Too much power-matching?
Back when I was coaching debate in the 1970’s I became annoyed at what I considered to be the excessive use of “power-matching” in tournaments. A debate tournament, at least in those days, usually consisted of eight rounds in which all the teams (fifty or so) participated followed by elimination rounds in which the top sixteen (or occasionally thirty-two) teams faced off.
In order to assure that the teams in the elimination rounds had to “debate their way in,” power-matching was implemented for the last few preliminary rounds. In power-matching every team competes against another team with a similar record. Because of other constraints this is not as simple as it sounds. In debate a team cannot face another team that it has already debated, it cannot face another team from the same school, and every team must have four rounds on the affirmative and four on the negative.
In the early seventies power-matching was only employed for the last round or two. By the time that I left the activity in 1979 it had generally spread to every round after the first one. Few or no tournaments had access to computers in those days. So, the process was slow (two hours per round was standard) and unreliable. In one case my team was scheduled to meet the same team in the second round as in the first and on the same side!
Nevertheless, it was taken as an article of faith that power-matching was the fairest way to schedule, and nearly everyone embraced it. I was never enthused about it. I even considered doing a study to try to document the effects.
The format used for Swiss Teams at bridge tournaments is similar. The opponent for the first round is usually determined by when a team signs up. Team #1 plays team #2, 3 plays 4, etc. After that the computer determines the match-ups based upon each team’s total victory points in previous matches. Every match has a total of twenty (or occasionally thirty) victory points that are divided between the two teams. So, the possible scores are 10-10, 11-9, up to 20-0. The only constraint is that no team can play the same team twice.
At the top and the bottom this works quite well. The team with the most victory points at the end is almost always one of the very best teams. The team at the bottom is almost always one of the weakest. The problem concerns the teams in the middle two quartiles. Teams that get clobbered in the first two or three matches are rewarded with a weak schedule the rest of the event. The ones that start strong are forced to face strong competition the rest of the way. The effect can be so dramatic that it can arguably be an effective strategy for some teams to throw the first match or two. It is beyond dispute that for the teams in the middle the result of the last match is much more important than the first.
This is not sour grapes; I am certain that I have benefited from this phenomenon as often as I have suffered from it. This last weekend, however, the results were so bizarre that I felt a need to vent. There were only six matches. My team won four matches, including victories over the team that won and the team that came in second. Nevertheless, we finished sixth out of ten teams, and that was not the worst part. There were two strats, and we finished third in the lower strat! Our losses were to the team that came in fourth and the team that came in fifth. The team that won the lower bracket and finished third overall lost the second, third, and fourth rounds, but won their last two rounds against weak teams by large margins. We played six of the other nine teams, but we never got to play against them head-to-head.
Is there an alternative? I think so. If the strats are set by the computer so that there is an equal number in each one, the first few rounds can be seeded so that each team meets an equal number of teams from each strat. Then, the last couple of rounds can be power-matched regardless of the strats. I have a database of results from previous Swiss tournaments. I will think about how it might be possible to evaluate various hypothetical formats on their ability to provide a clear-cut set of winners that reflect performance and fairness.