Luck (運) is a stat whose tooltip often describes it as a measurement the divine favor a character has, or some variant thereof. It 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: Rekka no Ken's Morphs always have 0 Luck. In the modern games, Luck can be increased by 2 points by the means of a statue of a deity, called 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. Cain'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 Karel's 120% in FE6).
In Fire Emblem: Genealogy of the Holy War, the characters with Ulir blood (such as Adean and Briggid) tend to have the highest Luck growths in the game (if not in the whole franchise), which is 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 Leen and Corpul) also show good Luck growth boosts, of 10%.