On Oblivion
Strength is used to determine your Encumbrance, at a 1:5 ratio. In other words, your Encumbrance is equal to your Strength stat multiplied by 5.
Strength is a key factor in determining how much damage you do with a Melee weapon.
While it is possible to increase your Strength over 100, damage dealth with a Melee weapon is not increased for increased Strength. However, your Encumbrance does continue to increase, so having over 100 Strength will allow you to carry more.
 On Morrowind
Affects how much you can carry, how much Fatigue you have, your starting Health, and how much damage you can do with melee weapons such as swords and axes. Governs the skills of Armorer, Blunt Weapon, Axe, Long Blade, and Acrobatics.
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