The Wedge Attack
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The Wedge Attack offers two benefits. (1) An increase in the statistical "safe area" to which a disciplined player should hit; and, (2) more importantly, an opportunity to challenge your opponent's conditioning. When a player's conditioning is challenged, they begin to feel pain and inflicting pain is the primary factor in breaking the opponent's will.

The technique of using the wedge may vary from player to player; however, if you can entice the opponent to attempt to an angle from the center of the court, they will provide you with an opportunity to initiate a wedge attack. In short, the first player to attempt an angle will place themselves at a disadvantage to a player who has a mastery of using the wedge attack. Nadal, among all players, is the most skilled at the wedge attack because his topspin allows him to hit to a safe area while assuring that the apex of his shot will land well wide of the court forcing the opponent to expend considerable energy to defend the attack; and, the wedge attack will further induce the natural, scientifically proven evolutionary hedonic fear of moving objects that will likely weaken their resolve. Any dent in the opponent's resolve is first be reflected in weakness in their movement and, more generally, their legs. Any weakness a player's legs will begin the process of their hitting ever more shorter shots or even inducing an unforced error, or errors of judgement, which will accrue to your advantage.

Two more points: Defending against the wedge attack is no more than the classical "bisect the angle of possible return shots". Bisecting the angle of return is very important to minimize the energy loss incurred by having to defend the wider distance created by the wedge attack. The specific physical reason to bisect the angel of return is to avoid excessive acceleration because it is in the acceleration phase of a movement where the most energy is expended, just as accelerating in a car. Second, the wedge attack highly favors the heavy top spin hitter over the flat ball hitter.

Figure 1