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Say, in a USTA adult league match or a NCAA match, what is the purpose of numbering lineup positions by theoretical skill level?

For example, if teams are of four players, then the best player from each team will play each other, the second-best player of each team will play each other, and so on.

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The idea here is to prevent "unfair" results which can be caused by random matchups.

For a very simplified example, consider a situation where a higher ranked player always beats a lower ranked player, and the two teams are:

  • Team A: players ranked 1, 3, 5, 7, 9
  • Team B: players ranked 2, 4, 6, 8, 10

It's clear here that team A is the better team, and that's the result which happens if the players match up in order: 1 beats 2, 3 beats 4, 5 beats 6, 7 beats 8, 9 beats 10 and team A wins the match 5-0.

Now consider what happens if team B plays the 10th ranked player "out of order": 1 beats 10, 3 loses to 2, 5 loses to 4, 7 loses to 6, 9 loses to 8 and team B wins the match 4-1.

That's obviously a very simplified and exaggerated example, but even with some less simple models you can show that you get the "correct" result more often with in-order pairings than with other schemes.

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  • Are there typically restrictions on how teams set their lineups, based on past performance? In USTA it seems that lineups are moved around loosely, even though the better players are in the higher part of the lineup roughly.
    – Curious
    May 10 at 19:15
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    @AustinConlon I couldn't comment on specific tennis leagues; as hinted above, I know this from chess matches where it is generally fixed - although of course chess has a well-defined rating system that tennis leagues may not.
    – Philip Kendall
    May 10 at 19:18

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