Here's a solution for you: beg, cajole, threaten, bribe, or otherwise convince two D2 teams to play D1 so that you have four teams in D1. Maybe they'll have enough staff that you can talk Chris Romero into entering as a solo team. I don't think there's a rule that says you _have_ to play in D2 if you are D2-eligible. In all seriousness, any method of picking teams is going to have some inefficiency, and you are always going to be in a position where you have x+y bubble teams contending for x slots. 100% efficiency is impossible in praactically every endeavor. It's quite possible that a straight statistical formula will undervalue teams that are speed and tossup oriented, or one that is slow and bonus-strong. Maybe the stats will devalue a tossup-strong team that consistently nails the clue just after the power point. Any formula is potentially biased against teams who are extreme outliers in some measure. In any case, I think it a reasonable hypothesis that the bubble teams are going to be so close in ability that who makes it and who doesn't are going to be separated by 5% of their S-values. NAQT may have reached the point where decreasing unfairness towards one team will increase unfairness towards another team. I'm not privy to the NAQT S-value formula, but there are a few thought experiments one could run using last year's data with the formula. If you take a weak field of six teams and add a hypothetical strong team that decimates everyone else 500-100 in every game it plays, how many places do the other teams in the field shift in S-value rank? In an SCT with a combined D1-D2 field, if you could isolate the stats from only games between two D1 teams, how are S-values affected by adding enough top, median, or bottom D2 teams to fill out the D1 field? (If you want to test the advantage of running up the score, perhaps assume it nets teams an additional tossup per round and a bonus at their normal conversion and see what happens.) And this is just off the top of my head. NAQT has had a lot more time to think about this, and they have at least a couple of statistically savvy people in their ranks. My point is, it's never going to be possible to exactly order teams barring a nationwide full round robin (and even then, you will run into things such as polygons of death). For any quizbowl tournament or organization, quibbling about things such as qualifying or formats or distributions reaches a point where you can only eek out improvements so miniscule that you are better served worrying about the questions, as even the best of tournaments have a few stinkers. Anthony, quizbowl philosopher
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