# Predicting the Winning 3x3x3 Average for World Championships 2009



## Fobo911 (Sep 28, 2008)

After reading that "Next WC?" thread, I felt inspired to try to use math functions to predict the winning 3x3x3 average for 2009, since the times have dropped dramatically each year.

(I'm not going to use the 1982 WC results because that would be erratic data.)
In 2003, Dan Knight won with an average of 20.00 seconds.
In 2005, Jean Pons won with an average of 15.10 seconds.
In 2007, Yu Nakajima won with an average of 12.46 seconds.

x
---- 
2003 
2005 
2007
2009

y
-----
20.00
15.10
12.46
?????


Using linear regression from my graphing calculator (I tried exponential regression, but that's not working out for me, so linear regression is probably fair enough, for now), the equation for the line of best fit is: *y = -1.885x + 3795.278333*

Let's predict results for x = 2009.
*y = -1.885(2009) + 3795.278333 = 8.313333 = 8.31 seconds*

Therefore, according to linear regression, the winner of the 2009 World Championships will average *8.31 seconds!* 

I won't be surprised at all if that happens. After seeing Harris Chan's 8.79-second average video, anything is possible. 

P.S. Is there a way to do this for an exponential function? An exponential function is much more accurate since in this case, the time will never reach 0, unlike linear functions, which will soon make times sub-0. 

For example, if we go continue on with the equation...

f(2011) = -1.885(2011) + 3795.278333 = 4.543333 -> 4.54 seconds
f(2013) = -1.885(2013) + 3795.278333 = .773333 -> .77 seconds 
f(2015) = -1.885(2015) + 3795.278333 = -2.996667 = -3.00 seconds 

Plus, as you get faster, it's much harder to get even faster (much harder to get to 0 seconds, which is impossible), so that models the behavior of an exponential function in the form of f(x) = a^x where 0 < a < 1.

So yeah, there is a huge problem with my calculations, but I don't know how to make it work for an exponential function. Anybody know how?

EDIT:
Vault312's method below this post is much more accurate. 10.42 seconds.


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## DavidWoner (Sep 28, 2008)

linear regression clearly does not generate a good fit, its obviously exponential decay. you are extrapolating far far beyond the limits of linear regression. ill crunch some numbers in a second

Edit:
first of all, you should use 1,2,3,4 for your x values instead of 2003, 2005 etc. it makes everything nicer.

if you do linear regression with this data then you get an R value of .98 which is pretty good, but exponential regression gives .994 which is much better and looking at the graph you can see that its much better.

and i stand even further corrected, since logarithmic regression gives an R value of .99977 which is phenomenal.

the equation for this is:
19.966 - 6.885ln(x)=y
so the winning time in 2009 would be closer to *10.42 seconds*, which is 1000 times more realistic.

2011 would be 8.88, which is still extrapoltin beyond the bounds of reason.


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## pjk (Sep 28, 2008)

I'll guess the winning 3x3 avg in Worlds '09 is 10.73 seconds.


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## DavidWoner (Sep 28, 2008)

Fobo911 said:


> Yeah, I tried ExpReg on my TI-84 calculator, but there was an overflow error. Is it possible that maybe there are too few values?



thats probably because you used 2003, 2005 etc instead of 1,2,3,4

whenever you are handling data involving years, you should establish a base year and go in a set interval from that point. this avoids the exact type of problem you just had.


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## Crickets (Sep 28, 2008)

10.61, no math in this guess, just skills. haha


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## Fobo911 (Sep 28, 2008)

Vault312 said:


> Fobo911 said:
> 
> 
> > Yeah, I tried ExpReg on my TI-84 calculator, but there was an overflow error. Is it possible that maybe there are too few values?
> ...



That makes a lot of sense. Thanks. 

If only we had more values so that we can get a more accurate equation with more accurate future times, more or less...


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## waffle=ijm (Sep 28, 2008)

I'm thinking sub 10.2 sup 9.9 set by either harris or erik. I think nakaji is currently at a standstill at sup 10 sub 11


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## Dene (Sep 28, 2008)

I think the winning average will be sub10. I'll go with 9.86.


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## ConnorCuber (Sep 28, 2008)

I'm probably overshooting this, but 8.50


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## shelley (Sep 28, 2008)

8.xx? Seriously? You think that the 3x3 record average is going to drop by three whole seconds in a year's time?


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## ConnorCuber (Sep 28, 2008)

shelley said:


> 8.xx? Seriously? You think that the 3x3 record average is going to drop by three whole seconds in a year's time?



Well, with Harris Chan's amazing new video out with an 8.xx second average, I think It is 100% possible that he, Yu, Erik, or any of the best cubers out there could achieve this with enough practice.


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## shelley (Sep 28, 2008)

100% possible? You seem very confident. How much money would you be willing to put on this?


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## DavidWoner (Sep 28, 2008)

ConnorCuber said:


> shelley said:
> 
> 
> > 8.xx? Seriously? You think that the 3x3 record average is going to drop by three whole seconds in a year's time?
> ...



did you try those scrambles? they were very easy. theres no way the record average will be sub-9. its like 3% possible.


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## blah (Sep 28, 2008)

I'm suggesting another approach: Why don't we translate everything down by, say, ~5 seconds? i.e. let a 6.00 average be the winning average at year infinity, isn't that even more realistic? And then try all different types of regression and find the one with the highest R value, and that _should_ be accurate for at least, say, the next ten years?

I dunno what I'm talking about actually, it's all just hypothetical, I suck at stats, if it's plain wrong, tell me where it went wrong


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## hawkmp4 (Sep 28, 2008)

How about we predict what the next great physics discovery will be?
I think we'll have better luck with that. We're all talking out of our asses here.


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## ConnorCuber (Sep 28, 2008)

shelley said:


> 100% possible? You seem very confident. How much money would you be willing to put on this?



Well, maybe I am over confident, but I still think that it could happen.


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## hdskull (Sep 28, 2008)

10.3-10.8 seconds


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## Inusagi (Sep 28, 2008)

Interesting thread. I think the 10 seconds is wayyy more realistics...


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## DavidWoner (Sep 28, 2008)

hawkmp4 said:


> How about we predict what the next great physics discovery will be?
> I think we'll have better luck with that. *We're all talking out of our asses here*.



thats the second time today where i've read a post where you say that. we are not _all_ talking out of our rears(need i remind you that this is an all ages forum?) the equation i gave is perfectly reasonable, and well within the bound of extrapolation, given such a high R value. since Erik almost got a 10.97 at Brussels, i dont think its unreasonable at all to think that one year from now someone will be able to pull of a 10.7 or so in compitition. Last year, i dont think anyone would have though that we would have 3 non-lucky sub-9 solves by 3 different people. and the progress made on 4x4 and 5x5 is frankly insane. sub-11 is very reasonable.

i will admit that people who think a sub-9 avg will be possible in a years time are indeed talking out of their tushes, but they are not the majority.


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## Leviticus (Sep 28, 2008)

The average will be 10.78 but not WR.


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## FU (Sep 28, 2008)

11.xx wins the championship. (yes I'm just guessing that everyone will get nervous on that day)


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## Pedro (Sep 28, 2008)

sub-11...something like 10.5 to 10.8


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## Derrick Eide17 (Sep 28, 2008)

11.19 

message too short


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## sheriff (Sep 28, 2008)

11.10

no way sub10, impossible. 10.8 or so maybe the best avg in the WC

how can you guys talk about 9, or EVEN 8 SECONDS!!??!?! that way you seem not to appreciate how how difficult is to be sub11...seriously...


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## trying-to-speedcube... (Sep 28, 2008)

9.63, by erik:

(7.48), 9.96, 10.13, (10.56), 8.80


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## Harris Chan (Sep 28, 2008)

If you round off some winning averages, you get this:

20, 15, 12.5, which has change of 5, 2.5. Perhaps the next change will be 1.25, so that means 11.25 average. Of course, it'll probably be sub 11. I don't think that WR averages will be set in WC though, as it never happened before (except in 2003, because that's the first time it was done).

P.S. The limit of this "function" would be 10 seconds. Haha


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## blah (Sep 28, 2008)

Harris Chan said:


> P.S. The limit of this "function" would be 10 seconds. Haha



So I was a little too optimistic when I mentioned 6 then?


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## hawkmp4 (Sep 28, 2008)

Vault312 said:


> hawkmp4 said:
> 
> 
> > How about we predict what the next great physics discovery will be?
> ...



Well, really, we have no idea at all. Especially with an average of 5, which isn't all that indicative of someone's ability. Plus, with it being in competition, with the pressure, that allows for even more variability. Someone could be having a bad day, be under a lot of stress, anything.
And its not like we're looking at 20 years of times to look at. We're trying to fit an equation to 3 points...
And as for talking out of our asses, my theory is, if something isn't filtered out by the forum then its fine.


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## shelley (Sep 28, 2008)

We may only have three points to look at, but trying to fit a linear regression to something like this is just silly.


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## Fobo911 (Sep 28, 2008)

shelley said:


> We may only have three points to look at, but trying to fit a linear regression to it is just silly.



Well, linear regression was the only thing I could do with such big x values as 2003, etc. I didn't know that I could have used 1, 2, 3, etc. instead. Well, I learned something from this thread.


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## pjk (Sep 28, 2008)

I think a 10.73 second avg will win the competition, as I mentioned earlier.

However, I think the WR avg by the time Worlds '09 comes about will be sub 10.5.


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## Neutrals01 (Sep 28, 2008)

10.6x wr avg...just guess...hmm..


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## cubejunkies (Sep 28, 2008)

Let's see... I did a linear regression and got a best fit line equation of -3.77x+23.393333333333 which means that my guess for the winning average is... 8.31 seconds as well , which is only for WC averages, my real actual guess is...

Take the best averages of each single year from 2003 to 2008 you get a best fit line equation of -1.5214285714287x+19.553333333334 and my actual guess is an average of 8.9 seconds


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## fanwuq (Sep 28, 2008)

Too difficult to say exact number. Best prediction is sub-12. I think that is probably 99.999999999% likely. Perhaps it will be somewhere around 10.5? sub-10 is possible, but not too likely.


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## cubejunkies (Sep 28, 2008)

fanwuq said:


> Too difficult to say exact number. Best prediction is sub-12. I think that is probably 99.999999999% likely. Perhaps it will be somewhere around 10.5? sub-10 is possible, but not too likely.



Well (while i still have my calculator out), the averages have dropped on average 1.744 seconds each year, so assuming a constant rate of change, then the average in one year is 9.536, so it may be a lot more possible, actually


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## fanwuq (Sep 28, 2008)

cubejunkies said:


> fanwuq said:
> 
> 
> > Too difficult to say exact number. Best prediction is sub-12. I think that is probably 99.999999999% likely. Perhaps it will be somewhere around 10.5? sub-10 is possible, but not too likely.
> ...



But it's not a linear relationship...


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## cubejunkies (Sep 28, 2008)

fanwuq said:


> cubejunkies said:
> 
> 
> > fanwuq said:
> ...



okay then, i did the exponential regression and the average in 2009 according to the equation 20.011389731627*.90239559299936^x is 9.75 seconds, again, sub 10

haha that rhymed


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## Hadley4000 (Sep 28, 2008)

I'm going to say high 10s-low 11s.


I think that there will be a sub-10 average some day, though.


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## Dene (Sep 28, 2008)

I don't see why sub10 is so out-of-range. One solve sub9 (which is happening now), 2 solves sub10, 1 bad solve (12+), and one solve sub10.5ish, and you could have a sub10 average.


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## cubejunkies (Sep 28, 2008)

Dene said:


> I don't see why sub10 is so out-of-range. One solve sub9 (which is happening now), 2 solves sub10, 1 bad solve (12+), and one solve sub10.5ish, and you could have a sub10 average.



We did all, however, assume that a WR average would be set, which is sub-10 at the moment, and according to my calculations, a WR average of sub-10 seconds is probably going to happen at the end of next year, which could be at the WC09, but, keep in mind that last year, WR average was not set at the WC


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## KConny (Sep 28, 2008)

11.11

Are you able to read this? I only wrote it because my message was too short. I hope no one quotes me. If so everyone in the world would see this secret message.


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## philkt731 (Sep 28, 2008)

I see your secret message


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## shelley (Sep 28, 2008)

cubejunkies said:


> Dene said:
> 
> 
> > I don't see why sub10 is so out-of-range. One solve sub9 (which is happening now), 2 solves sub10, 1 bad solve (12+), and one solve sub10.5ish, and you could have a sub10 average.
> ...



Nobody assumed a WR average would be set at WC 09. I only mentioned the WR average because of all the people predicting that the winning average at WC 09 would be at 8 or 9 seconds. If that's the winning average, the WR average at that time would obviously have to be at least as fast.

If we look at the progress of the WR average so far (for which we have more data points to work with), most of us would probably conclude that an 8 second WR average in a year is highly unlikely. I would of course love to be proven wrong, but I'm just trying to take a realistic view on things.


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## pjk (Sep 28, 2008)

You guys can't look linearly, since cubing has progress greatly over the last several years. 20 second avg to sub-15 avg to sub-12 avg. It will be leveling out soon.


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## blah (Sep 28, 2008)

fanwuq said:


> Too difficult to say exact number. Best prediction is sub-12. I think that is probably 99.999999999% likely. Perhaps it will be somewhere around 10.5? sub-10 is possible, but not too likely.


Ditto to everything you said. The 0.000000001% is when everyone's having a very very bad day, like this: http://www.worldcubeassociation.org/results/c.php?top3=Top+3&competitionId=ItalianOpen2008.



cubejunkies said:


> ...so assuming a constant rate of change...


Err... it's called the Law of Diminishing Marginal Returns, at least I think it is. Stupid Economics jargon. I hate Econs.



Dene said:


> I don't see why sub10 is so out-of-range.


Everyone pray that Jason Baum finishes ZBLL in time!  (or are there any others who (intend to) practice full ZB out there?)


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## EmersonHerrmann (Sep 28, 2008)

Maybe I'm being unrealistic, but there are so many variables to determine (e.g. new methods), why not just guess? 8.78 is what I say. This is a really fun thread


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## cubejunkies (Sep 28, 2008)

pjk said:


> You guys can't look linearly, since cubing has progress greatly over the last several years. 20 second avg to sub-15 avg to sub-12 avg. It will be leveling out soon.



I don't know, if you do an exponential regression of years vs. averages and then look at the graph, it levels out in times that are really incomprehensible, and in a really long time, according to my equation made by 8 made wr averages, (20, 16.53, 15.38, 14.52, 13.22, 11.76, 11.48, and 11.28) giving us an equation of 20.095933921477*.92299933741117^x


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## hawkmp4 (Sep 28, 2008)

That function has an asymptote of y=0. Not very realistic for this application.


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## cubejunkies (Sep 28, 2008)

blah said:


> cubejunkies said:
> 
> 
> > ...so assuming a constant rate of change...
> ...



Yeah, I already corrected myself in after that posting the exponential regression I got



hawkmp4 said:


> That function has an asymptote of y=0. Not very realistic for this application.



okay, change it, I'm a bit rusty on my algebra, but i believe that it still levels off in a number of years


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## Hadley4000 (Sep 28, 2008)

Let's just look at Erik, Edouard and Harris. The only three who have gotten the equvilant of a sub-10. Let's take their 5 fastest times and make them into an average.

[7.08]
9.77
[9.96]
8.90
9.93

9.53 average.



Edouard.
9.18
9.66
[8.66]
9.90
[10.36]

9.58 average



Harris.
[9.44]
9.80
9.96
10.03
[10.15]


9.93 average.



So there are 3 cubers out there who have hit enough times to make them reach a sub-10 average. I think that this means that sub-10 average in competition can happen.


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## Sa967St (Sep 28, 2008)

10.94, just a guess


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## blah (Sep 28, 2008)

@Hadley, doesn't your data mean it _can't_ happen? Even with their 5 fastest solves, of which most are undeniably lucky, they're barely sub-10 (actually 9.5 is quite a convincing sub-10 to me, but whatever), and you expect them to get such results under pressure in the WC? By the way, did you forget an extremely fast Japanese cuber who has very good shampoo/hair conditioner?


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## cubejunkies (Sep 28, 2008)

blah said:


> @Hadley, doesn't your data mean it _can't_ happen? Even with their 5 fastest solves, of which most are undeniably lucky, they're barely sub-10 (actually 9.5 is quite a convincing sub-10 to me, but whatever), and you expect them to get such results under pressure in the WC?



actually, some aren't lucky. like harris' 9.44 and edouard's 9.66, both were full step.

anyway, I was reading the beginning of this thread, and the original poster said that they couldn't calculate the winning average because they couldn't do exponential regression, and then vault312(i think) went on into doing a logarithmic equation, more accurate, but I don't think we've even gotten an exponential regression equation from the original data set of the WC winning averages. So, i took the liberty of doing it and, if you're curious, the equation is:
24.96626725*.7893034904^x​
Just thought that might help a bit...


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## blah (Sep 28, 2008)

pcharles93 said:


> I might try that instead of sleeping tonight. I can probably make it out of K'nex pieces.



Good luck. Send me a prototype when you're done, I'll PM you my mailing address as soon as you PM me a picture of it 

My inspiration for that idea:

Quoted from a Wikipedia article on Claude Shannon:


> One of his more humorous devices was a box kept on his desk called the "Ultimate Machine", based on an idea by Marvin Minsky. Otherwise featureless, the box possessed a single switch on its side. When the switch was flipped, the lid of the box opened and a mechanical hand reached out, flipped off the switch, then retracted back inside the box. In addition he built a device that could solve the Rubik's cube puzzle.



The last sentence is just a coincidence  This guy is the coolest Mathematician ever.


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## brunson (Sep 28, 2008)

We should make a pool. Everyone who wants to participate picks a time, accurate to 2 decimals and puts in a dollar. Closest to the actual result without going under takes the pot.


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## blah (Sep 28, 2008)

brunson said:


> We should make a pool. Everyone who wants to participate picks a time, accurate to 2 decimals and puts in a dollar. Closest to the actual result without going under takes the pot.



I think the forum management team has had quite an unenjoyable experience with the V7.


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## pcharles93 (Sep 28, 2008)

Or PJK could make a contest out of this. He sets up a range of times from 8-11.5 by .25 increments and to participate, you have to submit at least 2 dollars. Whoever has the most money on the closest time interval wins half the total money to spend. The other half goes to me, the original creator of this contest


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## Harris Chan (Sep 28, 2008)

blah said:


> cubejunkies said:
> 
> 
> > blah said:
> ...



Well I do have 9.80 and 9.96 non lucky official solves too, without the 2 move crosses


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## cubejunkies (Sep 28, 2008)

blah said:


> brunson said:
> 
> 
> > We should make a pool. Everyone who wants to participate picks a time, accurate to 2 decimals and puts in a dollar. Closest to the actual result without going under takes the pot.
> ...



I agree. But if anything, the betting should be done outside of here. Here's my idea of how it could happen:
Money is collected by people who know they can go to the WC, like WCA delegates, so that whenever you go to a comp, you can sign up, giving your name, info, money, and guess of the average, to the delegate or whatever, and at the WC, everyone gets together and sees who guessed correctly, splitting the money between same guess winners, etc.


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## blah (Sep 28, 2008)

Harris Chan said:


> Well I do have 9.80 and 9.96 non lucky official solves too, without the 2 move crosses


I had a feeling you'd be offended, but I didn't know how to phrase that better  No offense, really, just pointing out a fact.


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## cubejunkies (Sep 28, 2008)

Harris Chan said:


> blah said:
> 
> 
> > cubejunkies said:
> ...



Don't be offended harris, blah is an ass to me too


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## pcharles93 (Sep 28, 2008)

cubejunkies said:


> blah said:
> 
> 
> > brunson said:
> ...



Or we could not gamble on WC's winning averages. I'd like to keep all of my college tuition and I'm sure no one else wants to be suckered into this kind of a deal. Man I wanted that Nintendo.


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## hawkmp4 (Sep 28, 2008)

cubejunkies said:


> Harris Chan said:
> 
> 
> > blah said:
> ...


He doesn't mean to be an ass to Harris, nor does he have reason to.
You on the other hand...



cubejunkies said:


> okay, change it, I'm a bit rusty on my algebra, but i believe that it still levels off in a number of years


It does level off, I just said that, it levels off at 0. Take any number between 0 and 1, raise it to a variable x...as x approaches infinity, the expression approaches 0.


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## Dene (Sep 28, 2008)

blah said:


> Harris Chan said:
> 
> 
> > Well I do have 9.80 and 9.96 non lucky official solves too, without the 2 move crosses
> ...



He was offended? It didn't sound like it to me.

Heil Hitler! (For the sake of Godwin's law)


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## hawkmp4 (Sep 28, 2008)

Invoking a Hitler reference purely for the purpose of fulfilling Godwin's Law doesn't count.

And yeah, lets not gamble on cubing, yeah? Keep the sport clean and friendly? If we start doing that, think of the problems it will cause with cheating.


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## cubejunkies (Sep 29, 2008)

hawkmp4 said:


> Keep the sport clean and friendly?



Amen... but you should practice what you preach


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## Hadley4000 (Sep 29, 2008)

blah said:


> @Hadley, doesn't your data mean it _can't_ happen? Even with their 5 fastest solves, of which most are undeniably lucky, they're barely sub-10 (actually 9.5 is quite a convincing sub-10 to me, but whatever), and you expect them to get such results under pressure in the WC? By the way, did you forget an extremely fast Japanese cuber who has very good shampoo/hair conditioner?





No, it means it CAN. Two of Edouard's solves were in the same round. Two of Erik's were in the same tourny. It's just a matter of time until these start piling up.

And yes, they ARE close. But incase your math has fail you, even 9.99 is sub 10 =P


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## masterofthebass (Sep 29, 2008)

this thread has completely gotten off topic. 

CLOSED!


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