Numbers

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The Independent Online
MODERN tennis, people sometimes complain, is boring and predictable. This is because the big serve dominates. For example, in 94 matches last year, Pete Sampras served 1,011 aces. He won 82 per cent of the points in which his first serve was not a fault, 53 per cent of his second serves. For a big hitter like him, the advantage of serving is about 2 1/2 -1. For other top players, it is nearer 2-1.

So each point in the matches at Wimbledon will be roughly equivalent to the toss of a biased coin for which heads is twice as likely as tails. A five-set match will have about 300 points. If the winner were simply the player who scored most points the complaints that tennis is boring would be even greater. The chance of an upset is increased by dividing matches into 'games' and 'sets', which are statistically more unreliable.

If serve is to be broken, we need, on our biased coin, two more tails than heads in a series of six tosses or more. The probabilistic calculations tell us that, where the server's advantage is 2-1 this will happen about once in seven games. If the server's advantage is raised to 3-1, he will be broken only once in 20 service games. Indeed, such a player would still be marginally the favourite to win a game from 15-40 down. Sampras wins 90 per cent of his service games, and has a better than evens chance at 0-30 down.

But a single break of serve is enough to win a set. Even a man whose serve is broken only once in 10 games can lose in straight sets

if the statistical bounce goes against him.

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