Holding/break percentage vs points won on serve/return

[Benhur]

I was looking at the match statistics on the ATP site. The last section on each match is the "point statistics" where they break down the points into points won on serve, and points won receiving serve.

I was a bit surprised to learn that the correlation between this statistic and the break/hold percentages is much less linear than I thought. The correlation is there, of course, but variations in the holding/breaking percentage are strongly magnified by variations in the percentage of points won on serve. By this I mean the following. Let’s assume a match where 50% of points are won on serve, and 50% on return. In such a match, you would expect the break percentage (and the holding percentage) to be both also 50%. It is a safe assumption.

But now what happens is that as you increase the points won on serve above 50%, the holding percentage increases much faster. Thus, winning about 60-65 percent of points on serve, translates in a holding percentage between 75 and 80 percent! And winning above 70 percent of points on serve brings your holding percentage above 90%, making you almost unbreakeable.

An extreme illustration of this strong non-linearity can be seen in the Federer-Roddick match at Wimbledon. Consider. Federer won 78% of his points on serve. Roddick won 71% if his points on serve. So the combined percentage of points won on serve, for the entire match, was just above 74%. And yet the holding percentage for the match was a staggering 96% (only 3 out of 75 games were breaks).

Of course looking only at a few matches is not at all statistically meaningful. An interesting exercise would be to compare break or holding percentages in different tournaments (all matches) with the percentage of points won on return or on serve also for the entire tournament.

I am thinking that calculations done by points, rather than games, may increase the accuracy of comparing the behaviour of different surfaces when it comes to their friendliness toward servers. It just seems like a finer tool. In other words, I would expect the variations within the same surface, year in year out, to be even less pronounced than the variations you obtain by measuring break or holding percentages, though I may be wrong. I wish the organizers of all majors and master level tournaments made these statistics available.

 

[ubermeyer]

check out karlovic's stats on this

 

[Benhur]

check out karlovic's stats on this

Based on the few stats I have seen, I would guess that Karlovic wins above 70% of his points on serve, and above 90% of his service games. But I am not so much interested in individual statistics as in whole tournament statistics as a means to compare the relative "friendliness" of different surfaces toward servers, or if you prefer, their relative hostility toward returners.

We could introduce the ideal concept of a "serve-neutral" surface. This would be a hypothetical surface where the advantage of the server would be completely neutralized, and so it would produce 50% of points won on serve and 50% on return, over statistically meaningful samples. No such surface seems to exist, and perhaps they are impossible. But it is still a useful conceptual tool.

From there, we classify surfaces by the degree to which they increase the advantage of the server. There are, of course, those who maintain that there is no relation between a surface and the percentage of points won by servers on that surface, but this school of thought is not based on rational thinking. If different surfaces keep producing stable differences in these numbers, the Agent responsible for such remarkable regularities needs to be named, or at least guessed. If the Agent does not lie in the differences between the surfaces, then perhaps it is the Holy Ghost, who assigns certain numbers to each tournament and allows little deviation from them.

To be fair, variations in Altitude could be such an Agent. So it is important to consider only tournaments at similar altitudes. Fortunately for our investigations, most major tournaments are at or near sea level. So we are left with variations in surface to explain those numbers, or... the Holy Ghost.

 

[bolo]

I was looking at the match statistics on the ATP site. The last section on each match is the "point statistics" where they break down the points into points won on serve, and points won receiving serve.

I was a bit surprised to learn that the correlation between this statistic and the break/hold percentages is much less linear than I thought. The correlation is there, of course, but variations in the holding/breaking percentage are strongly magnified by variations in the percentage of points won on serve. By this I mean the following. Let’s assume a match where 50% of points are won on serve, and 50% on return. In such a match, you would expect the break percentage (and the holding percentage) to be both also 50%. It is a safe assumption.

But now what happens is that as you increase the points won on serve above 50%, the holding percentage increases much faster. Thus, winning about 60-65 percent of points on serve, translates in a holding percentage between 75 and 80 percent! And winning above 70 percent of points on serve brings your holding percentage above 90%, making you almost unbreakeable.

An extreme illustration of this strong non-linearity can be seen in the Federer-Roddick match at Wimbledon. Consider. Federer won 78% of his points on serve. Roddick won 71% if his points on serve. So the combined percentage of points won on serve, for the entire match, was just above 74%. And yet the holding percentage for the match was a staggering 96% (only 3 out of 75 games were breaks).

Of course looking only at a few matches is not at all statistically meaningful. An interesting exercise would be to compare break or holding percentages in different tournaments (all matches) with the percentage of points won on return or on serve also for the entire tournament.

I am thinking that calculations done by points, rather than games, may increase the accuracy of comparing the behaviour of different surfaces when it comes to their friendliness toward servers. It just seems like a finer tool. In other words, I would expect the variations within the same surface, year in year out, to be even less pronounced than the variations you obtain by measuring break or holding percentages, though I may be wrong. I wish the organizers of all majors and master level tournaments made these statistics available.

The scoring system in tennis probably generates at least some of this non linearity. That's very interesting to see it in the stats. like that.

 

[Nadalfan89]

Tl;dr.....

 

[fps]

interesting. 60% points won on serve would translate to the server winning 3 out of every 5 points. this would put him at 40-30 on average, and then there'd be a 60% chance he'd win the next one. assuming his opponent won the next point, statistically the server is winning 3 out of the next 4 points. this would mean the server, from deuce, is likely either to win the next two points (75% chance first point, then 66.6.% chance second), or win one, be pegged back to deuce, then win the next two.

if you look at it that way, the high hold % isn't that surprising IMO. but i am definitely not a mathematician, so that may logically be gobbledegook.

 

[Benhur]

interesting. 60% points won on serve would translate to the server winning 3 out of every 5 points. this would put him at 40-30 on average, and then there'd be a 60% chance he'd win the next one. assuming his opponent won the next point, statistically the server is winning 3 out of the next 4 points. this would mean the server, from deuce, is likely either to win the next two points (75% chance first point, then 66.6.% chance second), or win one, be pegged back to deuce, then win the next two.

if you look at it that way, the high hold % isn't that surprising IMO. but i am definitely not a mathematician, so that may logically be gobbledegook.

I think your reasoning is on the right track. An expert in statistics could probably do the calculations and show the correlation between the two measurements for each percentage point. My blind guess from what I've seen is that by the time you reach about 82% of service points won, you may be at about 98 percent in holding percentage. Almost unbreakeable.

Of course within one given match freak things can happen, and even winning 82% of your service points could in theory produce enough breaks for you to lose the match in straights, if it turns out that the few points you lose on serve come lumped together in two or three games, while you barely lose a point in all your other service games. But over the course of a whole tournament (or a whole individual career) the averages will look more like described above.

 

[kidbourbon]

I would think about it like this:

Let's say you and a friend were having a contest to see who could hit ten free throws first. You alternate shots. Your free throw shooting percentage is 60%. Your friend's is 70%.

Your friend only shoots 10% better from you from the foul line. But he'll beat you way way way more than 10% of the time that you beat him. I would venture to guess he'd beat you 9 out of 10 times.

Why? Because for each shot your friend takes he has a better chance of making it than you do. And each shot is an indepdent event, so as you go further into the shots you are likely to fall further and further behind.

Similarly, with tennis, the percentage of winning the single event (a point) will be less than the percentage of winning a game, which is an aggregation of points.

I wish I knew how to show this with math, but I don't. But I do see how it makes intuitive sensen.

 

[joeri888]

This is becomes it's games. If you win 75% of points, the chances you lose 4 out of 6 (or 5 out of 7) are lower than 25%. Pretty obvious