Preheat the oven to 425 degrees F. Line a baking sheet with foil or parchment paper, and set a wire rack on top if you have one for better air circulation.
Pat the chicken drumsticks dry with paper towels so the skin can crisp up.
In a large bowl, toss the drumsticks with olive oil, salt, garlic powder, onion powder, smoked paprika, black pepper, chili powder (if using), and baking powder (if using) until evenly coated.
Arrange the drumsticks in a single layer on the prepared baking sheet or rack.
Bake for 35 to 40 minutes, flipping halfway through, until the skin is browned and the internal temperature reaches 165 degrees F.
Remove the drumsticks from the oven and brush generously with barbecue sauce.
Return to the oven and bake for 5 more minutes to let the sauce set and caramelize.
Serve warm, with extra barbecue sauce on the side if desired.