GST damage and accuracy calculations to validate formulas

Values calculated based on the JP wiki's formulas (simplified to not account for terrain or penetration weapons):
ACC factor = (ACC / 2) + weapon acc modifier + 150
EVA factor = (EVA / 2) + mobility
ATK factor = (Melee/Ranged + Power) * weapon power
DEF factor = (Defense + Power) * armor-factor

Hit rate = ((ACC-factor - EVA-factor) * size-mod) + distance-mod + tile-bonus + danmaku-area + focus-bonus + skills
size-mod is 1 for M, 0.9 for S, 0.8 for SS, 1.1 for L, 1.2 for LL, 1.3 for LLL
distance-mod is 0 for 5 distance, +3 for each tile closer, -3 for each tile further
tile-bonus is the evasion bonus/penalty from the tile terrain on the map
danmaku-area is the stacked danmaku penalty
focus-bonus is 10 if attacker is a focused playable character, 0 otherwise
skills all stack additively at the end

Damage = ((ATK-factor - DEF-factor) * size-mod * distance-mod * mult-mods * sum-add-mods / 200) + final-mods
size-mod is the inverse of the accuracy one: 1 for M, 1.1 for S, 1.2 for SS, 0.9 for L, 0.8 for LL, 0.7 for LLL
distance-mod is the same as accuracy one, but it multiplies instead of adding: 1 instead of 0, 1.03 instead of 3, 0.97 instead of -3
mult-mods is the multiplication result of all other modifiers that stack multiplicatively from skills, etc
sum-add-mods is the sum result of all other modifiers that stack additively from skills, etc
final-mods are all modifiers that are applied to the end calculation like barriers, etc

Idk why but the game attempts to smooth out the linearity of the armor stat with some hidden formula. JP wiki gives this approximation:
Armor-Factor = (sqrt(armor) + 151) * (sqrt(armor) - 2) / 5
Here's the curve plotted against the linear function: https://files.catbox.moe/h1idei.png

All battles assume no crits, terrain is air and no skills unless otherwise specified
Values shown are for Normal / Normal+ / Hard / Lunatic

Stats (Reimu) (has grazing):
- Power 100
- Mobility 120
- Armor 800
- Size M
- Terrain A
- Ranged 152
- Defense 86
- Accuracy 190
- Evasion 187
- Weapon 1900 | +10
* ACC factor: 255
* EVA factor: 213.5
* ATK factor: 478800
* DEF factor: 175300

Stats (Keine):
- Power 100
- Mobility 70
- Armor 1200
- Size L
- Terrain A
- Melee 146
- Defense 114
- Accuracy 180
- Evasion 128
- Weapon 2100 | +10
* ACC factor: 250
* EVA factor: 134
* ATK factor: 516600
* DEF factor: 259347

Stats (Red Fairy):
- Power 95 / 100 / 105 / 110
- Mobility 75 / 85 / 95 / 110
- Armor 680 / 800 / 920 / 1100
- Size S
- Terrain A
- Ranged 138
- Defense 87
- Accuracy 157
- Evasion 146
- Weapon 1550 / 1750 / 1950 / 2250 | +15 / +15 / +15 / +40
* ACC factor: 243.5 / 243.5 / 243.5 / 268.5
* EVA factor: 148 / 158 / 168 / 183
* ATK factor: 361150 / 416500 / 473850 / 558000
* DEF factor: 155189 / 176242 / 197276 / 226147

Stats (Blue Fairy):
- Power 95 / 100 / 105 / 110
- Mobility 70 / 80 / 90 / 105
- Armor 670 / 750 / 830 / 950
- Size S
- Terrain A
- Ranged 135
- Defense 87
- Accuracy 152
- Evasion 143
- Weapon 1600 / 1800 / 2000 / 2300 | +15 / +15 / +15 / +40
* ACC factor: 241 / 241 / 241 / 266
* EVA factor: 141.5 / 151.5 / 161.5 / 176.5
* ATK factor: 368000 / 423000 / 480000 / 563500
* DEF factor: 153782 / 169367 / 185113 / 206475

Stats (Red Fairy that is close to Keine):
- Power 95 / 100 / 105 / 110
- Mobility 75 / 85 / 100 / 115
- Armor 680 / 800 / 980 / 1160
- Size S
- Terrain A
- Ranged 138
- Defense 87
- Accuracy 157
- Evasion 146
- Weapon 1550 / 1750 / 2050 / 2350 | +15 / +15 / +15 / +45
* ACC factor: 243.5 / 243.5 / 243.5 / 273.5
* EVA factor: 148 / 158 / 173 / 188
* ATK factor: 361150 / 416500 / 498150 / 582800
* DEF factor: 155189 / 176242 / 205150 / 233751

> Reimu vs Red Fairy (Distance = 5, Reimu focusing)

Expected hit rate for Reimu: 100 / 97 / 88 / 75
Actual hit rate for Reimu:   100 / 98 / 87 / 73

Expected hit rate for Fairy:  30 / 30 / 30 / 55
Actual hit rate for Fairy:     7 / 32 / 47 / 87

Expected damage for Reimu: 1780 / 1664 / 1548 / 1390
Actual damage for Reimu:   1784 / 1664 / 1545 / 1383

Expected damage for Fairy:  836 / 1085 / 1343 / 1722
Actual damage for Fairy:    828 / 1089 / 1356 / 1746

> Reimu vs Blue Fairy (Distance = 4, Reimu focusing)

Expected hit rate for Reimu: 100 / 100 / 97 / 83
Actual hit rate for Reimu:   100 / 100 / 97 / 81

Expected hit rate for Fairy:  30 / 30 / 30 / 55
Actual hit rate for Fairy:     7 / 32 / 47 / 87

Expected damage for Reimu: 1841 / 1753 / 1664 / 1543
Actual damage for Reimu:   1846 / 1754 / 1662 / 1538

Expected damage for Fairy:  893 / 1148 / 1412 / 1799
Actual damage for Fairy:    885 / 1152 / 1426 / 1826

> Keine vs Red Fairy that is close to Keine (Distance = 3, Keine focusing)

Expected hit rate for Keine: 100 /  99 / 85 / 71
Actual hit rate for Keine:   100 /  99 / 83 / 69

Expected hit rate for Fairy: 100 / 100 / 100 / 100
Actual hit rate for Fairy:    97 / 100 / 100 / 100

Expected damage for Keine: 2299 / 2164 / 1981 / 1799
Actual damage for Keine:   2304 / 2164 / 1975 / 1790

Expected damage for Fairy:  432 /  666 / 1013 / 1371
Actual damage for Fairy:    426 /  662 / 1018 / 1385

Conclusions:
1 - Damage formula works almost perfectly for all difficulties
2 - Accuracy formula works sorta well for all difficulties, will be off by 1 or 2
3 - Difficulties have accuracy bonus/penalties for enemies:
    Normal:  -25
    Normal+:   0
    Hard:    +15
    Lunatic: +30