#### Sysyphus

##### Talk Tennis Guru

[Trigger warning: this thread is directed primarily at those who are unduly interested in the nitpicky and trivial aspects of tennis stats. If that ain't you, this thread's probably not for you.]

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As many of you already know,

Say player A wins 70% of his serve points of his service points and 35% of his return points. Assuming an equal number of points played on serve and return, this should suggest that he wins 52.5% of points overall. His DR would be 35/30 ≈ 1.17

Player B wins 65% of service points and 40% of return points, which (assuming equal amount of serve and return points played) suggests the same % of total points won. However, played B would end up with a lower DR of 40/35 ≈ 1.14.

Therefore, it looks like ceteris paribus DR is slightly skewed toward players with better serve stats. Now, I wasn't sure whether this slight skew meant that DR is slightly inaccurate compared to just % of points won, or whether it's actually a clever way of weighting for an actual advantage of stronger serving. Perhaps the ratio of return points won vs. service points lost tells us something important beyond what just total % of points won tells us. That was my hunch, that DR would be a slightly stronger predictor.

To check this, I ran a quick regression analysis comparing first the connection between DR and match win %, then % of points won and match win %. Thanks to this excellent thread by Falstaff, where he shows that DR explains a lot of variance in match win %, there was already a data set to look at where half the data was already plotted in (the clay seasons of Nadal, Ferrer, Djokovic and Federer through 2012/2013), so I used that sample for convenience's sake.

What were the results?

As such, this seems to me to beg the question:

This was pretty spur of the moment, and I may have overlooked something obvious. Calling tennis stat enthusiasts @falstaff78 @Chanwan @TheFifthSet @Gary Duane @Meles and the rest.

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As many of you already know,

**dominance ratio (DR)**is a nifty little stat to show how dominant a player has been in a given match, season, or similar. It has been shown to explain a lot of the variation in players' win %, and is thought to be a good predictor of future results. On the face of it, it's pretty similar to looking at what % of points a player wins, but not quite. How is it calculated? By dividing**the percentage of points you win against your opponent's serve versus the percentage of points your opponent wins against your serve**. Wouldn't that amount to pretty much exactly the same as just % of total points won? Not entirely – let's look at two hypothetical examples.Say player A wins 70% of his serve points of his service points and 35% of his return points. Assuming an equal number of points played on serve and return, this should suggest that he wins 52.5% of points overall. His DR would be 35/30 ≈ 1.17

Player B wins 65% of service points and 40% of return points, which (assuming equal amount of serve and return points played) suggests the same % of total points won. However, played B would end up with a lower DR of 40/35 ≈ 1.14.

Therefore, it looks like ceteris paribus DR is slightly skewed toward players with better serve stats. Now, I wasn't sure whether this slight skew meant that DR is slightly inaccurate compared to just % of points won, or whether it's actually a clever way of weighting for an actual advantage of stronger serving. Perhaps the ratio of return points won vs. service points lost tells us something important beyond what just total % of points won tells us. That was my hunch, that DR would be a slightly stronger predictor.

To check this, I ran a quick regression analysis comparing first the connection between DR and match win %, then % of points won and match win %. Thanks to this excellent thread by Falstaff, where he shows that DR explains a lot of variance in match win %, there was already a data set to look at where half the data was already plotted in (the clay seasons of Nadal, Ferrer, Djokovic and Federer through 2012/2013), so I used that sample for convenience's sake.

What were the results?

**Dominance ratio explained 76.9% of the variation in winning percentage**(like Falstaff found).**The correlation between DR and match win percentage was .877.****Percentage of total points won explained 78.3% of the variation in match win percentage, and the correlation was .885.**

DR

% points won

% points won

As such, this seems to me to beg the question:

**does using dominance ratio really add anything useful compared to just using the simple nuts and bolts metric of % of points won?**The explained variation and correlation is almost exactly the same. If anything, % of points won seems to do slightly better, which may give credence to the idea that DR has a slightly unnecessary skew in favor of better serving.This was pretty spur of the moment, and I may have overlooked something obvious. Calling tennis stat enthusiasts @falstaff78 @Chanwan @TheFifthSet @Gary Duane @Meles and the rest.

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