And the magic number is minus two

When did this become a math blog? I don’t remember getting that memo. Oh, well…

We are, of course, working from the pyramid structure, starting with 2 presets and then a variable number of further prelims, leading to a variable number of elims.

Some issues beyond the math:

First of all, everyone does not clear. A lot of people come to a tournament to debate. They may hope to clear (sometimes they even hope against hope), but most of the people who pay their admission fees to eat the debate ziti (literally and figuratively) do not break. On one utilitarian plane, we have an obligation to provide the non-breakers with the most for their money. This would be, of course, the most prelim rounds.

Secondly, we want to do our best to fulfill the hopes of clearing. So we need to have a system of prelims that best leads to elims from a sort of Rawlsian perspective. We need to be behind the tabroom veil of ignorance to determine what seems the most fair. This is harder to gauge than the simple utility of more prelim rounds = more for your money overall. To provide elim fairness, everyone behind the VOE needs to agree that the determination is the correct one, i.e., the best one possible. I would suggest that a tournament that breaks most of its down-twos is distributively just. A tournament that breaks all of its down-twos or most of its down-twos and provides a runoff for the small minority at the bubble is probably more just, although often unfeasible.

Thirdly, we need to work with the materials at hand. A judge pool is what a judge pool is. (I want to talk about judge pools absent this particular discussion, so the VCA need not worry that we will go there soon, and in depth. There have been some issues lately…) It really doesn’t matter if one manages a tournament totally at random or if one goes all the way to 9-step MJP, a given debater will get some good decisions and some sketchy decisions and maybe some terrible decisions. Given the human factor, we need to build in some leeway for sketchy and terrible. I would say, let’s allow you to lose one round because of terrible judging (although I would point out the classic issue, as my daughter does, that your opponent also had that terrible judge and somehow managed to pick up that ballot), and another round because of a bad draw. This is a competition, and that seems reasonable. That the same people break all the time, with strong winning records, regardless of which tournament they’re at, regardless of the nature of the judge pool or the tabbing paradigm, indicates that this works, that good debaters get through whatever judges they have to, however they get through them, most of the time (but not necessarily undefeated). Also, the quality of the pool is a big determinant of elims when we go by straight rankings. Rounds adjudicated by all As versus rounds of all As and Bs versus pure randomness? What you break to, depending on the philosophy of the judge selection, will be what you can reasonably accommodate with the pool that you have.

Fourth, we have space/time constraints. Depending on the venue, we have all the rooms we need as long as we need them, or we don’t, and we have all the time we need, or we don’t, or some combination of the two. High schools, excluding the big octo tournaments, are usually limited in both space and time to one and a half days of competition. Colleges have pressures on space (the entire campuses are not given over to the tournament, and often fees are paid per room). Other factors play into this, with varying results.

So, here’s what we want. We want as many prelims as possible to satisfy the vast number of people who attended with competition. We want that number of prelims to intelligently lead to a correct number of elims, with an assumption that most or all down-twos should break. We need to fit those prelims and elims (and bubble rounds) into the time and space we have available for the tournament.

Simple, right?

I want to throw in one more piece of information. I did the math on Princeton, comparing the 4-2s after 6 rounds to the 5-2s after 7 rounds. Assuming no runoffs, breaking 32 of these people meant 29 were the same, 3 were different. In other words, adding the 7th round meant that 3 people who would have broken after 6 were replaced by three other people. If this is meaningful and not merely anecdotal, it would seem as if 7 rounds + a straight break to doubles makes a lot more sense intuitively than 6 rounds + a straight break. 7 breaks almost all of the down twos and 6 doesn’t. In the event, 3 people are harmed. Very utilitarianly sound. The only viable alternative is 6 rounds + a break to triples. This provides fewer rounds to the non-breakers, and probably advances a radically different group to octos than either of our straight 6 or 7. Whether this latter is good or not remains to be seen. I would say not, but I have no way of testing the hypothesis.

Bottom line? Each tournament has to be balanced on its own from both directions. The tournament directors need to figure what makes sense for their time and space, then provide the field with the right amount of both elims and prelims on a case-by-case basis. The participants need to weigh the costs of the tournament against the returns on the investment. In other words, CBAs on both sides. Tournaments that don't balance well the needs of the many will find themselves hosting a smaller and smaller few as tournaments that are responsive to the community will continue to be popular. Rule of thumb? Seems to me that it's probably this: provide as many prelims as possible and as many elims as possible, always with the goal of breaking all the down-twos. The closer you are to that goal, the better you'll look in everyone's cost benefit analysis. And any individual team's decision to go or not go to a particular tournament is an indication of how well or poorly a tournament is doing its job.