In table tennis there's an ongoing controversy about "illegal" serves. Often the question arises how strong the influence of serves on winning probability is. I stumbled upon a recent paper, but I find it not convincing.
The problem to me is how to calculate the influence of serves while the two opponents have a difference in playing strength and a different number of serves. (In table tennis serve changes every two points and every game another player is serving first, so depending on the results of the games there may be a small difference in number of serves.)
Here's an example:
Player A vs. Player B: 11:7 9:11 11:5 11:9 11:7
Points played: 92
Points won: A = 53, B = 39
Serves: A = 48, B = 44 (A started serving in games 1, 3 and 5)
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| | Won on own serve | Lost on own serve |
| Player A | 32 | 16 |
| Player B | 23 | 21 |
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Player A won 57.6% of all points. While serving he won 66.7%. Player B won 42.4% of all points. While serving he won 52.3%. It' obvious from these numbers that serving helps to win the point.
Given these numbers how can I calculate the advantage of having the right to serve in table tennis?
Won on own serve
and "Lost on own serve", if you are interested in comparing the means. Although these are proportions really, so maybe you could use a proportion test. $\endgroup$