Place eggs in a saucepan with a lid, pour in water to cover, bring to a boil, and remove from the heat. Cover and let stand for 10 to 12 minutes. Remove eggs from hot water and let cool. Peel the eggs.
Cut each egg in half lengthwise, remove the yolks, and place the yolks in a bowl with the mustard, mayonnaise, Worcestershire sauce, hot pepper sauce, and salt and pepper. Mash the yolks, and stir the mixture until smooth and thoroughly combined.
Fill each egg half with the deviled yolk mixture, using a spoon, piping bag, or a sturdy plastic bag with a corner cut off. Dust each egg with a pinch of paprika, and place an olive half, round side up, in the center of each. Refrigerate until chilled, 20 to 30 minutes, and serve cold.