The value of an 'average' video depends on how many of the other participants try to make their 'best' videos. The greater the number of participants, the less likely any single individual is going to put in their best effort. On the other hand, the fewer the number of participants, the more likely a 'best' effort is going to get eliminated, regardless of its quality relative to other brackets.
It's mainly a prediction on the average number of videos that will cross a "worth keeping" threshold. With 2 participants, there's a high likelihood that both are worth keeping, but only one is allowed to proceed. Similarly for 3-4 particpants. At 4-5 participants, there's a high likelihood of 1-2 entries -not- being worth keeping, and as you get up to 8 you'll probably have a fairly wide spread of quality. I expect that spread, when graded, to most often fall out like:
- Code: Select all
|x x x
| x x
IE: a few at the upper end of quality that are clustered together, a few moderate ones, and then a few that fall off quickly.
Anyway, I would consider the selection of a particular elimination format to be done for three goals:
1) to mitigate against random distribution errors
2) to generate as many videos by the best participants as possible
3) to encourage participants to put their best effort into each round
Suppose we have 4 participants. For comparison, we will set the quality of what these participants can produce as: 9.1, 9.0, 8.0, 7.0. However we don't know where they're going to fall within the brackets. The two primary combinations we'll see are:
1) A: 9.1 vs 9.0, B: 8.0 vs 7.0; final round is 9.1 vs 8.0
2) A: 9.1 vs 8.0, B: 9.0 vs 7.0; final round is 9.1 vs 9.0
In these cases we get to see either:
1 video by 7.0
2 videos by 8.0
1 video by 9.0
2 videos by 9.1
1 video by 7.0
1 video by 8.0
2 videos by 9.0
2 videos by 9.1
With the random distribution of the participants we don't know which we're going to end up with, but we would -prefer- to see the second option, as that would give us more videos by the best participants.
This example is a little weak since I'm trying to keep it simple, but the effect can be seen with how those two brackets were generated in the first place -- two groups of four that each contained those participants.
If it had been a combined bracket, we'd instead have one elimination with all 4, of which 9.1 and 9.0 would proceed regardless of which brackets they originated from (A or B). It would have the same number of videos, but we'd have one less song.
However, which configuration is likely to push the participants to do their best? With two one-on-ones, second place gets dropped immediately. With a combined set of 4, second place is 'good enough'. On the other hand, with the combined set you have to beat at least 2 other people, while with the one-on-one you only have to beat one person. So there's balances in both directions.
Perhaps the mahjong bracket size of 4 would do better in terms of forcing tighter competition, but it would be problematic in the first round due to issues of participants dropping out, and the fact that quite a few are really not going to be so great. I can see 8 as being excessive to maintain over the entire tournament, but it's certainly a stronger choice for the first round.
Drops are also a problem. One person dropping out of a set of 4 puts the end result critically low on participants. Two dropping out means there's no point in running that round at all. Further, if someone drops out of a later round, there's not as much of a pool to pull from if you wanted to re-seed empty slots.
With a set of 6, one person dropping out has a pretty limited effect on that round, and two people dropping out still allows for the round to be run. It also allows better options for re-seeds if that was done.
With a set of 8, dropping out is mostly a non-issue.
Overall, I could see it done in one of two ways:
1) Groups of 8 for round 1, then groups of 4 from then on, until the finals. Re-seed empty slots from the nearest ancestors based on score if anyone drops out.
2) Groups of 6 for the entire run, with the finals being a 3-way showdown instead of one-on-one. Re-seed empty slots from the nearest ancestors based on score if anyone drops out or if you're short participants due to non-power-of-2 numbering.
I'm more inclined towards #2, since that allows brackets to mix together immediately, whereas for option #1 brackets wouldn't combine until round 3. It also never allows a one-on-one, even in the finals.