I outlined the general procedure followed by NAQT in issuing Division I ICT invitations in a previous message. The key thing there (and the only thing, for Division II) is that we rank all participating teams according to their "SCT performance." The question is always asked, "well how do you do that?" And we never answer, precisely. But, here's the basic idea, hopefully forestalling the annual barrage of "but we beat so-and-so head to head; why are they invited and we aren't? or "we finished in 4th place -- why was the 5th place team in our region invited first, and why was the 7th place team in another region invited?" Ranking teams statistically within tournaments isn't too hard, especially tournaments that play full round robins and don't wind up splitting their field later into different groupings for secondary round robins; doing so across tournaments with greatly differing strengths of field is a challenge. We need to attempt it however, and wish to be as fair as possible. For the record, official order of finish within an SCT is not itself a factor in how we rank SCT "performance," for the purpose of ranking teams in invitation order. That ranking is largely a factor of points scored per tossup heard and bonus conversion, with an adjustment for strength of schedule, so that teams from different sectionals may be compared, and we try to minimize statistical advantages to teams who fatten their tossup numbers against opponents who collectively rate as below the average team across all teams in their division at sectionals, and minimize the statistical disadvantage to teams whose numbers are presumably deflated by facing better-than-average opponents. By whatever percentage a team's actual opponents throughout the tournament average out to be better or worse than the overall average for all teams in the same division (and playing on the same question set; Division II teams in mixed-division fields excepted) across all tournaments, to the same degree a team's initial rating of points scored on tossups (not bonus conversion averages, which are not affected by opponents' strength) is adjusted up or down. We also then tweak a little bit based on actual won-loss percentages, which usually has little effect, but can move a team up or down in relative rankings a little bit as a reward or punishment for compiling a won-loss record much different from what statistics would predict. (i.e., you'll get a little boost in your ranking if you win most of your close matches, and have your ranking a little deflated if you lose most of your close ones. It rarely happens that our rankings diverge wildly from a tournament's order of finish, though it is fairly common that we will rank teams adjacent in official standings in reverse order for purposes of ICT invitations. It was an unfortunate necessity this year to be rather more subjective in trying to compare Division II teams who played only other Division II teams, on Division II questions, with Division II teams who played in a mixed field, on Division I questions. Basically, statistics there are apples and oranges and can't be compared. So we ranked both types of Division II teams separately, and apportioned invitations between the two types using our best judgment and considerations such as field size, and the amount of statistical gap between teams above and below in the rankings of the two types. It is probably true nonetheless that sectionals that were unable to provide separate play for their Division II teams did make it somewhat harder for those teams (other than the champions) to rank highly in the invitation derby.
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