## Redundancy is great

##### Jul 05, 2023

I have been watching some tennis recently, and noticed that some venues (or broadcasters) have adopted a more streamlined way of showing tiebreak results.

(This is an old example I found online. Can't seem to find more recent ones. Will take a screenshot next time I see this on my TV.)

For those not familiar with tennis scoring, the match is best-of-three sets (for Grand Slam men's tournaments, it's best-of-five sets); each set is first to six games, but if the scoreline reaches 5-5, a player must win two consecutive games to win the set at 7-5, or else, the scoreline reaches 6-6, and a tiebreak is played. The tiebreak is first to seven points, or if 6-6 is reached, it's first player to get two points clear. Thus, the possible tiebreak scores are 7-0, 7-1, ..., 7-5, 8-6, 9-7, etc.

A tiebreak score is usually represented in two parts, e.g., 7-6 (7-2).

At some point, some smart person discovered that the score 7-2 contains redundant information. In fact, it is sufficient to show just the score of the losing side in a tiebreak - because the winner's points can be inferred from it.

The rule can be stated as: if the displayed number is 5 or below, then the winner of the tiebreak scored exactly 7 points; and if the displayed number is 6 or above, then the winner scored two points more than that number.

For example, in the attached image, Djokovic won a tiebreak 7-6 (2) which means 7-6 (7-2) while Del Potro won a tiebreak 7-6 (6) which means 7-6 (8-6).

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While this discovery satisfies my mathematical side - we always like to find the most concise way to do a proof or computation - it is bad for data communications!

It's just bad practice to make readers do calculations in their heads when the information can be displayed visually.

I found where I saw this single-digit display. It's on the official ATP Tour website.

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Just for fun, if we applied the same principle to the display of the entire scoreline, we would arrive at something even more succinct :)

4-6, 7-6(6), 6-4 can simply be written as 4-, -6(6), -4

6-3, 7-6(4), 6-3 is -3, -6(4), -3

6-1, 6-4 is -1, -4

7-5, 4-6, 6-1 is -5, 4-, -1

The shortened display contains the minimal information needed to recover the long-form scoreline. But it fails at communications.

In this case, redundancy is great.