The dumbbell single leg squat jump exercise is going to be great for developing strength and explosiveness in a players one leg jump. This is really good for finishing at the basket off of one foot, but it is also great for sprinting up the floor and developing that strong driving power in your legs. When you do the exercise you want to be thinking about explosiveness and really driving off of the leg you are jumping from.
Along with working on developing strength and explosiveness, this basketball exercise is great for working on the stabilizer muscles around the knees and hips. Hopefully this will also help to prevent playing injuries from happening, or keep them from being as severe. This exercise is going to translate directly to your on court basketball training and games, and is recommended for all basketball players (that are old enough).