From PokéFarm Q Official Wiki
Long Chain Bonus
The Long Chain Bonus is a bonus which increases a user's chances of hatching a Melanistic Pokémon. This boost depends on a user's rank.
- Below Champion Rank: the boost is 1% per 100 eggs up to a maximum of 50% at 5,000 eggs.
- At Champion Rank: the boost is based on a user's EggDex and Pokédex completion progress after obtaining the Champion Rank. The Long Chain Bonus will gradually scale up in both power and cap, the closer users are to Arceus rank.
- Note: (0.375 x Egg% x Poke% + 1)% per 100 eggs / max 3750 x Egg% x Poke% + 5,000
- At Arceus Rank: the boost is 1.5% per 100 eggs up to a maximum of 150% at 10,000 eggs.