2

Looking at Befair tennis, what is the percentage of broken service games? If both players are fairly evenly matched, how many times does a player lose his service game?

3

I found some statistics here. It will depend on whether they're playing on grass (relatively hard to break), hardcourt (medium) or clay (relatively easy).

Wimbledon (grass)           1998: 19.78%  2007: 17.34%  2008: 16.77%
US Open (hardcourt)         1998: 21.53%  2007: 21.87%
Australian Open (hardcourt)                             2008: 23.18%
Roland Garros (clay)                      2007: 24.13%  2008: 23.68%

So on the professional level, it's less than 1 in 4, but more than 1 in 6.

1

20%

This post refers exclusively to ATP World Tour matches, and includes no data from the Challenger or Futures circuits. As you specifically said "his", it also includes no data from the WTA Tour.

Over the last decade[1], the returner has won 21.3% of games. This ranges from a peak of 22.7% in 2011 to a low of 20.2% in 2015. 2018 so far[2] has been fairly typical, with the returner winning 20.6% of games.

Surfaces make a huge difference. Here's a table showing the surface by surface difference for the last decade, the lowest and highest yearly rates, and the 2018 break percentage:

+---------+------+------+------+------+
| Surface | Avg  | Low  | High | 2018 |  
+---------+------+------+------+------+  
| Clay    | 24.2 | 23.0 | 26.1 | 23.1 |  
| Hard    | 20.8 | 19.8 | 21.7 | 20.3 |  
| Grass   | 16.9 | 15.5 | 18.6 | 16.6 |  
| Carpet  | 18.9 | 16.1 | 24.4 |  ——  |  
+---------+------+------+------+------+  

If the table doesn't display properly for you, here's a screenshot of it. Note that carpet was discontinued as a ATP World Tour surface in 2008, so its inclusion in this table is from just 728 games played at the 2008 Grand Prix de Tennis de Lyon, and 331 games played in Group II of the 2016 Davis Cup.

If both players are fairly evenly matched

Balance does make some difference, but not a huge amount. If we make the assumption that matches later on in a tournament are going to be more balanced, then you can see a clear trend in the data by looking at the numbers per round:

Percentage of games won by the returner, all surfaces (2008–2018):

  • R128: 21.9%
  • R64: 21.3%
  • R32: 21.7%
  • R16: 20.7%
  • QF: 20.8%
  • SF: 19.8%
  • F: 20.2%

It's worth noting that for many events the Round of 32 is the first round, so you would not expect there to be a drastic increase in average matchup quality until the Round of 16, where in nearly all tournaments, each participant has to have won at least one match. Indeed, as soon as you get to this point service is broken a percentage point less often. If you look at just semifinals and finals, it drops another percentage point, to 19.9%.[3]

It's fairly evident that in completely one-sided matches (6–0, 6–0), the average percentage of service games that get broken will come out to 50%. The round-by-round data seems to show that a match being even remotely competitive (a.k.a., between two players good enough to be in the ATP World Tour) will bring this average down to the low twenties, at which point it will more slowly decline to a plateau of about 20% in heavily competitive matches. So there's your answer.

Other notes:

  • Service is significantly more secure in an indoor match than an outdoor one. Returners win just 19.5% of games indoors, compared to 21.7% outdoors.
  • There's almost no difference between best of 3 and best of 5 matches as far as broken service games go (21.4% and 21.1% respectively).
  • In a fairly even best of 3 match, both players would expect to be broken 4-5 times on average.

1: for the purposes of this post "the last decade" refers to the 31st of December 2007 (start of 2008 Adelaide, Doha, and Chennai events), through to the 23rd of September 2018 (end of 2018 St. Petersburg and Metz events)
2: excluding the ongoing Chengdu Open and Shenzhen Open.
3: As there are twice as many semifinals per tournament than finals, the 19.8% in semis drags the average down more than the 20.2% in finals brings it up.

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