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The Bug-Catching Contest on Tuesdays, Thursdays, and Saturdays in the National Park is a decent source of Evolution stones.

TL;DR: Save before your entry. Pursue Lv. 15 Venomoth/Butterfree/Beedrill (in the Regular version), a Lv. 14 Scyther/Pinsir, or a no-damage-caught Lv. 16 Venonat. Quit as soon as you catch one and see if you’re the winner. Soft-reset if you're not.

Basic Mechanics

Main databases: bug_contest_mons.asm, contest.asm, bug_contest_winners.asm, specials.asm

• First-place prizes now depend on times of day:
  • Morning: Shiny Stone
  • Day: Sun Stone
  • Evening: Dusk Stone
  • Night: Moon Stone
• Encounters now include Venomoth and Yanma.
• The scoring system has been slightly updated, aiming for more intuitive IV bonus points than in vanilla's bitwise calculations accounting for the DV-dependent Shininess.
• The opponents are the same as vanilla. Watch out for Cooltrainer Nick earning {349, 357, 368} points!

Scoring

Score = BasePoints + Bonuses, where:

• BasePoints = 4*MaxHP + Atk + Def + SpAtk + SpDef + Spe
  • It takes the actual stats. Make sure to consider the Base Stats buffs in the Regular version!
• Bonuses:
  • Shiny bonus: +150
  • IV bonus: +6 for each 8+ IV
  • Remaining HP bonus: + floor(RemainingHP / 8)
  • Item bonus: +1 for a held item

The highest score in Regular would be 561 by full-HP Shiny Venomoth. (368 + 150 + 6*6 + floor(50/8) + 1 = 561.)

List by Base Points (Regular)

#	Pokémon	Catch Rate	Encounter %	MaxLv	MaxLv HP	MaxLv BP
49	Venomoth	75	5%	15	46–50	329–368
15	Beedrill	45	5%	15	44–49	317–359
12	Butterfree	45	5%	15	43–47	315–352
123	Scyther	45	5%	14	43–47	315–352
127	Pinsir	45	5%	14	42–46	313–350
48	Venonat	190	10%	16	45–50	281–325
193	Yanma	75	5%	14	42–46	282–318
11	Metapod	120	10%	18	46–51	263–310
46	Paras	190	10%	17	38–44	259–308
14	Kakuna	120	10%	18	44–49	258–304
10	Caterpie	255	15%	18	44–49	253–300
13	Weedle	255	15%	18	42–47	247–294