Mudville Complement' is a phrase that originated from the poem 'Casey at the Bat' by Ernest Lawrence Thayer. The poem tells the story of a baseball team from Mudville, and the phrase refers to the team's supporters who were disappointed when their star player, Casey, struck out in the final inning. The crossword solution for the term 'Mudville Complement' is NINE, which is a reference to the NINE players on a baseball team.