Set drumsticks on a baking sheet in a single layer. In a small bowl combine garlic powder, paprika, salt and pepper. Sprinkle over the drumsticks and flip to coat all sides. In the same small bowl, combine the olive oil, mustard, honey and ketchup. Then smother the chicken, again flipping to reach every side.
Cook in the oven, flipping once and baking for 10 minutes on each side. Let sit for 5 minutes before serving.