Returning to an older thread, in 11376, STI writes: << (1) No matter what system is used, somebody is going to be unhappy about it, and somebody is going to "just miss out;" (2) No one can foresee every eventuality, and any system that did would be complicated almost to the point of uselessness; (3) NAQT has never said "X is the formula that will be used for the rest of time." If the results bother a lot of people, I'm sure they'll change it for next year. >> Ah, but there's the problem: we won't know that there's something wrong with the formula until *after* something happens that bothers a lot of people. A couple of years ago, if I recall correctly, NAQT invited a third-place team and a fourth-place team but not a second-place team from one of the sectionals. After people complained about this, NAQT changed the secret formula so that this outcome would be less likely. If NAQT had told us that this order of invitation was possible, and asked beforehand what people thought of it, NAQT might have changed the secret formula earlier and *avoided* the outcome that proved to be unpopular with its customers. << (4) If you want to suggest a system for choosing teams, send it to NAQT, or post it here. NAQT people do actually read this board. >> The proposal I wrote in 11353 is to use the current secret formula for (unadjusted) S-values to determine the number of teams to invite from each SCT site, and then invite teams by order of finish at the SCT. I just thought of something else about this scheme: if a team declines an invitation, then the invitation could go to the next team *from the same SCT*. This rule would help the geographic diversity at the ICT to reflect more accurately the geographic diversity of the good SCT teams. The obvious argument against this rule is that there could be a steep drop in quality from the last invited team from a particular SCT to the next ranking team at the same SCT. It may seem unfair or unwise to invite such a "bad" team when there are wait-listed teams elsewhere that are likely to do better at the ICT. But NAQT doesn't invite actual SCT teams of players to the ICT: it invites a certain number of teams from each school, and the school can put anyone on those teams, regardless of whether they ever even played at any SCT, as long as they are eligible students. This leniency is a bit unusual, but there doesn't seem to be much complaint about it. (I don't disagree with it myself, because it seems to work well in practice.) In a similar way, just as top players who can't make it to the ICT can be replaced with other players from the same school, if top teams from a particular SCT can't make it to the ICT, then they can be replaced with other teams from the same SCT. Another nice thing about this invitation scheme is that the waiting list becomes a lot simpler. If, say, your school had one team, which placed fifth in its division in the SCT, and the top three teams got ICT invitations, then you know that you will be invited to the ICT if and only if two of the top three teams decline. In message 11473, R. suggests a situation in which NAQT might invite a non-champion of a small division of an SCT while not inviting the champion: << An extreme case would be one in which 2 DI teams play with 10 DII teams, the first team wins its games by an average of 400 points and gets 80% of the tossups but loses to the other DI team by 5 points. The other DI team beats the DII teams by an average of 5 points and answers 35% of the tossups. In this case, at least, S-values will cause the first DI team to be invited ahead of the second, even though the second is the champion of the SCT. NAQT believes that there is strong reason to think that the first team will do (much) better at the ICT than the second, despite the second team's championship. >> I would tend to agree with this last sentence, although the championship win suggests that the second team performs better against tough competition -- or, probably the likeliest reason for this outcome in practice, the best players were staffing before the finals and didn't play (much) until the finals. In any case, I think that the players involved in this would expect that winning the championship should outweigh the difference in S-values. In this example, the second team has pulled off an upset. I wouldn't want to be the NAQT person who has to say to that team, "Congratulations on your upset championship win, but the other team performed better overall, so we'll invite them instead of you." In message 11479, R. writes: << our S-value calculations make it impossible for a team from a lower playoff bracket to be invited ahead of a team from an upper playoff bracket since the difference in quality of opponents faced is usually considerable. >> Hm, "A is impossible because B is usually true?" Just to clarify this, is it a mathematical impossibility or just very unlikely?
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