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My question is to ask how the scheduling for the WTFs is done. I understand the grouping. There is Group A and Group B with the following properties: seed 1 is assigned A or B uniformly at random (50-50 probability), and seed 2 goes in the other; repeat this for pairs (3,4), (5,6) and (7,8). However, how are the matches scheduled?

Specifically, is the case that, in each of the groups, the first match the top player plays is against the bottom, and the two middle play each other. Looking through the history, I see that since 2009 this has been the case since 2009 (at least), with the exception of 2013 (when seed 5 played 7 to open up).

It's possible that there was some reason for it not happening this one year, or maybe it's just that 8 out of 9 years this has happened! (Note that it happened in both groups for all years except for 2013, and neither group in 2013.)

Does anyone have any evidence to suggest what the answer to this is? I'm not interested in unfounded hypotheses, but actual evidence, such as "too unlikely" on a small sample. (For example, at one point Djokovic was drawn in the same half as Federer in 17 out of 21 grand slams -- but these are done randomly, this was just an exceptional event.)

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First, a minor correction in OP's understanding of the grouping In the ATP World Tour Finals with regards to the first two seeds.

According to The 2017 ATP Official Rulebook (Page 42):

"The field shall be divided into two (2) groups of four (4) players each. The topseeded player shall be placed in Group "A" and the second-seeded player shall be placed in Group "B""

So, this is indeed not random, but the systematic selection method for determining the 1st seed being placed in the first group, and the 2nd seed being placed in the second group.

From this point on however, The 2017 ATP Rulebook does not prescribe a specific order of play in which the seeds of each group must play, nor on which day of the tournament the seeds will play, but only states that each seed must play 1 match against the other players in his group; 3 matches in total.

Traditionally yes, the way the matches have been broken down is that within Group 1 and 2's first round of matches, the (1) or (2) seed will play the lowest seed (7) or (8), and the two middle seeds will play each other; (3) plays (5) or (4) plays (6). The 2017 ATP World Tour Finals follows this format as well!

Indeed, it appears the 2013 World Tour Finals is the only instance in which this format was not followed, and the reasoning for this is ultimately conjecture.

However, we can deduce from the absence of Official ATP Rule direction on the matter that the order of play is ultimately up to the discretion of the venue hosting the event.

Also, as long as each player plays the other three in their respective groups, the event is still abiding by ATP rules, so the tournament organizers really have the ability to schedule the order of play however they see fit, perhaps with player feedback. The rationale behind this sort of information is rarely disclosed to the public though, and is shrouded in doubt and ambiguity; as seen with this year's controversy in Rafael Nadal supposedly asking tournament organizers to push back his day of play.

Ultimately however, the ATP has produced no official order of play that The World Tour Finals must abide by and has left this up to tournament organizers and directors.

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    Ok, good point on the grouping. What I said was right modulo a symmetry condition ;) (but what you said was just plain right!) – Sam T Nov 14 '17 at 13:53
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    My feelings were basically the same as what you've written but, as you say, there is no evidence to suggest that they in general do it a certain way. Maybe the organisers feel doing it this week is best for publicity -- not sure. (And a note on Nadal: I feel that almost surely that's pure conjecture, based only on the fact that it was better for Nadal to play on day 2) – Sam T Nov 14 '17 at 13:55

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