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At the 2017 US Open, Murray (seed 2) withdrew 2 days before the tournament began, but 2 days after the draw had been posted. After his withdrawal the draw was changed with the following movements:

  1. Cilic (seed 5) took Murray's place
  2. Querrey (seed 17) took Cilic's place
  3. Kohlschreiber took Querrey's place
  4. Lacko came in as Lucky Loser (LL) into Kohlschreiber's place

In other tournaments, I have seen the LL take the place of the player withdrawing. For example in Cincinatti Masters 2017 Fabianno took Federer's seed 2 place in the draw. No other rotations happened here. Why is it different in the US Open?

What is the criteria for these movements? Is it random, or do they answer to certain rules?

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It has to do with the tournament trying to keep competitive balanced opponents for as long as possible throughout the duration of the tournament. It's the same reason why the tournament distributes seeded players evenly into the draw to begin with so that they avoid high-profile matches until the later rounds of the tournament.

Related: See my answer about the makeup of tennis tournament draws here.

If Murray had not been seeded at all, then Lacko probably would have taken his place directly, instead of the shifting around of the draw that happened. But since Murray was seeded #2, it would throw off the distribution of competition in Murray's quarter of the draw to replace him with a lucky loser (LL). Now instead of playing Murray, his initial opponent (Sandgren) will play Cilic instead - which isn't much of a change in terms of the ranking and talent of the opponent.

The reason you might have seen the LL take the place of the player withdrawing in other tournaments is because the player withdrawing wasn't seeded. That's my guess, but if you can find a specific draw you're referring to maybe I can look at that case specifically.

You can read about the specific rules regarding the replacement of seeded players and lucky losers that starts at the bottom of page 24 of this document :
http://www.wimbledon.com/pdf/GS_Rulebook_2015.pdf

For tournaments sanctioned by the ATP (non-grand slam events) - see the ATP rulebook starting on page 106 for rules regarding the placement of seeds and vacancies: http://www.atpworldtour.com/-/media/files/rulebook/2017/2017-atp-rulebook_30dec16.pdf

  • I think you can quite often see LL to replace seeded player. For example, Rublev taking Coric's place in Umag. And in tournaments where some seeded players have byes in the first round, you can quite often see LL starting in the second roungs, such as Tipsarevic in Cincinnati. Since I was able to find these examples just by looking at recent tournaments, I'd guess that this is quite common. – Martin Aug 27 '17 at 10:01
  • I suppose that in examples I mentioned above (and in other similar cases) it was too late to make changes in the draw when the player withdrawn. – Martin Aug 27 '17 at 10:02
  • Those tournaments you mention are also ATP events and the US Open is ITF so they might follow some different rules. – jamauss Aug 27 '17 at 10:34
  • The key is in the document that jamauss linked. It shows a separate rulebook only for grand slam tournaments. I would have assumed that all professional tournaments would follow the same rules. The question then is why the rules for replacing withdrawn seeds is different in grand slams from other tournaments. – twalbaum Aug 27 '17 at 16:39
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    Good answer. I get the logic behind it. Move the player next in line to the next "tier" of rankings (so 5th goes into the top 4 if someone drops out and 17th goes into the top 16 to replace them). I am a little surprised that they skip the 1-2 "tier" and the 5-8 tier but I guess that is to minimise disruption. (I use tier for a group of seeds that are equivalent for working out who you end up playing against throughout the competition, as in if you switch the 5th and 8th seed you still get a valid draw). – Christy Aug 29 '17 at 9:30

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