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Psychological momentum is a term used to describe a player's confidence. When you are winning, whether at cards or outdoor sports, you tend to go on winning. As a winner, naturally enough, you feel on top of your game, "one up", while your opponent, "one down", feels out of form. This kind of momentum often carries over to the next game.

I wrote here recently that betting on Pete Sampras to lose at Wimbledon might be a good proposition. (As it happens he lost the very same day, but I make no forecast for next week's US Open!) Such "disasters" often happen in sport.

Tennis is a good example of how psychological momentum works: in estimating a player's chances, it is usually assumed that tennis players perform to their official ranking. When it comes to betting, there is another way of looking at it. If a player wins the first set in a five-set match, is it more likely that the same player will win the next set, and the match?

The answer is a resounding yes, according to an analysis of tennis matches by statistician David Jackson of Trinity College, Dublin. (He explains, with cheerful modesty, that the bookies helped fund his research via his winning bets.) He analysed results of all 251 best-of-five-sets matches at the Wimbledon and US Open tournaments in 1987 (Applied Statistics, Vol 8, No 3) in two ways: first on the assumption that the probability of winning a set depended on the official ranking of the two players and was the same for all sets; and secondly on the assumption that winning a set increased the odds of winning the next set by a constant factor.

This second method gave a very close prediction of the actual outcome, both when the favourite won and on upsets. Figures on the upsets showed that 33 matches were decided by a 3-0 margin in sets, compared with a prediction of 26.8; 24 matches ended 1-3, exactly as predicted; and 15 matches ended 2-3 (prediction: 16.8). The same-for-all-sets prediction method was way off.

As sports betting firms allow betting "in running", this analysis offers interesting possibilities, and not just for tennis. Anyone for snooker?

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