This is a short review of the concept of "folding the last round" or "creating a bubble". Opiniated, yes, so if you want to change it (it is a wiki after all) please use a new part of the page or a new page to show your opinion. This is not supposed to be well written, or balanced, mainly a small writeup so I'm not telling the same story, same arguments again and again. —Klaas van Schelven.
Update 31st may: I've gotten some responses from Meir Maor on these simulations. I've posted them in notes-bubble-meir. The discussion is ongoing and may have very interesting results.
What is Powerpairing?
In debating tournaments there is some way of matching up teams in the prelims. Power pairing is such a way. In power pairing teams who have done well so far are matched up with teams that have done well so far, teams that have done, well, not so well, are matched up with teams who have done not so well. This is determined by the number of points so far. If there's not exactly a multiple of 4 of each number of points some shifting is necessary.
The idea is that teams that have performed (possibly due to bad luck) less than one would expect on how good they really are meet (usually) teams that are less skilled, therefor these teams have an easier time and make up for some poins. Same vice versa… bad teams with lots of points have an unusual moment of glorious defeat. Evenly balanced rooms are fun because everyone is really fighting for it.
Power pairing is the official only possible way to match up at the Worlds and the only supported way of matching up teams using "Tabbie".
What is a bubble / folding / power protection?
A bubble / folding / power protection (bubble from now on) is exactly the opposite of this. The best performing teams are protected by putting them in one room with the worst performing ones. This effectively gives the teams on low points a very slim shot at still making the break. (1) they're already on low points and (2) they're now facing the, statistically so far, very best teams of the tournament. Usually this is done (if done at all) only in the last round. Sometimes it is only done for the teams that are still in the running for the break.
Why would someone do this?
(This is where strong defenders should put in some links of their own for the sake of debate).
Anyway… the argument goes something like this: "In tournament so and so I've seen the following happen. Team so and so which are a real bunch of losers made it to the break only because they were on very low points in the last round. They met even worse losers and had a horrible judge… so they made it to to the break. The other really good team so and so hit the top room in the last round and lost only barely from Oxford A, B and C. And this happens a lot!
Shortly: low points in the last round may propel bad teams over really good ones who had a top room in the last round… so we should protect the good teams in the last round by "power protection".
(In fact, there's even teams that try to use this hocus pocus logic to their advantage, by getting to a certain low amount of points in the last round and then "propelling" themselves. I hereby advise this strategy to all my opponents)
Why is this a bad thing?
Shortly the argument runs as follows: "(1) It's the opposite of power pairing, (2) power pairing works fairly well. (3) so it's a fairly bad idea.
Moreover:
The evidence as given in the "pro bubble" argument above is highly anecdotal. In fact, the great majority of teams that make it to the break do very well troughout the entire tournament. This can now be verified by looking up some tournaments in www.smoothtournament.com and looking at how the teams did before they made the break. I'd be very happy to hand over the data (SQL) for structural analysis. But trust me: if you want to make it to the break, there's no substitute for winning.
A slightly more formal analysis is the following. (I'm no statistical wizard, so anyone who wants to formalize this is more than welcome to do so).
The "Tab" is basically an ordering of teams… for each round this ordering gets better, because teams face each other, good teams win and therefore move up, and bad ones loose, so move down. Before round 1 the ordering is random. As the tournament progresses, the ordering gets better and better… in the first round the probability of being (un)lucky is higher than in a later round. If you're using full power pairing, the standings before the round (last - 1) will be expected to be worse than the standings right before the last round. (after the last round they're even more well ordered/ correct) Hence the pairings will be more fair in the last round than in the round (last -1). Since a bubble uses the results of round (last - 1), an unfairer pairing and standing, as the basis for protection, the bubble is less fair.
I've run this as a simulation on my personal laptop, and for anyone who's willing to read it the results are in this page discussion-on-bubble-klaas-and-avihu. Short summary: running a bubble on a n-round tournament will give you exactly the fairness of running a fully powerpaired tournament with n-1 rounds. In other words: you're throwing the possibility of extra fairness from the extra round in the garbage for no good reason.
Update: I've gotten some responses from Meir Maor on these simulations. I'll post them in notes-bubble-meir
It seems that these numbers say that powerpairing and bubbling would give equal results for the break in the context of worlds (400 teams, 9 rounds).
Why is there no option to do a bubble in Tabbie?
1. It's a bad thing
2. If you really want it, find someone to put it in for you…. it's Open Source.
Further thoughts (short)
Powerpairing is, though much better than a bubble, by no means perfect. I'd be very happy to exchange some serious thoughts on a different system with some smart people.
(In fact, there seems to be a point at which power pairing is not improving the ordering of the teams any further and a total competition (like all national football competitions) would be better… but then we'd be talking about a lot of rounds…)
(? do different tournament variables change the use of the bubble - eg number of teams, number of teams breaking, number of rounds: 3 rounds, breaking to final and 50 teams one might want to fold the tab)
Very short thoughts from John Harvey
Ages ago I ran some relatively crude simulations on this using Excel. It seems to me that the smaller the tournament, shorter the tournament and the smaller the break, the less reliable power-pairing is. Where 8 teams are breaking, more often than not the 4th strongest team is 4th after four rounds, and after the fifth and final round they are gone.
Folding the competitive teams for the last round has always seemed to me to be a good way to allow the teams currently in the break to defend their position against the teams clamouring to get in. The teams seeking entry into the break have to prove themselves against the presumed good teams. Whenever I folded a competition, I usually only folded 16 teams (with 8 to break) and they were normally teams 2-17, since 1 had already broken. I can't remember my precise rationale. I always considered competitions to really only be four rounds long, with secret quasi-quarter-finals taking place during round 5 while everyone else was debating for fun.
I think the most interesting analysis we need to see here is one on small tournaments (say 30-70, standard IV size) with five rounds breaking to semis. I don't think it's worth worrying about WUDC sized tournaments as they're so big and long that the Law of Large Numbers allows power-pairing to work better than anything else.
Some analysis from Haran Pilpel
I used a Poisson modeling system to simulate tournaments of various sizes and with various numbers of teams breaking.
Since no one really knows what a "bubble" is (as opposed to a fold, which is well defined) I picked a definition arbitrarily (teams which are more than 3 points from the bottom breaking team are out of the bubble.)
There are a bunch of parameters, of which perhaps the most significant is whether you care only about whether the breaking teams are the ones that deserve to break, or whether you also care about how well the non-breaking teams are ranked. I'll assume more people care about the former.
It turns out to depend significantly on the size of the tournament, number of rounds, etc.
Bottom line: for a WUDC-sized event you should bubble. For a EUDC-sized event you should probably not bubble and do a standard power pairing round (the data is marginal.) For an IV, you should do a standard power pairing round.
From Richard Swales
On the point of national soccer competitions being a good model (ie all play all) but not practical in debating because of the number of teams and number of rounds - a compromise could be making sure that the same teams don't meet twice (and prioritising this even over number of points), with less teams or more rounds - (like EUDC99 32 teams seven rounds) it would grade towards an all play all tournament. I think it is a problem with a conventional tab that teams "bounce" up and down the rankings - if they bounce up because they are too low and then bounce down because they are too high, well what if the competition finishes then? On a conventional tab this happens more because teams are concentrated in the middle of the possible points range more than in football style system. Has anyone ever simulated what I propose?
On power protecting - giving the top 16 an easy draw for the last round, this effectively just makes the competition one round shorter and the arguments about "bouncing" apply equally strongly.
