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Does the School of Evocation wizard's 10th-level Empowered Evocation feature increase the damage of the booming blade spell?

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Yes it does, but only to one of the damage rolls.

Empowered Evocation allows you to add your Intelligence modifier to the damage roll of any wizard evocation spell you cast and Booming Blade is an evocation spell, qualifying it for this class ability. Although, according to the PHB's errata:

Empowered Evocation (p. 117). “The damage roll” has been changed to “one damage roll".

However, it doesn't specify which roll it will be added to, so you can choose which one you will add the bonus damage (I suggest the initial roll).

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