Here is some data on Max Luck+Chances I collected~

[SakuraKoi]

Teal Deer at the bottom.

Well, I was curious about how luck works in this game (crit chance is already noted to be 20% in the wiki) and so I then took the two missions, the one about Fiestas and the other about Torpedos and reloaded them 100 times each, noting the number of the weapon levels in a spreadsheet.

With a sample size of of 2000 the Fiesta Mission is very well suited for checking a weapon with just two levels since the large amount fo given weapons increases the sample sizes and reduces the margin of error. I think... I actually played A Link to the Past during my high school math lessons which were about stochastic (so all I really just did was calculating % with the formula I know from 6th grade/put the formula into the spreadsheet and linked the right cells), don't ya ask me how to calculate an acceptable margin of error for whatever sample size.

I'm not even certain whether margin of error would be the right term for accounting randomness but anyway, the data for the first test:

Pinata/Level 1:
768

Fiesta/Level 2
1232

Translated into %, there is a 38.4% chance to get Level 1 and 61.6% Chance to get Level 2, plus minus whatever margin of error, if I were to make an educated guess, the real chance is 40/60 with maxed luck

The torpedo mission sadly only presents 5 weapons of the same kind to one so that the sample size is just 500, where I then had

Level 1
86
Level 2
121
Level 3
115
Level 4
178

This'd be 17.2% for lvl 1, 24.2% for lvl 2, 23% for lvl 3 and 35.6% for lvl 4.

Now, interestingly enough, if one adds the chances for lvl 1 and 2 as well as 3 plus 4, one will get:
Lvl1+2=41.4% and Level 3+4=58.6% which is quite close to the chances noted above for weapons with just two levels. 40/60

I'm quite curious whether my guess now is right that at least with max luck the last tier/level is favored by 10% and the first level has -10% while the middle levels are neutral.

Additionally, what might be obvious but could also be designed differently, is that all weapons might be equal (well, maybe there is actually just a 10% chance to get a Mega Nuke even with max luck but I'd need to reset the last mission over and over again to check, very slowly)

Best guess for weapons with 3 levels atm: 22,2% for 1, 33,3% for lvl 2 and 44,4% for 3 considering, well, math... give and take one-third of the chance which would make all even/as likely as the other. This is taken from the values for weapons with 4 levels which could very well follow the same logic, the margin of error in all of this is no higher than 2,3% (the 35,6% of the level 4 sampling would be just 33.3%)

This took by the by just 40 minutes or so to set up and do plus whatever to write this. If you want and if it is allowed (well it should be) I can also share the spreadsheet I used to note (it's just a lil embarrassing, I'd need to make it look more neat and make it less obvious which lil shortcuts I used)

Note. Some many numbers would be endlessly repeating the same number after the decimal so I left the repetition out and rounded. Now even if I could not actually find the "truth" behind the (max) luck in SSL, I hope that this at least one step closer to finsing and knowing with this little research and essay.

To-Do, maybe:
1 Find a mission with a weapon with three tiers and do the same data collection with that set
2.1 Maybe find missions that are better suitedfor this and where I also have all tiers unlocked
2.2 Reset my level to have 0 luck investment and do this all over again.
3.: Do this all over again another time and record this on video so no troll can just call me a liar
3.2 and with 0 luck as well
4.1 (Unlock and) check OP weapons
4.2 also with 0 luck
4.3 and record it
4.4 another time with 0 luck
5 Find some math wiz who can tell what kind of margin of error/variance/deviation/whatever is acceptable for what test to consider

tl;dr, with max luck the apparent chance to receive each level for weapons with 2 levels: 40%/60%, 3 levels: maybe 11%/probably 33%/maybe 44%, 4 levels: likely 16,7%/likely 25%/likely 25%/likely 33,3% (1/2/3/4). The chances with 0 luck for each level to appear are merely presumed to be flat 100 divided by the number of levels, however the inverse may also be possible, where first and last % may actually be switched.

[GET CLOSE SMELL MY FART TEAMMATE]

You definitely need to get laid -.-

[GET CLOSE SMELL MY FART TEAMMATE]

I suspect Baby Batgirl is your girlfriend :D

[Dr. Cheech]

Really cool to see the math behind the Luck mechanic. Thanks for sharing.