LogFAQs > #935297460

Since we're talking about, let's bring some math into this. Let's pretend that every song has a strength that is (a) consistent, (b) transitive, and (c) unalterable. Obviously, none of those things are true. Then let's also pretend the placement in the bracket is purely random. Now let's rank the songs in a division 1-12.

The 1 seed will make round 3 100% of the time.
The 2 seed will make round 3 8/11 (73%) of the time and be eliminated by the 1 3/11 (27%) of the time.
The 3 seed will reach round 3 {8/11 * 4/10 + 3/11 * 8/10} (51%) of the time. It AND the 2 will lose 6/110 (5%) of the time. So it will be the bonus poll winner about 44% of the time.
It's nearly guaranteed that the remaining 29% of the time, the 4 seed will win the bonus poll.

Using more math...the chance the overall 2 seed across two divisions is in the same division as the 1 is 11/23 (47%). The chance that it loses to it in the first two rounds is 3/23 (13%). So there's roughly a 13% chance of the top two songs retiring as a result of one invading the other division. (As opposed to 52% they simply start in opposite divisions.) The chance the overall 3 seed across two divisions is ALSO in the same division is 21.7%. If it wins the bonus poll 44% of the time, as noted above, this means an invading 3 seed surpassing the other division is roughly 9.5%. Between the two, averaged across 16 divisions, we can expect roughly 3.5 division winners making the runback after losing in their initial division.

And y'know what? I'm fine with that, as long as that number is under 4. Because 4 out of 16 is the likelihood the bottom fourpack winner would triumph if we had normal 16-entry divisions. What this back-of-the-envelope math tells us is that -- with some REALLY heavy assumptions, particularly about how bad the bracket designers are -- the second-chancers have a realistic chance of winning, but not a superior (or even equal) chance.

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VGMC13 champion: Ar Nosurge - Class::EXSPHERE_NOSURGE;