Botched comes from the Middle English word bocchen (meaning to mend).  And that word may possibly have come from the Old English term bōtettan (which can mean "to improve", "cure", "remedy", or "repair").  And that word may have come from the Old Dutch botsen, butsen, or  boetsen (meaning "to repair" or "patch").  You may not find it interesting, but I enjoy learning the origins of the words Myr selects for the Word of the Day.