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In the score below, what do the 7 and 4 superscripts mean in the first set?

a screenshot of a finished tennis match score between Carreno and Muller

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    Not worth an entire answer by itself, but I would add that sometimes only the lower of the two tiebreak point numbers is shown in the score. Such as in the example above being shown as 7-6(4), 6-4, 6-5. The number in parenthesis indicates the points accumulated by the player that lost the tiebreaker - which also allows you to know the other player won by either getting 7 points or by getting 2 more than the number shown in parenthesis.
    – jamauss
    Commented Jan 20, 2018 at 4:33

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When a set reaches 6-6, a tiebreaker is used to determine the winner of the thirteenth game and hence the set. The first player serves once, then the players alternate serving twice consecutively, scoring one point per point won, until one player has both

  • seven points or more, and

  • a lead on the opponent of two points or more

The superscript numbers record the final score in the tiebreaker. The first set went to 6-6, where a tiebreaker was played to a score of 7-4 in Carreno Busta's favour, winning him the set 7-6.

Compare with other matches in the competition on the same day.

  • Dolgopolov wins first set versus Schwartzman, tiebreaker 7-1.

  • Seppi wins second set versus Karlovic, tiebreaker 7-4.

  • Karlovic wins third set versus Seppi, tiebreaker 7-3.

  • Edmund wins first set versus Basilashvili, tiebreaker 7-0.

  • Kyrgios wins first set and third set and fourth set versus Tsonga, tiebreakers 7-5 and 8-6 and 7-5.

  • Cilic wins first and third sets versus Harrison, tiebreakers 7-4 and 7-4.

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Per ITF rules (see link for 2018 rules), if a set is tied at 6-6, a 7 point tie-break is played:

When the score in a match is one set all, or two sets all in best of five sets matches, one tie-break game shall be played to decide the match. This tie-break game replaces the deciding final set.

The player/team who first wins seven points shall win this match tie-break and the match provided there is a margin of two points over the opponent(s).

What you see in the superscript is the scoring for the 7 point tie-break game - Carreno won the tie-break 7-4 vs Muller.

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    .. you're quoting appendix V, which is the alternative scoring section. It is not the normal or original scoring system, and irrelevant for the purpose of this question.
    – Nij ♦
    Commented Jan 19, 2018 at 7:26

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