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jdonn, on Apr 20 2007, 12:47 PM, said:
Gerben42, on Apr 20 2007, 12:36 PM, said:
Not the best team, the team who played best in the tournament.
No, exactly what I said. Read the original post.
"We consider event formats in which the sample statistic [swiss team results] closely mirrors the population statistic [skill level or ability of the teams] superior to formats in which {this is not the case}."
That's a false issue that just has to do with applying the model to real life. Consider the population statistic that was used to be the teams raw "skill level" plus a modifier based on conditions of the day (I.e., current form). So a team that in the OP's model had been rated as a +2 team could be a +1.5 team that is "playing well" (well rested, good frame of mind, etc.) or a +2 team playing normally or a +2.5 team playing below their average skill level. Thus even if the "best team" according to the model won it doesn't necessarily translate into the best same 4 or 6 people winning.
With respect to the more general point there is a procedure for this from the Chess world where many tournaments are swiss tournaments (and in fact where swiss tournaments began) with limited rounds and a 0-1 VP scale (with .5-.5 for draws) and further constraints (have to decide W vs B color issues with the pairings). Obviously in chess tiebreakers are pretty important since with a small range of scores many players can end up tied. See swiss perfect tiebreaking site for all the methods.
The simplest method that sort of works to adjust the SoS that is even simpler than the OP is to simply take your cumulative score. This works as a proxy for your strength of schedule but is very simple to calculate since you only have to look at your own team's score. For instance if you went 20-0, 16-4, 11-10, 2-18 you would have 49 VP out of 80 but your cumulative score would be 20+36+47+49 = 152. If some other team scored 0-20, 11-9, 20-0, 18-2 they also have 49 VP but they were taking the easy side by getting blitzed in their first round and have a cumulative score of 0+11+31+49 = 91. Thus you win the tiebreak.
Of course in chess this only works as a tiebreaker, not as something that gets added to your score. And the problem in bridge swiss events is that the victory points lead to an expanded range so what if that second team was 19-1 in their 4th round match and had 50 VP. Was that a more impressive finish than the first team who played up but only ended up with 49 VP? Probably not. But if you are going to make any adjustment at the end I think you clearly also want that the same kind of bonus/adjustment to be used after each round to set up the next rounds pairings.
To the OP, what exactly was you adjustment formula? You said it depended on the number of rounds, but how did it work?
