Anyone know what’s going on? I think I’m Audi (out) but the rules aren’t worded too well.

Andy Murray tweeted this shortly after Juan Martin del Potro beat Roger Federer.  When that happened, 3 players in the Group A had a record of 2-1, each winning and losing the same number of sets.  Indeed, Federer had asked del Potro whether he made the semifinals or not.  del Potro shrugged thinking he had not made it.   This lead to a state of confusion.  Apparently, Federer knew enough that he had made the semifinals, but he knew it was close for Murray and del Potro.  Based on the results discussed below, we see why del Potro, probably not a math-whiz, was confused (as even ardent fans might have been).

Let’s discuss the tiebreak rules for deciding who makes the semis.  We’ll do the math to see why Federer and del Potro made the semifinals.

Only 2 players from each group make the semifinals.  The 2 are picked based first on their win-loss record.  Federer, Murray, and del Potro each won 2 matches and lost 1.  All three players beat Fernando Verdasco for one of their wins.  Murray beat del Potro but lost to Federer.  Federer beat Murray but lost to del Potro.  del Potro beat Federer, but lost to Murray.

The next tiebreak rule is the percentage of sets won.  Since every match in group A went 3 sets, and each of the top 3 players in group A had the same win loss record, each player also had the same win percentage of sets won.  In particular, each of the 3 players won 5 sets (winning 4 sets in their two wins and 1 set in their one loss) and lost 4 sets (losing one set each in their two wins, and two sets in their one loss).

The next tiebreak rule is the percentage of games won.  Let’s look at the record of each player.

First Roger Federer.

  • Federer d. Verdasco 4-6, 7-5, 6-1 (17 games won/12 games lost)
  • Federer d. Murray 3-6, 6-3, 6-1 (15 games won/10 games lost)
  • del Potro d. Federer 6-2, 6-7 (5-7), 6-3 (12 games won/18 games lost)
  • Total for Federer: 44 games won/40 games lost
  • Win percentage for Federer: 44 / (44 + 40) = 0.524

Now to del Potro

  • Murray d. del Potro 6-3, 3-6, 6-2 (11 games won/15 games lost)
  • del Potro d. Verdasco 6-4, 3-6, 7-6 (16 games won/16 games lost)
  • del Potro d. Federer 6-2, 6-7 (5-7), 6-3 (18 games won/12 games lost)
  • Total for del Potro: 45 games won/43 games lost
  • Win percentage for del Potro: 45 games won/88 games played = 0.511

Finally, Andy Murray

  • Murray d. del Potro 6-3, 3-6, 6-2 (15 games won/11 games lost)
  • Federer d. Murray 3-6, 6-3, 6-1 (10 games won/15 games lost)
  • Murray d. Verdasco 6-4, 6-7 (4-7), 7-6 (7-3) (19 games won/17 games lost)
  • Total for Murray: 44 games won/43 games lost
  • Win percentage for Murray: 44 games won/87 games played = 0.506

The final tally:

  • Federer win percentage: 52.4 percent games won
  • del Potro win percentage: 51.1 percent games won
  • Murray win percentage: 50.6 percent games won

One could argue that Verdasco played the role of spoiler.  Verdasco was mathematically eliminated, but played Murray very tough.  Murray had a very difficult time breaking Verdasco despite numerous break point opportunities.

Oddly enough, Murray needed Federer to win the match over del Potro (Federer would be 3-0, Murray 2-1 and del Potro 1-2) or he needed Federer to lose in straight sets (Federer, Murray, del Potro have 2-1 record, but del Potro and Murray would have best set percentage win).  With Federer able to win the second set, each player had the same set win percentage and the tiebreak went to game win percentage.  This is where Federer’s risky style of play pays off.  When he wins, he can create lopsided set scores.  Against both Murray and Verdasco, Federer had a 6-1 set.  Murray can have lop-sided set scores like that, but his style generally leads to closer matches.

So Murray fails to make the semifinals by the smallest of percentage.  Had he won the third set 7-5, then he and del Potro would have identical game win percentage.  In this hypothetical scenario, they probably would have applied head-to-head again and Murray would have won that tiebreak by virtue of beating del Potro.