The weird scoring system used in tennis makes the game more exciting by boosting the chances of the underdog winning, a mathematical analysis shows.
“The result is not unexpected,” says Chris Hope of the University in Cambridge. “But as far as I know no one has quantified it.”
In most sports, what matters is the total number of goals, runs or points. But in tennis – where players compete for games and sets – some points are more equal than others.
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In fact, found that in 5 per cent of pro tennis matches, the winner scores fewer points than the loser. But as many players say they save energy by not fighting for every point if they don’t need to, this finding does not reveal what difference the scoring system makes.
Virtual tennis
To find out, that assumes each player has a fixed chance of winning a point each time they serve. He then “played” 100,000s of virtual matches to see what role chance and the scoring system play.
Some of the top male players win 78 per cent of points when they serve. Hope found in a fairly close match against an opponent with a 73 per chance of winning their service points, the underdog would win 16 per cent of matches if you only count the overall number of points. But with the actual scoring system used in tennis, the underdog won nearly 24 per cent of matches – an 8 per cent boost.
The results show the best player does not always win in a tennis match – chance alone can play a surprisingly big part when players are closely matched. And the scoring system increases the odds of the underdog winning even further.
“They could still win by random chance under a points-based system but it wouldn’t happen as often,” says Hope, who did the out of curiosity – his day job is modelling the effects of climate policy.
The reason is that in matches where players win most of their service games, breaking someone’s serve is a big advantage. And just a short run of bad luck – losing four points on the trot – can hand the game to the opponent.
The tennis scoring system makes less difference when there’s a greater gap between players’ abilities or when players are less likely to win service points. For instance, the best female players win only 70 per cent of points when they serve. If a top female player plays an opponent who wins 65 per cent of service points, the underdog has a 24 per cent chance of winning on points only and 27 per cent chance with the actual scoring system – a boost of only 3 per cent.
Hope isn’t suggesting that tennis should change its scoring system. On the contrary, other sports such as basketball would be more exciting if they also chopped the scoring up into smaller chunks like tennis does, he says.
