Davis Cup

France meets Serbia in the Davis Cup final in Belgrade this weekend. The straightforward final match is just the smooth tip of the Davis Cup iceberg. Below the surface the event is massive, sprawling and asymmetric.
The Davis Cup that you pay attention to, if you do, is the World Group, consisting of 16 national teams in a single-elimination format. The quirkiest element is the determination of home-court advantage. It goes to the team that played away the last time the two teams met  in the Davis Cup, no matter how long ago that was. Serbia gets to host this year's final because in a 1991 semifinal France hosted Serbia ... when it was known as Yugoslavia. 
Home court is crucial in any competition in any sport, and in the Davis Cup the home side has the additional advantage of choosing the surface the match will be played on. In last year's World Group, home teams were 12-3; this year they are 9-5. It seems odd to determine something so important based on an event 20 years ago.  But it beats a coin toss, the method used when the teams have never met.

The Davis Cup's real interest for sports structure aficionados begins with the level below the World Group. The eight first-round losers from that stage fall into a playoff against eight winning teams from the next level down, Group I. The eight playoff winners get to play in the World Group next year along with the eight World Group quarterfinalists. The losers drop to Group I. (After losing to Serbia in the World Group, the United States won its playoff against Colombia and stays up for 2011.)

There are three regional Group I's, Americas, Asia/Oceania and Europe/Africa. (Weren't those also the nation states in "1984"?) Group I's are single elimination tournaments, but with numerous byes because of odd numbers of teams.
Let's look at Europe/Africa Group I as an example.  Eleven teams were entered, 10 from Europe plus South Africa. So five need byes and the other six play in the first round. Next, the three winners join the five bye teams; the four winners of these second-round matches get to advance to that playoff that we mentioned.
But that's not all. We have to determine who will fall down to Group II.   Who's going to be in the mix for this? Well, we'll start with the three first-round losers. Then we'll throw in some of the second round losers. Which ones? The ones that haven't won a match yet. Slovakia got a bye, then lost to Austria in the second round. So it is in the relegation mix. But Finland, another second round loser, isn't, because it had won a first-round match to get there.
This year that left us with five teams. So three need byes again. Then in the second relegation round those three are joined by the loser of the only first-round relegation match, and the losers of those two matches drop to Group II.
Whew. Here's a chart that clears it up. A little.

Group II? More of the same, though this year mercifully bye-free. Sixteen teams playoff to determine 2 teams to go up (this year, Slovenia and Portugal) and 4 to go down (Turkey, Norway, Egypt and Macedonia)
Got it figured out yet? Too bad, because it all changes in Group III. At this level Europe and Africa are divided into separate regions, and all the minnows gather at a single site for a round robin tournament.
That's it for Africa and Europe, but in the other regions we sink as far as Group IV, where the likes of Paraguay, Barbados, Yemen and Qatar face off. Even if Roger Federer and Rafael Nadal were to take up Iraqi citizenship, they couldn't lift the Cup until December 2015 at the earliest.