By Franc Klaassen
The sport of tennis increases many questions which are of curiosity to a statistician. Is it actual that commencing to serve in a suite offers a bonus? Are new balls a bonus? Is the 7th video game in a suite fairly vital? Are most sensible gamers extra reliable than different gamers? Do actual champions win the massive issues? those and lots of different questions are formulated as "hypotheses" and validated statistically.
Analyzing Wimbledon additionally discusses how the result of a fit might be anticipated (even whereas the fit is in progress), which issues are very important and which aren't, the way to opt for an optimum carrier approach, and even if "winning temper" really exists in tennis. aimed toward readers with a few wisdom of arithmetic and records, the e-book makes use of tennis (Wimbledon particularly) as a automobile to demonstrate the ability and wonder of statistical reasoning.
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Extra resources for Analyzing Wimbledon: The Power of Statistics
The reason that the simple method works in practice is that, at many points, mi does not much depend on pi + pj , as we saw in the previous chapter. Still, there may be points where pi + pj matters. For two players I and J in a speciﬁc match, we should perform a sensitivity analysis to check whether the match proﬁle changes when the estimate of pi + pj is changed. We shall do so below and conclude that the inﬂuence on the match proﬁle is small and that the proposed simple method thus accurately estimates the match probabilities.
Best-of-three versus best-of-ﬁve The usual format for a tennis match is best-of-three: the player who ﬁrst wins two sets has won. In the majors the women play 22 Analyzing Wimbledon best-of-three, but the men play best-of-ﬁve. 4 we plot the probability mi that I wins the match as a function of pi − pj , for a cluster of values of pi + pj , calculated at the beginning of the match. Again we see that the dependence on pi − pj is much stronger than the dependence on pi + pj . 4: Probability of winning the match, bestof-ﬁve (dark) versus best-of-three (light) The best-of-ﬁve curve (for the men) is always above the bestof-three curve (for the women) when pi > pj (and below when pi < pj ).
Second, it may be the case that the probability si that I wins the set (which is what interests us here) depends primarily on one of these two new parameters and very little on the other. We shall see that both ideas hold here. The interpretation of the new parameters is as follows. The probability pi that I wins the point on service depends not only on how well I serves (and plays in the rest of the rally, servi ), but also on how well J returns (recj ). Thus we can write pi = servi − recj , pj = servj − reci , and this implies that pi − pj = (servi + reci ) − (servj + recj ) , pi + pj = (servi − reci ) + (servj − recj ) .