[IKE]

Ed,
Your even average opponent strength has an inherent flaw that the performance metrics for teams do not follow a distribution that would be reasonable to apply such an algorithm.

For instance, last year the average match score was aroun 24-30 points, which would mean in theory the average team contribution would be 8-10 pts. In reality, the middle teams had a much lower contribution because several teams (5%) were able to do 60+ points on their own.

In order to balance the competitive levels, the good teams will invariably have the lowest scoring partners way more often. For games like last year or 2008, this might not be a deal breaker, but games like 2009 would be extremely difficult with the poorest performing partners. If you add in these parameters, teams may intentionally "game" such a system. If you are using OPR, they might shave points (2010). With other performance metrics, you could see other behaviours that one may not want to see.

Like coin flips, sample size with a more random generator will help a lot more than forcing a "fairness algorithm" function.

An important think to keep in mind is that this is 3 vs. 3. This can be demonstrated with some dice pretty well (actually the dice are even more "fair" in distribution and probability). If your team is a 3, and your partners are random draw, then on average, you will have a 6 on your alliance about 1/3 of the time (2 of 3 dice are rolled with 6 outcomes thus 2*1/6=1/3 in having at least one 6). On the other hand, the opposing alliance will on average have at least one 6 1/2 of the time (3*1/6=1/2). This would lead you to believe you were given an unfair schedule, even though it doesn't get much more fair than 3 dice vs. 3 dice. The "6" knows that 100% of the time, they will have a 6 on their alliance (its them), and 1/3 of the time (2*1/6), they might even get another 6. This would appear that they have a "stacked" schedule. The average combination for the "3" team would be 10 (3+2*(6+5+4+3+2+1)/6=10), where as the actual average would be a 10.5 (3*(6+5+4+3+2+1)/6=10.5), and the average for a "6" team would be 13 (6+2*(6+5+4+3+2+1)/6=13). The numbers only get worse if you are a 2 or a 1.

This is not to say that crappy schedules do not happen. You can roll double 1s in a game 2 times in a row.

I think the match scheduling challenge is a really neat exercise, but be warned that good intentions can have dire consequences. As others have mentioned, the "algorithm of doom 2007" was really tough on lot of teams. I did some trials after that year. With a 2x2 format, you can use a geometric progression in order to do pairings for many sizes of events. I tried using a similar geometric progression for a 3x3 and accidentally stumbled upon results very similar to "the algorithm of doom". Make and test your programs, and you will find that "easy" methods collapse after the first 3 rounds.