Are some points in Tennis more important than others?

If they are, do some players do better on important points than they do on unimportant points?

Tennis lends itself to Simpson’s Paradox. Simpson’s paradox is the observation that a trend which appears in A, B and C disappears, or even reverses itself when considered for the combined A+B+C record. In Tennis the paradox is evident when a player wins a majority of the points but loses the match.

This leads some people to conclude that in Tennis some points are more important than others. That all points are not created equal. Further, this leads to a wide array of pseudo-psychological tropes like “coming good on the big points”, “mental toughness” etc. As Roger Federer pointed out, what appears to be “mental toughness” is really just a demonstration of a wider array of skills. Players who appear to be mentally tougher have more types of shots, react faster and move better and this enables them to stay in a larger variety of points. But Federer’s argument runs into a thick brick wall of sports punditry which sees a sporting contest as a question of who is the better man (or woman), and not a question of who is the better player. The former idea has wider appeal in the public and is thus popular in sports writing. The latter idea is only of interest to people who are curious about that particular sport. But this does not make the former idea true and the latter idea untrue.

I looked at point-wise data from Tennis Abstract for Grand Slam tournaments since 2011. I selected players who had featured in at least 50 matches over this period and they are shown in the table below. There are between 9-15 thousand points for each player. I organized their win % by the score at the start of the point as shown in the table below. The average win percentage for a score is listed under the column ‘Average’.

Plotting the table above provides this picture. A uniform decline from the point in the game where the player is ahead the most to the point in the game where the player is behind the most.

The table below shows a comparison of each player on each point to the average. Unsurprisingly, the four most successful players - Djokovic, Nadal, Federer and Murray are above average on more points than the others.

Finally, since the existence of 40-0 depends on the existence of 30-0, which in turn depends on the existence of 15-0, I looked the distribution of points. I grouped the points into five categories as shown. It shows that the difference between the more successful players and the less successful players is that the more successful players are behind in a game less often than the more successful players.

Its safe to say that the idea that the better players are better on what might be considered more important points in a game than on less important points is unfounded. The better players are generally better on all points in a game. They win more points because they are generally better players.

It is also obvious that there is no such thing as an important point and an unimportant point. Every point weighs exactly the same and matters exactly as much as any other. Why? Because the so-called ‘important point’ would not come about without prior points. So the fact that the important points are called important is a problem of the observer. Much as in Edwin Abbott’s Flatland, it is the observer being stuck at a certain shallow depth in the point chain, and being unable to notice that extra link. Take Carl Sagan’s famous description of the tesseract from the series Cosmos, and replace the idea of the higher dimensions with the idea of a greater depth in the point chain, and you’ll see what I mean.

The better players are better players because they are better at more things. The greatest players also add to this the ability to learn new things extremely quickly and solve problems faster. This is a question of skill and ability - virtuosity, and not a “big heart”.

In fact, when we hear comments about how a player has a “big heart", or “the uncanny ability to come good when it matters”, what we’re really hearing is a complete inability to describe Tennis. These phrases are stand-ins for the inability to describe how Federer might have mastered three or four different types of backhand which he can play with different types and amounts of spin, different speeds and different trajectories, compared to his opponent who might have mastered only one or two and may be less sure of the the other two. If each is more suitable to a particular position in a point, then the player who commands a wider array of strokes is more equipped to respond from a wider array of positions. It is this difference which decides who wins and who loses.

How often have you read about these differences in reports and match stories? If you know of people who write about actual Tennis, please leave your recommendations in the comments .

Carl Sagan describes the idea of higher dimensions.