Power from the wrist is needed greatly in Badminton because using power to drive your opponent to the back of the court and then suddenly tipping it over the net could win you many points. Not only that but the badminton smash, the equivalent to a volleyball spike, needs a lot of power as you must hit the birdie in a way that it shoots down and then your opponent can't get it.
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Not a lot, though the harder you hit the shuttlecock, the more precicision you get in your shot.
Players need to have enough physical strength so they can have better foot work thats just one of the reasons