (9+6 + (9+6)^2 + (9+6)^3)
= 195210

Let's move to classes. To optimize for higher affinity coverage, my strategy is to have 8 diverse jobs (leaving one out) and 6 diverse races (with the 2 remaining squadron members being different races). I have also run simulations for non-diverse choices (e.g. all gladiator, etc), but found that this did not otherwise give benefits. This limits our search space to just 9 possibilities (leaving out only one of each job)

As for training, you may have 3 stats, in intervals of 20, summed up to 400. There are 231 possible training configurations.

This leads to 2079 possible squadrons.

Additionally, squadron members may have chemistries. For the purposes of meeting stats, there are really only 3 chemistry effects that matter: (physical, magic, tactical increased by 15%). Let's assume the optimistic case where we can always trigger it (e.g. we have a condition like "all of a different class"). In the case where the race or class of a mission affinity matches the character, this is doubled (30%).

So far I have confirmed via simulations:
There is no combination of training/jobs (including with replacement) with full 15% bonuses (no affinities) that grants you 3 completed stats on any level 50 priority mission under any profile index.

I am still working on simulating different racial combinations + affinities, but it seems like 3-statting might be possible under some conditions.

I was not expecting this system to be so hardcore.

Some more details I'm finding as I trim the search space to be more tractable:

Among the 9 missions and 6 profiles (which should represent up to 54 different stat goals), there are actually only 6 different sets of stats.

Code:

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Stats { physical: 295, mental: 430, tactical: 600 }
Stats { physical: 430, mental: 295, tactical: 600 }
Stats { physical: 590, mental: 305, tactical: 430 }
Stats { physical: 590, mental: 430, tactical: 305 }
Stats { physical: 275, mental: 620, tactical: 430 }
Stats { physical: 430, mental: 620, tactical: 275 }

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Additionally, as I evaluate race distributions, I'm only looking at unique distributions. (e.g. 8 Miqo'te and 8 Lalafell are identical, though Miqo'te are cuter).

This brings us down to around 12870 * (9 choose 8) * (8 choose 4) * (17 choose 3) * 6 in total, which is still a lot, but simulating feels a lot more tractable!

My final goal is a "set and forget" preset of races+jobs+training that gets me fairly consistent 3-stats.

Quote:

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Originally Posted by jadeharley

I was not expecting this system to be so hardcore.

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I suspect these results have come as a surprise to nearly everyone.

I never really did the math but it felt like it was impossible to reach all 3 stat requirements no matter who I put in the party as I'd always be heavily deficient in one stat.

I usually just fling them at the mission that gives Gold Saucer VIP Cards and figure they'll be successful at least once in a given week unless my luck is truly horrendous.

I usually just do whatever mission I want to have some stock of (exp, spiritbond, MGP, gc seals, maybe food duration if a raid is coming up) but recently I favor having higher mission success rate. The reward-based chemistries (+mgp, +scrips) give so few that I've found it's better to focus on stats.

The scrolls are vendor trash to me, so I just aim for the lev-40 quests which are doable.
All my squads are attributed for crafting/gathering scripts, so I go for whichever gives the most up-arrows.

That said, felt the same way about Island Sanctuary workshops.
From appearances, figuring out tomorrow's optimal workshop seemed straight forward - stock is low and demand is high.
Nope, that was yesterday's stock & demand. Use a player-made excel spreadsheet because it's all a series of behind the scenes patterns?
Really killed any kind of personal engagement realizing that.

Some surprising numbers from my simulation:
Time elapsed: 11 hours (at this point, i'm running an extremely efficient Rust program on a 16 core machine, and idk if I can speed it up)
Jobs: unique only
Races: all unique combinations (meaning races are substitutable with any other race so long as the count is preserved)
Chemistries: all 15% guaranteed
Missions: all 6 variants of the level 50 missions
Affinities: all combinations

Code:

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Aura MRD
Aura GLA
Aura ARC
Aura ROG
Aura LNC
Aura CNJ
Aura THM
Aura ACN
Training:
Stats { physical: 200, mental: 180, tactical: 20 }
Performance:
3 stats: 55.80%
2 stats: 23.37%
1 stats: 20.83%
0 stats: 0%

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Conclusion: assuming you can get a guaranteed chemistry (e.g. stay constrained to unique jobs and use "when all jobs are different [maxstat] increased by 15%"), it's actually more beneficial to have all your squadron be one race instead of a diverse set. (Note that the race is "all of the same race" and not "all au ra")

I personally like having a diverse squadron so this makes me a little sad, but the strict requirement of 30% stat boosts to hit breakpoints means you have to go for cases where an affinity triggers 30% across the board.

There is one more potential set of cases I have not yet considered: unrestricted jobs (9^8) rather than unique jobs (9). As-is, this computation would take 2.3 million days.