The single-handed backhand is a thing of beauty.
Firstly for its flexibility.
Secondly for its aesthetics.
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Thirdly for its rarity.
Roger's is one of the best single-handed backhands there has ever been. And there are only a handful around today, including most notably Richard Gasquet, Nicolas Almagro, Tommy Haas and Feliciano Lopez.
Federer can do so many things with his backhand. Topspin cross-court or down the line, gentle slice, cutting slice, defensive lobs, backhand overhead volley, backhand drop-shot and reach more balls that other guys with a double-handed backhand can't.
The single-handed backhand of Federer is particularly good at finding impossible cross-court angles by reducing the power, or by using incredible power to blast the ball past his opponents into the open court.