Predicting the Winning 3x3x3 Average for World Championships 2009

[Fobo911]

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.

 

[DavidWoner]

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.

 

[pjk]

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

 

[DavidWoner]

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.

 

[Crickets]

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

 

[Fobo911]

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.

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...

 

[waffle=ijm]

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

 

[Dene]

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

 

[ConnorCuber]

I'm probably overshooting this, but 8.50

 

[shelley]

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

 

[ConnorCuber]

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.

 

[shelley]

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

 

[DavidWoner]

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.

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

 

[blah]

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

 

[hawkmp4]

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.

 

[ConnorCuber]

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.

 

[hdskull]

10.3-10.8 seconds

 

[Inusagi]

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

 

[DavidWoner]

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.

 

[Leviticus]

The average will be 10.78 but not WR.