Luck (幸運 Kōun) is a stat whose tooltip often describes it as a measurement of the divine favor a character has, or some variant thereof.
Luck is a stat that affects the ability to both hit and dodge attacks. Also, on desert maps where objects lie in the sand, Luck sometimes affects the ability to unearth them. It also reduces the enemy's critical rate chances. In most games, enemy units have either 0 Luck or very low Luck compared to player-controlled units. Fire Emblem: The Blazing Blade's Morphs always have 0 Luck. In most games, Luck can be increased by 4 points by the means of a statue of a deity called a Goddess Icon.
In most games, 1 point in Luck will increase both hit rate and evasion by 1, and reduce enemy critical hit rates by 1. In most games where a Devil Axe exists, 1 Luck will also reduce the backfire chance by 1%.
In Fire Emblem: Shadow Dragon, the effects of Luck on hit rate and evasion are halved. Elice's Luck growth in Fire Emblem: Shadow Dragon is 80%, the highest in the game, and one of the highest in the series (the highest is Fae's 150% in FE6).
In Fire Emblem: Genealogy of the Holy War, the characters with Ulir blood (such as Edain and Brigid) tend to have the highest Luck growths in the game due to the 30% boost. Characters with Baldur (like Sigurd and Seliph) and Blaggi blood (like Claud and Sylvia, as well as Sylvia's children Lene and Coirpre) also show good Luck growth boosts, of 10%.
In Fire Emblem Fates, Luck is used for calculating the activation rates of Dragon Ward, Salvage Blow, Miracle, Profiteer, Good Fortune, and Witch's Brew. It will also determine the activation rates of the personal skills of Kaze, Keaton, Velouria, and Anna.
Though the other traditional Fire Emblem stats are reflected in Tokyo Mirage Sessions as normal, the Luck stat is treated in a more unique manner. Rather than a numerical value, each party member's Luck is rated on a scale of Poor, Weak, Normal, Good, and High. A party member's Luck can be raised by ordering a food or drink they enjoy from a vending machine or business. The effects do not stack, however, and are reset each time a different food or drink is consumed.