King Morgoth:
I've never been a fan of the theory you've been using for the X-stats.

Why so? It seems a pretty good model of the reality of voter behavior actually.

The main problem is segmentation; certain segments of the population will have highly different preferences - SFF (think a matrix of strength, each character having a different strength against every other character, but generally it doesn't matter except in traditional SFF situations where one character is just kryptonite to another) and cult fanbases (where, say, for them Terra is a [0,.80] in strength rather than a [0,.34] in strength) are where the model is incomplete. But the theoretical basis seems correct, just not complete.

Now with that said, we'll have to figure something because the theory stops making sense in a 4-way-poll

But that can't be, if it makes sense 2-way it should make sense 4-way. There's no real difference; it's just a more general model, n=2 is just a specific case.

In practice accuracy and confidence should be lower, because you're dealing with more variables/unknowns. But the basis makes the same sense.

Using our classical x-stats theory we get the expected result:
Cloud : 54.36% = 28.96% + (.254/1.000)
Mega Man : 28.96% = 14.05% + (.168/.746)*.578 + (.168/.746)*.168/2
Ryu : 14.05% =
2.64% +
(.357/1.000)*(.357/.746)*([.578-.357]/.578) +
(.221/1.000)*(.221/.746)*(.221/.578)/3 +
(.221/1.000)*(.357/.746)*(.221/.578)/2 +
(.221/1.000)*(.221/.746)*(.357/.578)/2
Terra : 2.64% = (.357/1.000)*(.357/.746)*(.357/.578)/4

Hmm...I think you're on to something here! I'll have to look closer at this.

but 30,000 runs isn't enough to get something really close!

Actually 30,000 runs will get it pretty close; seems to have a deviation of half a point or so. If I was doing formula verification/validation I'd use more.

But I think we can all agree that those results don't make much sense...

How so? I'd say that Terra's low percentage is highly counter-intuitive, but it does make sense.

If I was actually predicting I'd probably give Terra in this scenario a "FF6 loyalty bonus", but not a huge one - possibly double (I guess that is huge, but still way below intuitive expectations would have it - and it might well be a mistake to adjust her up that much).


Haste2:
45.01% - Cloud
26.86% - Mega Man
18.27% - Ryu
9.86% - Terra

This massively overrates Terra almost for sure. It quadruples her expected 4-way strength. Like I said, I would probably adjust Terra up, I might even double her up and give her 5% (just because I'm a bit skeptical about characters getting that low - but I have a feeling that will be confirmed very early on once the tourney starts). But giving her 10% is at least doubling what she'd actually be capable of here I think.
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