# Winning tennis scores

So, the Australian Open is upon us once more.

I’ve noticed that, just occasionally, a player wins the match while winning less games in the match. I wondered how extreme this could get – for both games and points. That is:

*What is the lowest percentage of games (or points) you can won as a match winning player?*

The principles to follow are:

– if you lose (a game or a set), lose badly, winning nothing

– if you win, do so by the minimum margin

– and do so as quickly as possible, as extended play merely brings the percentage closer to 50%

**Scoring rules summary**

The final set is won by advantage – you must be 2 games ahead, having won at least 6 games.

In earlier sets, sets at 6-6 are decided by a tie break game, resulting in a game score of 7-6 for that set.

To win a tie break, you must be two points ahead, having won at least 7 points.

Also, women’s matches are best of 3 sets, men’s are best of 5 sets.

(For non grand slam events, there are always 3 sets for both men and women, decided, if necessary, by tie break.)

**1. Women**

*a. Games percentage*

Your ‘best’ (in the sense of our discussion) game score could be

– 0-6, 6-4, 6-4, winning 12 out of 26 games, or 46.2% or, even better,

– 0-6, 7-6, 6-4, winning 13 out of 29 games, or 44.8%.

So, between the two options, you play a little longer in the latter, but win only 1 of 3 (or 33%) extra games, dragging the percentage further down – as we want it to do.

*b. Points percentage*

For a game score of 0-6, 7-6, 6-4, you

– win the tie break game 7-5 (i.e. win 7 and lose 5 points)

– win 12 other games ‘to 30’ (i.e. win 4 and lose 2 points) and

– lose 16 games ‘to love’ (i.e. win 0 and lose 4 points)

So, you win 55 points of 148, or 37.2%.

**2. Men**

Using a similar line of reasoning to the above, we get the following…

*a. Games percentage*

Your ‘best’ game score would be 0-6, 0-6, 7-6, 7-6, 6-4, winning 20 out of 48 games, or 41.7%.

*b. Points percentage*

For a game score of 0-6, 0-6, 7-6, 7-6, 6-4, you

– win 2 tie break games 7-5 (i.e. win 7 and lose 5 points)

– win 18 other games ‘to 30’ (i.e. win 4 and lose 2 points) and

– lose 28 games ‘to love’ (i.e. win 0 and lose 4 points)

So, you win 86^{*} points of 244, or 35.2%.

You can apply the same arguments to other WTA and ATP events, or to team events such as Federation, Davis and Hopman Cup ‘ties’.

Amazingly, it is possible, over periods of 25 years or more, for a team to win the Davis Cup more than half the time while winning less than 17.5% of points played.

^{*} Oops! I had 84 instead of 86 before. Thanks to Thomas Oléron Evans for pointing this out.