Preheat the oven to 400F with the top rack of the oven in the middle position. For easy cleanup, line a 9x13 baking tray or sheet pan with foil.
Remove the drumsticks from the tray onto a couple of paper towels and pat them dry. This helps the seasoning stick.
In a large bowl, combine the olive oil, salt, pepper, garlic powder, onion powder, and paprika. Toss the drumsticks in the seasoning mixture, turning them to coat all sides. This is easier than brushing this wet rub over the tops of each. Place the seasoned chicken pieces in a single layer on the baking sheet.
Bake:
Bake the drumsticks in a preheated oven for 35 to 40 minutes, flipping them halfway through cooking using kitchen tongs. Around minute 30, the skins should be getting nice and browned. For crispy skin, keep the drumsticks uncovered; for softer skin, cover them with a foil tent. Large drumsticks can take longer, 45 to 50 minutes (organic chicken tends to be smaller).
When the drumsticks' internal temperature reads 175F and they're done cooking, remove the tray from the oven and baste them with some of the juices before serving.
Notes
Family-sized package note: A family-sized drumstick package weighs around 5lbs, with around 12 pcs on average. For this amount, adjust the seasoning to ¼ cup olive oil, 1 ½ teaspoons salt, ¾ teaspoon black pepper, 2 ½ teaspoons garlic powder, 1 ½ teaspoons onion powder, and 2 teaspoons paprika.