
BGonline.org Forums
Live PRs
Posted By: Henrik Bukkjaer
Date: Monday, 10 February 2014, at 2:08 p.m.
In Response To: Live PRs (Matt CohnGeier)
I suppose your idea is that in order to be averaging below 2.3, you would have to play around three quarters of your matches at 2 or lower, since you will have the occasional 3, 4 or maybe even 5 in the mix  and you cannot pull your avg. down the same way, by playing half, zero or negative PRs...
However, as Jake, I think there's still a long way to the 90% tournament favorite figure.
If I get the format right, all winners progress in the "win" side, and all PR winners progress in the PR side. The two sides the meet in the final, where you need to win both match and PR to win it all. You can progress in both sides if you win match and PR in the first round.
Say you're the worlds greatest player ever, and you have a chance of winning at a rate of about .55, and you have a chance of outplaying your opponent of around .8  I'm not sure if these figures are way off, but let's try:
You need to win two in a row to reach the final. Either two wins (30%), or two PRs in a row (65% there). That would give you:
19.5% chance of securing both final seats (and thus the outright win).
56% chance of getting one seat.
24.5% chance of not reaching the final.In the final, your .55 win and .8 PR chances combine to something like a 44:9 or roughly 83% advantage...
In a reg. 8 player single knock out tournament, your chance of winning would be up from 12.5% to 17% being a .55.56 favorite in each match. In the dualduel you're obviously much higher than that (66% according to the calculation above), but your tournament winning chance would certainly not be near the suggested 90%. Comparing these figures are a little like apples and oranges, since the dualduel is sort of a double elim, and the winchance in a double elim would be a bit higher than the 17%.
Please note: There are clearly some correlation between win and pr win in the first round, I have no clue how high that correlation is (if you play good you have a better chance of winning, but it's a bit easier getting a low PR when you loose). I suspect that correlation will bring the total win chance down, not up, but I'm not sure.
One thing is sure, the advantage certainly rise quicker in a PR contest, than it does looking at actual winning chances, when you're the better player.
The only question that remains is about PR variance  how much will a given advantage translate into. It must be possible to make a rough formula stating that if you're a x% favorite to win a match, then you're a y% favorite to win the PR contest in the same matchup.

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