You may have seen an orange bubble next to your gears name with the word RIOT, FIGHTER, THIEF, SCHOLAR, CLAN, SLAYER or ORACLE in it. This is the set of the gear and will give you boosts to your perks, and it is highly recommend you try to use as many set pieces as possible as they can give a very large boost to your stats.

Chance to have a set:

White/Green - 16%
Blue - 20%
Purple - 25%
Red - 50%
Yellow - 100%

Any rarity gear can be RIOT, FIGHTER, THIEF or SCHOLAR, however only yellow (godly) gear can be SLAYER or ORACLE and there are only purple, red and yellow CLAN sets.


Boosts provided by each set:
RIOT - 3% def, 1% hp
FIGHTER - 3% atk, 1% crit
THIEF - 3% drachma, 1% ev
SCHOLAR - 3% xp, 1% lp
CLAN - 2% all stats
SLAYER - 4% atk, 4% xp, 2% crit, 2% lp
ORACLE - 4% def, 4% drachma, 2% hp, 2% ev
EVENT - 3% all stats


The boost that a single piece of gear will give is dependant on the rarity of the gear, and can be calculated using the formula:

Set Bonus * Rarity Bonus

Where:
The set bonus is the % mentioned above

The rarity bonus is:
White - 1
Green - 2
Blue - 3
Purple - 4
Red - 5
Yellow - 7

Furthermore, having all 8 pieces of gear being of the same set (regardless of rarity) will give a 2x boost, and having 8 pieces of set gear with the same rarity (regardless of set, just requires every piece to be the same rarity and all be part of a set) will give a 2x boost. Thus, if you have a full matching set of gear with matching sets and rarity, you can get a 4x boost to the stat boost. Please note that EVENT gear will keep the 2x matching set bonus with any other gear set, allowing you to mix and match it and use it however you see fit.


TLDR:-
Bonus for sets and rarities:
Same set, Same rarity (color) = 4x
Same set, Different rarity = 2x
Different set (Each gear is part of a set, though not same set), Same rarity = 2x
Different set (One/more gear does NOT belong to any set), Same rarity = Nil
Different set, Different rarity = Nil


Bonus for full matching sets:

White - 96%, 32%
Green - 192%, 64%
Blue - 288%, 96%
Purple - 384%, 128%
Purple (CLAN) - 256%
Red - 480%, 160%
Red (CLAN) - 320%
Yellow (non SLAYER or ORACLE) - 672%, 224%
Yellow (SLAYER or ORACLE) - 896%, 448%
Yellow (CLAN) - 448%