The U.S. Amateur Team tie-break system seems to have a fundamental unfairness built in. If a team’s opponent scores zero match points in the entire tournament, then the team receives zero tie break points for that round. In a large enough tournament (many teams or rounds), it’s probably unlikely this situation would happen. However, with a smaller tournament, it could happen.
Has anyone tried a variant of this system to solve that problem? I’ve heard a suggestion based on combining this with the modified median tie-break. That leads to another question. Should one drop the opponent with the lowest match point score, or should one drop the opponent for which the product of the opponent’s match points and the team’s game points against the opponent is smallest?
Lastly, it seems odd that the tie-break calculation doesn’t use match point scores modified for byes or unplayed rounds (as is done for the modified median system). Wouldn’t that give a possibly unfair advantage to a team that had scored well (in game points) against a weak opponent who eventually got a bye compared to a team facing a weak opponent who did not get a bye?
No tiebreak system is fair. But they all work (i.e. they all break ties).
The fact that –
– is a testament to the relatively high quality of the current tiebreak system.
Bill Smythe
You could always use the IL High School Association team tiebreaks. They use eight weighted boards for 68 points in a match and the tie break points for each match is (points_scored_against_opponent + 10) * square of(opponents_total_match_points + 1). This usually matches the order of the standard USAT tie-breaks, but occasionally there is a difference. for a non-weighted match you would only add 1/2 or 1.
Another reason for the adds is so that a team gets more for being blanked by the tournament winner than for being blanked by a team that only won that one match.
I fail to see why the difference between 0 and 1/2 should be considered unfair but the difference between 1/2 and 1 is fair.
Every tie-break system is unfair and can be questioned. The trick is to find one that is unfair in a blindly fair manner. The IHSA went to a lot of trouble to correct the perceived deficiencies of the USAT tie-break, but it can still be argued about (the squaring was not done until this year and was designed to grant more emphasis to the opponent’s match score). The +10 add to the game score adds about 1/7 the possible game points, while adding 1/2 or 1 to a USAT game score would be adding 1/8 or 1/4 of the possible game points. That allows for being blanked by a low-scoring team to be worth less than being blanked by a high-scoring team. The +1 add to the opponent’s match score allows a high score against a winless team to be worth more than barely eking out a victory against such a team.
Considering how often the added calculations still match the USAT rankings, I’m not sure whether the apparent gain in accuracy is worth the complexity involved, but then you could make the same argument about comparing other tie-breaks such as solkoff and modified median.
I’m not a fan of the USAT tie break, or anything similar to it. If you had one game per match, the USAT breaker would be Sonneborn-Berger, whose only redeeming social value is that it can break ties in a RR.
The USAT tends to reward crushing wins over middle of the road teams compared with close wins over strong ones. And a close loss to a middle of the road team is better than losing badly to the top team. I think it is much more common for the USAT breaker to produce results which just seem wrong compared with how individual tie breakers perform in a regular Swiss.
WinTD has a “performance index” tie breaker, which is a weighted sum of the Solkoff and total game points. The relative weights change towards the Solkoff as the number of rounds increases. I don’t know if anyone has ever used it, but it might be interesting to see how it compares with the USAT tie breaker when applied to the USATE results.
Sonneborn-Berger doesn’t do such a great job in a RR, either. It rewards inconsistency, i.e. it is better to defeat a high-scoring opponent and lose to a low-scoring one than vice-versa.
Of course, since I’m inconsistent, I guess I’d like that. 
Bill Smythe