Smallest Deposit Group per Magic Wand Size

SELECT w.`deposit_group` FROM `avg_sizes_by_groups` AS w,
    (SELECT MIN(avg_sizes_by_groups.`avg_size`) AS minimum FROM
        (SELECT `deposit_group`, AVG(`magic_wand_size`) AS `avg_size`
        FROM `wizzard_deposits`
        GROUP BY `deposit_group`) AS avg_sizes_by_groups) AS `min_wand`
WHERE w.`avg_size` = min_wand.minimum;