Preheat oven to 400°F (200°C). Line and lightly grease a baking tray.
In a bowl, toss drumsticks with olive oil, garlic powder, smoked paprika, salt, and pepper. Arrange evenly on tray.
Bake drumsticks 30 minutes, flipping halfway.
Meanwhile, simmer barbecue sauce, honey, Worcestershire sauce, and hot sauce until thickened (5–7 min).
Brush drumsticks generously with glaze. Bake additional 10–15 min until caramelized and cooked through (165°F internal). Broil briefly if desired.