Preheat your oven to 425°F (220°C). Line a baking sheet with parchment paper or a wire rack for even crisping.
In a large mixing bowl, combine the paprika, garlic powder, cayenne, salt, and black pepper. Whisk to blend the spices evenly.
Add the olive oil to the spice mix and stir to create a paste-like coating.
Pat the chicken drumsticks dry with paper towels. This helps the skin crisp up during baking.
Use your hands or a spoon to rub the spice mixture all over each drumstick, coating evenly and smoothly.
Arrange the coated drumsticks on the prepared baking sheet or wire rack, spaced apart so air can circulate around each piece.
Place the baking sheet in the oven and bake for about 40 minutes, flipping the drumsticks halfway through. Expect a bubbling noise as the skin crackles and turns golden.
Check for crispness by the color and texture of the skin; it should be deeply golden and crackling. The internal temperature should reach 165°F (74°C).
Remove from the oven and let the drumsticks rest for a few minutes to retain their juiciness.
Serve the chicken drumsticks hot, with the crisp skin crackling as you bite into tender, flavorful meat inside.