We might have enough material here to get our own paper on arXiv, you know.Alex Holowczak wrote: ↑Fri Apr 13, 2018 12:39 pmI'm not sure I agree with any of those three assertions. That it "causes teams and spectators to have to make last-minute travel plans" is not true at all. Whether you re-seed or not ... it's a knockout tournament. No one with any sense is going to book travel tickets to a round of a knockout tournament that they haven't qualified for yet, or when you don't know who or where you're playing. So wouldn't you just wait until the pairings are published?Chris Goodall wrote: ↑Thu Apr 12, 2018 10:49 pmhttps://pdfs.semanticscholar.org/a16b/e ... 95a2d3.pdf
"Baumann, Matheson, & Howe (2010) noted that reseeding causes teams and spectators to have to make last-minute travel plans, which both increases costs and potentially reduces demand, and that reseeded tournaments eliminate popular gambling options related to filling out full tournament brackets, potentially reducing fan interest in the tournament."
That's from a guy called Alexander Karpov, so you know it's applicable to chess.
Organisers can come up with their own ways of making life difficult for travelling fans without relying on the seeding of brackets, anyway. We see it in the Premier League with games moved for television, particularly to unhelpful times to access grounds on public transport or get home in an evening. The AFL came up with its own impressive way of upsetting fans - their lease of the MCG said that at least one game per round of the playoffs had to be played there. And so one year, Adelaide's fans had to travel to the MCG to watch their team play a home playoff game against ... Melbourne.
I don't know how popular "fill the bracket" gambling is in the UK - it's certainly popular in March Madness, but I don't think that has quite made it over to the UK. My not remotely educated impression is that match-by-match gambling, or potentially gambling on a series of events down a list (e.g. the Scoop6). I realise their comments are "potentially reduces", but I don't think either has a very large potential.
(The theorem that I thought I'd proved in a different way, is actually a different theorem from the same paper: For a given seeding, there exists at least one probability matrix that breaks it. That there exist probability matrixes that break every possible seeding, is a somewhat different theorem. But I'm still chewing it over.)