People looking for a partner: (Requests)
andylt
AmazingKirby
baubeta
BeTheMan
Biolizard28 (Suprak, pikaness)
consolefreak (HM)
DarkLink89
entropyx
Evil_REmade
freac
Gaddswell
GoldSlime35 (?)
HeroicTronBonne
Icon
jonthomson (Sine)
Kaidyn04
Link versus Cloud
Mantyke
marioinblack
NClark128
oneills1
PeaceOut64
pikaness
Radix
Ringworm
SF_Clowns
Shaduln
Shoenin_Kakashi (?)
somdude04
SpikeDragon (Stifled)
Starion
StifledSilence
supdawg
Suprak the Stud
Taslion (Tombawocxer)
Tombawocxer
Tom Bombadil (icon)

Teams:
1. Kaxon/King Morgoth - Team We Used To Be Good?
2. Janus5000/KleenexTissue50 - Team Battle with Gilgamesh = J-E-N-O-V-A
3. neonreaper/Sess - Team Jagermeister
4. amyvitality66/raytan7585 - Team Klonoa Alliance
5. Dekar TKB/Haste2 - Team Drunkadelict Armadillos
6. Explicit Content/Master Moltar - Team Big Black Wangs
7. linkhatesganon/ScorpionX3 - Team Los Gonzalez
8. DSRage/War13104 - Team RAGE OF WARCRAFT
9. _Yonex_/Ayvuir - Team The Shy Teds
10. Stingers/Tirofog - Team Eltbus
11. MajinZidane/Smurf - Team The X Crewstaters
12. Alanna82/kawaiifan - Team Jigglypuff
13. BBallman7/LinkLegend27 - Team omgcelticscouldmaketheplayoffs
14. Luis_Sera89/StifledSilence - Team StifledSera
15. TRE/Xcarvengerx - Team ???
16. FastFalcon05/kaonashi1 - Team Better Bettors
17. CrimsonOcean/Lady Ashe - Team Vector Industries
18. Applekidjosh/Jay Lv99 - Team Elitist Clique Members
19. outback/Rodri316 - Team High Society
20. Aprosenf/Draco1214 - Team Indomitable Force
21. satai_delenn/Lopen - Team The Council of Two
22. MaxedOutRyu/yoshifan823 - Team Boondock Saints
23. Sir Chris/yoblazer33 - Team ???
24. Forceful Dragon/SBell0105 - Team DragonBellZ
25. BZer0/ShatteredElysium - Team Ice Cream
26. basmeyer42/ps2rulezzz - Team mvp's
27. GameBopAdv/IhatethisCPU - Team It's An Upset! And You're On Your Own
28. Eeeevil Overlord/Maniac64 - Team Fodder
29. Camden/meche313 - Team Happy Happyists
30. Vlado/Zylo the wolf - Team ???
31. alpha door/Lagoona - Team LADS
32. Ness26/TheKnightOfNee - Team OH IT'S NESS
33. BlAcK TuRtLe/XxSoulxX - Team lol xstats
34. Jmast7/Leebo86 - Team ?Discovery Channel?
35. Dilated Chemist/Z1mZum - Team Awesome
36. Pats_Dynasty/SuperSmash Master - Team ?ISS GON RAIN?
37. creativename/Ngamer64 - Team Predestined Divination
38. StopPokingMe/ToadYoshi - Team Jinjo! Unless poking objects
39. GrapefruitKing/Xuxon - Team Team Helmasaur King
40. DpObliVion/WiggumFan267 - Team Mets & Sonic at the Oracle Games!
41. Canth/Scythe Marshall - Team Hyperion
42. Paratroopa1/swirldude - Team Paraswirlsion
43. ad00/cyko - Team ???
44. Darkash/Heroic Viktor - Team Battle Royale
45. Menji76/Seginustemple - Team magical innuendo pirates with guitars
46. Ed Bellis/transience - Team ???
47. Hartzenan/Tomoyo - Team ???
48. cokes/Giggsalot - Team ???
49. WhakkoJacko/XIII_rocks - Team ???
50. MegaTokyoEd/Redtooth - Team ???
51. kirbyjump/warning_crazy - Team ???
52. ActJef1077/Weird Kirby Dude - Team SPO*N
53. FigureOfSpeech/Luster Soldier - Team Jesus Wants Our Nuts
54. AlecTrevelyan006/DaruniaTheGoron - Team Two-Faced Gorons
55. th3l3fty/yazzy14 - Team ???
---
Kaxon is a figurehead. Morgoth has all the real power. - Janus5000
SpC2k4 Triple Crown WINNER (Oracle, Betting, Spread Betting)

Yeah, free shipping, can't beat that >_>
---
Einstein would turn over in his grave. Not only does God play dice, the dice are loaded.
Runner of Winning Streak

For Rydia... I am in! :)

*Waves to the King*
---
Steve Illumina: Sage of Board 8 & Elitist Analyst
In the name of my daughter Rydia, I shall win Battle VI!

For Rydia... I am in! :)

*Waves to the King*

And here comes one I didn't expect to see!
You need to get on AIM at some point!
---
Kaxon is a figurehead. Morgoth has all the real power. - Janus5000
SpC2k4 Triple Crown WINNER (Oracle, Betting, Spread Betting)

Team th3l3fty/yazzy14 shall be called Team One-Two Punch
---
Knight of the Cross of Sir Chris' Court
I have a third degree burn in flame-o-nomics. -Sir Chris

I'm still wondering how the Oracle Website is going to look for this contest.
---
100% Frog Log Quest: Current Progress- 400 of 627 Completed: Jaster, Kisala, Deego

They'll just do the same thing they did in the Battle Royale last year, that's all.
---
Knight of the Cross of Sir Chris' Court
I have a third degree burn in flame-o-nomics. -Sir Chris

Actually, we're trying to make it work a little better than that... it won't be a different match for each character anymore. =)
---
Tia mi aven Moridin isainde vadin

I'm still wondering how the Oracle Website is going to look for this contest.
Still working on the details of that!

They'll just do the same thing they did in the Battle Royale last year, that's all.
Nope. It'll look less thrown-in-at-the-last-second-and-only-the-totals-make-sense =P
---
Kaxon is a figurehead. Morgoth has all the real power. - Janus5000
SpC2k4 Triple Crown WINNER (Oracle, Betting, Spread Betting)

I post like twice a day and you still manage to snipe me? =P
---
Kaxon is a figurehead. Morgoth has all the real power. - Janus5000
SpC2k4 Triple Crown WINNER (Oracle, Betting, Spread Betting)

Yeah. If they stick to the old style, everyone's prediction list would be incredibly long.
---
100% Frog Log Quest: Current Progress- 400 of 627 Completed: Jaster, Kisala, Deego

yeah, this is okay for a team name:

Team We Won't Win 60$ from Kax and Morgoth.

this one is also fine by me:


Team free shipping, can't beat that

>_>

---
I support the following SC2K6 characters:
L-Block, Phoenix Wright, Magus, Agent J, Vincent Valentine, Miles Edgeworth, HK-47, Zero, Kefka

Prediction: To change or not to change...

*brainstorm thinking*

---
raytan. The Cream of Terra Branford Fanboyism.
http://img142.imageshack.us/img142/2675/11584879241lc9.jpg

Tomorrow I should be able to start fixing the things I need to get ready for the contest (like the script for entering predictions).
---
I made a living on time trial blowing myself off to cross the finish line at ludicrous speed. -transience

For Rydia... I am in! :)

*Waves to the King*

And here comes one I didn't expect to see!
You need to get on AIM at some point!

King, look for me tonight, around 1030 EST, I shall be on AIM!
---
Steve Illumina: Sage of Board 8 & Elitist Analyst
In the name of my daughter Rydia, I shall win Battle VI!

As a follow-up to creative's post in the other topic...

**********

Alright, it's time to throw everything out of the window...

No, seriously.

I've never been a fan of the theory you've been using for the X-stats. Unfortunately for me it works. And there's nothing I hate more than I theory I don't quite agree with being proved right empirically because it usually means the stuff in my head is rubbish. And it happens a lot!

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

I'll use your example from CS&D:
Cloud vs Mega Man vs Ryu vs Terra with their respective strengths (47.6%,35.5%,27.5%,17%)
We'll scale this to 1.000/0.746/.578/.357

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

Hey, never said it was going to be pretty...and yes it adds up close enough...but 30,000 runs isn't enough to get something really close!

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

I have an idea but it'll have to wait a few hours, I'm going outside for a change!
---
Kaxon is a figurehead. Morgoth has all the real power. - Janus5000
SpC2k4 Triple Crown WINNER (Oracle, Betting, Spread Betting)

I have a couple of other methods to calculate the x-stats... one is simpler, but one seems to be more accurate. They both seem to give reasonable results, though. I'll get more into that when I have the time, though.

---
"Ah, a party! We haven't had one of those. It could be fun! So...what is a party?"
"Well, you drink punch and eat CAKE! ...I think."

Here is the first, simpler way I introduced to estimate four-character results. I prefer assigning character their BL x-stat as I'm used to that format.

Let's use those same four characters: Cloud, Mega Man, Ryu, and Terra. I noticed creative used the SC2K5 x-stats, so I'll apply those here.

51.90% - Cloud
38.79% - Mega Man
29.98% - Ryu
18.65% - Terra

Now, since I don't want to do complicated math, I'll assign Cloud a value I'd roughly expect him to have. I'll say Cloud gets 40%. Now, let's figure out Mega Man's percentage from there. Do the math (38.79/51.90/2) to find that Mega Man gets 37.37% on Cloud. Then, divide that from Cloud's expected percentage on Mega Man (62.63%, of course). Mega Man's strength proportion is .5967 of Cloud's, so multiply it by Cloud's 40%. Mega Man gets an expected 23.87% if Cloud gets 40%.

Okay, that seemed complicated at first, but it's really not...and it's simple to do in practice. Anyway, do the same thing for Ryu and Terra. Ryu gets 16.24% and Terra gets 8.76%. Now, when you add all their percentages together, it adds up to.. 88.87%. So, divide it all by .8887, and you get...

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

There we go. I'll show the next method in the next past, which is fairly similar... but it makes more sense to me to use.


---
"Ah, a party! We haven't had one of those. It could be fun! So...what is a party?"
"Well, you drink punch and eat CAKE! ...I think."

If you can, get on AIM Haste...
---
Kaxon is a figurehead. Morgoth has all the real power. - Janus5000
SpC2k4 Triple Crown WINNER (Oracle, Betting, Spread Betting)

Okay, now the next method... um.... I just realized I did it all wrong. If I did it right, it would take, like, every possible combination of characters... so that's not good...

Well, I'll just type this up and see how it goes...and, I'm not a math major, so... I'm afraid I can't use complex formulas or shortcuts.

51.90% - Cloud
38.79% - Mega Man
29.98% - Ryu
18.65% - Terra

First, treat the match as Cloud vs. Mega Man... so, first set Cloud arbitrarily to 40% for his predicted percentage. Mega Man, skipping the processes shown in the last message, gets 23.87%. Now, here's where it changes...

In the last message, EVERYTHING was in relation to Cloud. This time, we're attempting to calculate x-stats in relation to EVERYONE. So... measure Ryu from Cloud AND from Mega Man. Ryu's expected percentage in the four-way poll would now be...15.03% based off Mega Man, and 16.20% based off Cloud. Now, from here you find Ryu's average (weighted) percentage... and you do the weighting based off the percentage Cloud and Mega Man are expected to get; in otherwords, Ryu's expected percentage based off Cloud matters more. So, Ryu's weighted percentage is now 15.76%.

Now, there's Terra... you measure her from Ryu, Mega Man, AND Cloud. So, do the weighting stuff all over again... Terra gets an expected 8.07%. Now, Cloud = 40%, Mega Man = 23.87%, Ryu = 15.76%, and Terra = 8.07%. Do the math so it all adds up to 100%, and...

PREDICTED RESULTS SO FAR:
Cloud = 45.61%
Mega Man = 27.22%
Ryu = 17.97%
Terra = 9.20%

Note that Cloud did a little better, while the others, especially Terra, did a little worse. But WAIT... that's only ONE of the possible combinations. Let's do the same thing, but start with... Cloud vs. Ryu. Yeah, as you can see, this is pretty nightmarish and I wouldn't want to ever calculate using this method.... though there might be a shortcut with this.

Cloud = 40%
Ryu = 16.24%

With Mega Man (won't bother to show details)... 23.87% * (40/56.24) + 25.79% (16.42/56.24) = 24.51%

With Terra... blah blah blah, she ends up at 8.17%.

Predicted Results with this Combination:
Cloud - 44.98%
Mega Man - 27.56%
Ryu - 18.26%
Terra - 9.18%

Note the slight changes. Cloud is slightly below his 45.01% from method 1, and Mega Man is above his 26.86% from method 1. Interesting.

But, now that I'm thinking about it... if I keep doing the combinations... I wonder if this will all average out to the x-stats above? I noticed that Mega Man was actually inflated when measuring from Ryu... likewise Cloud from both Mega Man and Ryu. Neat. It does seem pretty reasonable when I think about it (looking at the minute changes and my 1337 math skills)... I really do think that's what would happen.

And, while this turned out to be pointless, it actually shows evidence towards my first method above. Again, if I do every possible combination, it is likely it will all just average out to that method I mentioned first. Sorry to disappoint you. >_>

---
"Ah, a party! We haven't had one of those. It could be fun! So...what is a party?"
"Well, you drink punch and eat CAKE! ...I think."

Nobody9090:
People are seriously underestimating the Midgar Zolom. No, it won't win or anything but it will break 5% easily.

I would so totally agree with you, except...

Draco:
Zolom faces the main character of his game and two midcarders. He is getting utterly annihilated.

...is right I believe.

I think without SFF Zolom could be stronger than most weaklings, for what it's worth.
---
www.gamefaqscontests.com
www.gamefaqscontests.com/gallery

Second theory time. And we'll shake everything up.

Nothing totally incompatible with we've been using. In fact, it doesn't change the results we're usually getting in 2-way matches.

Right now we're usually something we could call "sticks", i.e. the longer sticks basically have an advantage over EVERYONE else for the "section" of the vote they have "over" them. Say if Cloud (.5) faces CATS (.2) and L-Block (.1), as long as he "rolls" over .2, he's getting that vote. And that's what we're going to change...

Starting from a 1-on-1 match.

Let's say we get Cloud 60% - Mega Man 40%
We'd give Cloud a range of [0-1.0] and Mega Man a range of [0-0.8]
Instead let's say this:
Cloud has a propability of likeability p of 100%
Mega Man's p is 80%

The idea is this. Instead of being a "max", the values we have is the probability you'll "like" the character. If you like more than one, you pick one of them randomly.

******

Cloud gets P[A¬B] + P[AB]/2 = P[A]-P[AB] + P[AB]/2 = 100%-80% + 80%/2 = 60%
Mega Man gets P[B¬A] + P[AB]/2 = P[B]-P[AB] + P[AB]/2 = 80%-80% + 100%*80%/2 = 40%

It's magic! Except it's not! We didn,t think it that way but the x-stats follow the same idea.

******

Let's throw in a 3rd character in there

Cloud's p of 100%
Mega Man's p is 80%
Ryu's p is 60%

Cloud gets P[A¬B¬C] + P[AB¬C]/2 + P[A¬BC]/2 + P[ABC]/3
=1*.2*.4 + 1*.8*.4/2 + 1*.2*.6/2 + 1*.8*.6/3 = 46.00%
Mega Man gets P[¬AB¬C] + P[AB¬C]/2 + P[¬ABC]/2 + P[ABC]/3
=0*.8*.4 + 1*.8*.4/2 + 0*.8*.6 + 1*.8*.6/3 = 32.00%
Ryu gets P[¬A¬BC] + P[¬ABC]/2 + P[A¬BC]/2 + P[ABC]/3
=0*.2*.6 + 0*.8*.6/2 + 1*.2*.6/2 + 1*.8*.6/3 = 22.00%

Direct proportionality gives : 41.67%|33.33%|25.00%
Old x-stats theory says : 52.50%|32.50%|15.00%

For some reason, I think the first one looks better!

******

This is where it hurts....4 characters

Cloud's p of 100%
Mega Man's p is 80%
Ryu's p is 60%
Terra's p is 40%

Cloud gets P[A¬B¬C¬D] + P[AB¬C¬D]/2 + P[A¬BC¬D]/2 + P[A¬B¬CD]/2 + P[A¬BCD]/3 + P[AB¬CD]/3 + P[ABC¬D]/3 + P[ABCD]/4
= 1*.2*.4*.6 + 1*.8*.6*.4/2 + 1*.2*.6*.6/2 + 1*.2*.4*.4/2 + 1*.2*.6*.4/3 + 1*.8*.4*.4/3 + 1*.8*.6*.6/3 + 1*.8*.6*.4/4
= 4.8% + 9.6% + 3.6% + 1.6% + 1.6% + 4.267% + 9.6% + 4.8% = 39.87%
Mega Man gets P[¬AB¬C¬D] + P[AB¬C¬D]/2 + P[¬ABC¬D]/2 + P[¬AB¬CD]/2 + P[¬ABCD]/3 + P[AB¬CD]/3 + P[ABC¬D]/3 + P[ABCD]/4
= 0 + 1*.8*.4*.6/2 + 0 + 0 + 0 + 1*.8*.4*.4/3 + 1*.8*.6*.6/3 + 1*.8*.6*.4/4
= 9.6% + 4.267% + 9.6% + 4.8% = 28.27%
Ryu gets P[¬A¬BC¬D] + P[A¬BC¬D]/2 + P[¬ABC¬D]/2 + P[¬A¬BCD]/2 + P[¬ABCD]/3 + P[A¬BCD]/3 + P[ABC¬D]/3 + P[ABCD]/4
= 0 + 1*.2*.6*.6/2 + 0 + 0 + 0 + 1*.2*.6*.4/3 + 1*.8*.6*.6/3 + 1*.8*.6*.4/4
= 3.6% + 1.6% + 9.6% + 4.8% = 19.60%
Terra gets P[¬A¬B¬CD] + P[¬A¬BCD]/2 + P[¬AB¬CD]/2 + P[A¬B¬CD]/2 + P[¬ABCD]/3 + P[A¬BCD]/3 + P[AB¬CD]/3 + P[ABCD]/4
= 0 + 0 + 0 + 1*.2*.4*.4/2 + 0 + 1*.2*.6*.4/3 + 1*.8*.4*.4/3 + 1*.8*.6*.4/4
= 1.6% + 1.6% + 4.267% + 4.8% = 12.27%

End result : 39.87%|28.27%|19.60%|12.27%
Direct prop.:35.71%|28.57%|21.43%|14.29%
Old x-stats: 51.39%|31.39%|13.89%|3.33% (cute)

************

Conclusion : I don't know if people are going to agree with me on this one....but i like it!

Better yet, it's very classic and basic probabilities theory. And we can actually throw SFF in there if we want!
---
Kaxon is a figurehead. Morgoth has all the real power. - Janus5000
SpC2k4 Triple Crown WINNER (Oracle, Betting, Spread Betting)

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.
---
www.gamefaqscontests.com
www.gamefaqscontests.com/gallery

I was reading GameFAQs one day when Classical vs. Bayesian probability debate sprung up... ;)

What does '¬' mean?

The idea is this. Instead of being a "max", the values we have is the probability you'll "like" the character. If you like more than one, you pick one of them randomly.

This actually seems to be the same basic assumption as the uniform random variable "classical" theory, if I'm understanding you correctly.

---
www.gamefaqscontests.com
www.gamefaqscontests.com/gallery

What does '¬' mean?

I believe it means "not".
---
Tia mi aven Moridin isainde vadin

My take is that both theories oversimplify things - we've already seen how this affects creative's theory in SFF matches.

My biggest problem with using uniform random variables as the underpinning of the stats is that the distribution clearly isn't uniform. This is most apparent with niche characters, where a few people like them a lot, while with other people they have a very low strength. CATS is an obvious example - the theory states that his strength maxes out at around 0.30 (for any given voter), while we know there are voters for whom CATS has a strength of 1.0. Because what we have is the average strengths, the uniform random variable simulation usually works as long as the two character's strengths with voters aren't correlated.

When I was thinking about stats last year, I was thinking a big breakthrough would be if we could figure out the actual distribution of strengths for a character, but I don't know how we could do that with the data provided. Although if there's any way to do it, it seems like we'll be getting some useful data for it this year.

As far as actually predicting anything that's going to happen this year goes... my thoughts haven't gotten that far yet. =)
---
Tia mi aven Moridin isainde vadin

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

Gut feeling really. I never really "felt" it if you will. And it works so I had no choice but to agree. And now I finally think I figured out where I've been trying to go all those years...

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

Those are simply the theoretical values you're trying to get through Excel. You'd probably need millions to get something really close though...

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.

Sorry 'bout that, I'm used to dealing with teachers with whom half a point or so is never close

How so? I'd say that Terra's low percentage is highly counter-intuitive, but it does make sense.
I don't think Cloud can take almost 55% in a poll like this. Or that Ryu would dive all the way under 15%. It just feels awkward
---
Kaxon is a figurehead. Morgoth has all the real power. - Janus5000
SpC2k4 Triple Crown WINNER (Oracle, Betting, Spread Betting)

Nice stuff, Morgoth. It sounds reasonable, but unfortunately, I have a hard time getting the feel for these "p" values for the characters, so it's hard to see how it looks in practice. Is there an easy way to convert an x-stat over to that?

Link got 43% on Cloud, Sephiroth, and Snake... so, Cloud (who's close to Link) getting 55% on Mega Man, Ryu, and Terra seems reasonable to me.

---
"Ah, a party! We haven't had one of those. It could be fun! So...what is a party?"
"Well, you drink punch and eat CAKE! ...I think."

Kaxon:
My biggest problem with using uniform random variables as the underpinning of the stats is that the distribution clearly isn't uniform.

Your word uniform I would interpret as non-segmented. By uniform I do not mean voter uniformity (because after all it is voter non-uniformity we are trying to model), but variable distribution. Segmented uniform random variables would be the more complex model; it would still use uniform r.v.s.

CATS is an obvious example

It's so funny how CATS is like the universal non-linearity example when he has yet to demonstrate non-linearity :) It'll probably happen in this contest though, but a lot of funky things should happen here.

while we know there are voters for whom CATS has a strength of 1.0

Indeed, segmentation.

I was thinking a big breakthrough would be if we could figure out the actual distribution of strengths for a character, but I don't know how we could do that with the data provided.

You'd be talking about a strength matrix (sort of like a covariance matrix) - but that is I think n^2/2 variables, whereas we'd only have I think 2n data points. So yeah, more or less impossible, unless you used a lot of guesstimation.

As far as actually predicting anything that's going to happen this year goes... my thoughts haven't gotten that far yet. =)

The utility for predictions here is sketchy, because of the non-linearity once you generalize past 2 characters: any deviations in actual strength from estimated strength will be magnified. If you overestimate a character, the difference between their actual and estimated performances will be greater than with only 2 characters.


King Morgoth:
I don't think Cloud can take almost 55% in a poll like this. Or that Ryu would dive all the way under 15%. It just feels awkward

I've already guaranteed plenty of awkardness in this contest! :) Now I just think that I have some better idea about what direction that awkardness might take.


Haste2:
Link got 43% on Cloud, Sephiroth, and Snake... so, Cloud (who's close to Link) getting 55% on Mega Man, Ryu, and Terra seems reasonable to me.

Indeed. I'd expect Cloud to be in that neighborhood somewhere against those opponents.

I posted some simulated results for the Battle Royale in the Stats topic. Underration of Snake seems to be huge (until it was 3-way), and overestimation of Sephiroth was also an issue. Also note that I was using 1-year old date there, except for Snake (most people would have probably used a higher value for Snake in the simulation that I did).
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*1-year old 2K5 data, not date
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Let's go to something basic: take Terra and put her against Dante. She gets about 30%. Now, add Ryu into the mix, who's about equal to Dante. The voters who voted Terra over Dante must like Terra quite a bit, right? Would the voters who voted Terra like Terra just as much as the voters who voted Dante like Dante? If so, Ryu wouldn't hurt Terra's 30% anymore than he would hurt Dante 70% (proportionally speaking). i.e., if Terra fell to 27%, Dante would fall to 63%.

If not... surely Dante is liked more among those who voted for him than for Terra and her voters. Basically, when Ryu joins in, Terra should get anywhere from 9%-18%. If Terra only got 9% (30%*30%), that would suggest that Terra has relied entirely on dislike (anti-votes) towards Dante and Ryu rather than Terra having any fans... so, a low 9% wouldn't make sense. If Terra got 18% against both Ryu and Dante, her strength is basically entirely her own, and didn't get many "not Dante" votes in the first place. Complicated...

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"Ah, a party! We haven't had one of those. It could be fun! So...what is a party?"
"Well, you drink punch and eat CAKE! ...I think."

For instance, assume there are four random variables, Cloud, Mega Man, Ryu, and Terra. Assume their (mean) strength's are 47.6%, 35.5%, 27.5%, and 17%. Thus their realized values are between [0, .952], [0, .71], [0, .55], and [0, .34]. This mimics voter preferences - the model is that for each voter, each character gets a random value between their ranges, and the character with the highest realized value receives the vote.

I thought about this for a bit, but then I found an apparent flaw: let's say Link is at strength 1.0, while another character is at strength .50. That characters getting 25% on Link makes sense, since every time a random number is between .50 and 1.0, Link will always win (50% of the time), and then when Link is below .50, he will win half the time on average (50%*50% = 25%). So, that adds to 75%. But... think about this: let's say Link is at strength 1.0, and he faces a million opponents at a strength of .5 (just pretending). Using that line of thinking, Link -will- get at least 50% of the vote, since he'll always wins with a random number of .5 or higher. That couldn't be true. So, in that case, this line of thinking will always inflate Link's expected percentage.

But, as to attempt to explain Terra's percentage being supposedly too low, that's over my head.

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"Ah, a party! We haven't had one of those. It could be fun! So...what is a party?"
"Well, you drink punch and eat CAKE! ...I think."

King Morgoth:
Cloud gets P[A¬B¬C] + P[AB¬C]/2 + P[A¬BC]/2 + P[ABC]/3
=1*.2*.4 + 1*.8*.4/2 + 1*.2*.6/2 + 1*.8*.6/3 = 46.00%
Mega Man gets P[¬AB¬C] + P[AB¬C]/2 + P[¬ABC]/2 + P[ABC]/3
=0*.8*.4 + 1*.8*.4/2 + 0*.8*.6 + 1*.8*.6/3 = 32.00%
Ryu gets P[¬A¬BC] + P[¬ABC]/2 + P[A¬BC]/2 + P[ABC]/3
=0*.2*.6 + 0*.8*.6/2 + 1*.2*.6/2 + 1*.8*.6/3 = 22.00%

I understand this now, and it makes a lot of sense. This is good stuff.

What I wonder about is the underlying behavioral assumption about a simple like/not like choice with possible split votes; I think a continuum makes more sense. However I like the way the math works out here. It's easy to follow once you see it, and logical.

I think we'll have an idea about which model is better after a while. It should become clear in terms of the skewness of the vote percentages - if the percentages are "flatter", then that will clearly favor your model. That very well may happen because of fanbase segmentation (i.e. cult loyalty), so your model might be superior in practice.

Another reason to look forward to these contests :) Always more questions to answer!

I tried working out the math according to this logic with the Battle Royale's last two matches.

Match #3:
Character - Actual % - Classical (simulated) % - King Morgoth Conditional %
Link - 42.68% - 34.70% - 28.390%
Cloud - 23.70% - 29.30% - 27.030%
Sephiroth - 16.79% - 25.23% - 25.127%
Snake - 16.83% - 10.77% - 18.830%

My %ages for the conditional approach here don't add up to 100% so I must have done something wrong.

Match #4:
Character - Actual % - Classical (simulated) % - King Morgoth Conditional %
Link - 44.65% - 43.63% - 39.327%
Cloud - 35.71%- 38.14% - 36.196%
Snake - 19.64% - 18.22% - 24.476%

I may have made math errors here too, feel free to correct me.

Obviously nothing conclusive here at all, we need more data. That will be a problem here in matches where we have new character. But I think (hope) eventually the picture clears up.

Anyone care to try and work out King Morgoth's math for the other BR matches? That's going to be a semi-Herculean task...
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BTW I was assuming strengths of:
Link - 50%
Cloud - 47.56%
Sephiroth - 45.06%
Mario - 39.59%
Samus - 38.21%
Snake - 35.84%
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The voters who voted Terra over Dante must like Terra quite a bit, right?

Yeah, there's some potentially tricky conditional probabilities here.

If Terra only got 9% (30%*30%), that would suggest that Terra has relied entirely on dislike (anti-votes) towards Dante and Ryu rather than Terra having any fans

Somewhat. If Terra has an overall cap of .34, then someone would have to innately like both Dante/Ryu something less than .34 for Terra to even have a chance at the vote. In reality, a Terra voter may have her strength very high in his own hierarchy; but for modeling a population I think this assumption may be viable.

But... think about this: let's say Link is at strength 1.0, and he faces a million opponents at a strength of .5 (just pretending). Using that line of thinking, Link -will- get at least 50% of the vote, since he'll always wins with a random number of .5 or higher.

Hmmm....this is an excellent catch! That's a huge flaw, and a strong point in favor of King Morgoth's model.
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Right now I think King Morgoth's conditional probability approach is correct.
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If Morgoth's method is correct: CATS, Matt, Mudkip, Bidoof and L-Block are so screwed. If creative's way is correct: CATS, Matt, Mudkip, Bidoof, and L-Block are so gonna win. The way I do it is somewhere in the middle...

End result : 39.87%|28.27%|19.60%|12.27%
Direct prop.:35.71%|28.57%|21.43%|14.29%
Old x-stats: 51.39%|31.39%|13.89%|3.33%
HASTE2ULTRA!: 42.63%|28.43%|18.27%|10.66%

If I reduced the error (used all four characters as a main reference besides just Cloud), Terra would go down about a percent and Mega Man would go up a little, while the other two basically stay the same.

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"Ah, a party! We haven't had one of those. It could be fun! So...what is a party?"
"Well, you drink punch and eat CAKE! ...I think."

>_>

what the .... are you three talking about..... ?

---
I support the following SC2K6 characters:
L-Block, Phoenix Wright, Magus, Agent J, Vincent Valentine, Miles Edgeworth, HK-47, Zero, Kefka

What I wonder about is the underlying behavioral assumption about a simple like/not like choice with possible split votes; I think a continuum makes more sense. However I like the way the math works out here. It's easy to follow once you see it, and logical.

The continuum makes much more sense but we can't model it without going through a lot of trouble... we can see this as a very rough approximation of a continuum, the more detailed one we can actually figure out with the data we have.


I think we'll have an idea about which model is better after a while. It should become clear in terms of the skewness of the vote percentages - if the percentages are "flatter", then that will clearly favor your model. That very well may happen because of fanbase segmentation (i.e. cult loyalty), so your model might be superior in practice.

The model I presented is too flat due to not taking into account any SFF. And any SFF will push the characters more apart. But it becomes a rather complicated thing to throw in....

My %ages for the conditional approach here don't add up to 100% so I must have done something wrong.

Link gets 29.013%, the rest is good. (including the 3-way match)
You forgot to add up [Link ¬Cloud Sephiroth ¬Mario] if you really want to know =P

Anyone care to try and work out King Morgoth's math for the other BR matches? That's going to be a semi-Herculean task...
Link - 20.144%
Cloud - 18.917%
Sephiroth - 17.703%
Mario - 15.169%
Samus - 14.553%
Snake - 13.515%

Link - 23.710%
Cloud - 22.200%
Sephiroth - 20.720%
Mario - 17.670%
Snake - 15.700%

Excel file coming up at some point...

Right now I think King Morgoth's conditional probability approach is correct.

I'm pretty confident about the approach but my numbers are getting killed by SFF...I'm trying to fix that...
There are two things I can't model at all though...
- Kryptonite cases (See Link/Ganon)
- rSFF

*****

what the .... are you three talking about..... ?

Trying to apply the x-stats to 4-way battles!
lol x-stats
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Kaxon is a figurehead. Morgoth has all the real power. - Janus5000
SpC2k4 Triple Crown WINNER (Oracle, Betting, Spread Betting)

Awesome theory KM. I don't think I could have come up with it myself, but it seems vaguely like what I was hinting at, and something I can definitely agree with. Any chance of an online calculator for that?
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FFXII NLB - finished - 39 marks
FFXII LLIENANMiNDM - Bhujerba (pre-Ba'Gamnan)

Any chance of an online calculator for that?

http://www.oraclechallenge.com/New-X-Stats.xls

Supports up to 6 characters, enter the names and x-stats values, everything's updated automatically.
If you want to try less characters, just remove the names and give them a 0 x-stats value.
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Kaxon is a figurehead. Morgoth has all the real power. - Janus5000
SpC2k4 Triple Crown WINNER (Oracle, Betting, Spread Betting)

uhh

well Ed Bellis and I will be ted crunkensteinsience and the AUGHs

don't ask, and I won't ask about these crazy posts!
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xyzzy
now playing: PW3, Jeanne d'Arc

http://www.oraclechallenge.com/New-X-Stats.xls

v2 is online now. It can do creative's method for up to 6 characters, same as before but the x-stats method will crash if you give strengths of 0, so you need to enter a negligible value (like 0.0001%)
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Kaxon is a figurehead. Morgoth has all the real power. - Janus5000
SpC2k4 Triple Crown WINNER (Oracle, Betting, Spread Betting)

hmph. my crazy number filled prediction is that x-stats really can't be applied to this different type of contest match and there really isn't a mathematical formula we can use to semi-accurately predict these matches.

---
I support the following SC2K6 characters:
L-Block, Phoenix Wright, Magus, Agent J, Vincent Valentine, Miles Edgeworth, HK-47, Zero, Kefka

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Kaxon is a figurehead. Morgoth has all the real power. - Janus5000
SpC2k4 Triple Crown WINNER (Oracle, Betting, Spread Betting)

So, I finally got around to updating the prediction-entering script, and I entered the first four pages of the other topic. Just for fun, here are the current consensi on the first match.

Knuckles - 30.33%
Yoshi - 34.47%
Rikku - 21.17%
Vaan - 14.18%

For some reason there were 99 predictions for Knuckles, Yoshi, and Vaan, but only 98 for Rikku... I need to figure out what happened there.
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Tia mi aven Moridin isainde vadin

Aprosenf left off a percent sign for Rikku, but no one else on message #109. Is that it?
---
Earthbound: It's like living inside your gym shoes.
Huh? Finger!? What the hell? -Cloud

Probably so. Thanks for pointing that out!
---
Tia mi aven Moridin isainde vadin

Uhh... only one "Team" in our name! >__>
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