Stir chili powder, salt, garam masala powder, vinegar, crushed ginger and garlic in yogurt and mix well.
Make diagonal slits in the drumsticks and coat in yogurt marinade. Cover and refrigerate for six hours or overnight.
Preheat oven to 450°F with a rack in middle. Place drumsticks in ovenproof dish, cover with foil and bake for 15 minutes.
Remove cover and let the chicken bake for another 15 minutes.
Increase heat to 500°F and bring oven to broil. Broil chicken for 8 - 10 minutes.