# Speed-Cubjectives: The tool that computes statistics-based speedcubing objectives



## kotarot (Feb 9, 2015)

Hello,

I've created a tool named "Speed-Cubjectives",
that automatically generates speedcubing objectives (=cubjectives).
Once you input your record or your WCA ID, you'll get list of computed objectives for all WCA events.

For example, if you input 15.0sec as record of Rubik's cube, it tells that you are likely to solve 4x4 in 1:14.75, 5x5 in 2:22.93, ... and so on. These can be your speedcubing objectives.
These estimated values are derived from the statistics based on the WCA database.
You can also view charts of relationship between WCA events.

I believe that there has been no dynamic statistics tools like this.
Give it a try!

http://www.terabo.net/cubjectives/


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## AlphaSheep (Feb 9, 2015)

Interesting tool. It's estimated times are very close to my actual times for 4x4, 5x5, blindfolded, one-handed, pyraminx, square-1 and clock. I'm much better at 2x2, skewb, and fewest moves than it says, but a little slower at 6x6, 7x7 and megaminx than it says I should be... Not surprising that those match the events I practice most and least often.


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## SpeedCubeReview (Feb 9, 2015)

So are the comparable times what my average "should" be or my record?


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## obelisk477 (Feb 9, 2015)

Depends on what you input. If you input your global average, it should output global averages. If you input PB single, it will ouput something more like PB single


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## lerenard (Feb 9, 2015)

This is so cool! Apparently I suck at 3x3... Because I put in my global average and it gave me times that were too high for everything...


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## StachuK1992 (Feb 9, 2015)

Neat!
Any way you could use all of the user's times in the estimates, rather than just 1 event?

Edit: my want might not be obvious.

From all of my official WCA stats, tell me what I'm doing WELL in and what I'm doing POORLY in.

So,
- get some base 'score' of me as an overall cubers
- order the events I participate in from my "best" event to my "worst" event, probably with some color-coding.


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## Hssandwich (Feb 9, 2015)

Apparently I should average 15.5 on Skewb, 1:10 on 4x4 and 12.99 on Pyraminx after putting in my global average.
I average 5.3, 58 and 5.5 respectively


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## lerenard (Feb 9, 2015)

StachuK1992 said:


> Neat!
> Any way you could use all of the user's times in the estimates, rather than just 1 event?
> 
> Edit: my want might not be obvious.
> ...



I like this idea.


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## Mike Hughey (Feb 9, 2015)

I'm very disappointed to discover that 3x3x3 speedsolve is no longer my worst event. By a slight margin, skewb is. I may have to practice skewb some more to fix that. (Actually, I suspect all I need to do is get a decent skewb and that would probably take care of it; I still use a rather bad LanLan.)

At least 3x3x3 speedsolve is by far my second worst event.  I actually *average* better than my predicted PB in all the other events.


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## okayama (Feb 10, 2015)

Great tool! 

Quick question about the records:

single for fmc/333bld/444bld/555bld/mbld, and average/mean for the rest?
Or single for only 444bld/555bld/mbld?


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## DGCubes (Feb 10, 2015)

Rubik's Cube	15.51
4x4 Cube	1:17.18: I average around 1 minute.
5x5 Cube	2:27.15: About my average; I'm a little faster.
2x2 Cube	6.26: I'm more 4-5 range.
Rubik's Cube: Blindfolded	3:46.48: Around 3 minutes
Rubik's Cube: One-handed	34.87: Around 40-45 seconds.
Rubik's Cube: Fewest moves	42.91 moves: IDK
Rubik's Cube: With feet	2:49.30: Pretty dang good.
Megaminx	2:32.59: A little less.
Pyraminx	13.44: 5 second average... but Pyra is my favorite event.
Square-1	56.11: Yup yup.
Rubik's Clock	25.02: IDK
Skewb	16.18: Sub-10. 
6x6 Cube	4:32.65: Yeah.
7x7 Cube	6:31.44: My PB is 8:59... 
4x4 Cube: Blindfolded	13:09.13: IDK
5x5 Cube: Blindfolded	24:38.82: IDK
Rubik's Cube: Multiple Blindfolded	3.14 cubes: Definitely possible, but 2/2 is my best (3/3 almost happened once.)

Overall, this was quite impressive, even though a bit inaccurate. Good job!!


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## kotarot (Feb 10, 2015)

Thanks for the many comments!



ViolaBouquet said:


> So are the comparable times what my average "should" be or my record?



The estimated times are not your real time.
You may have the ability to solve them in the shown times.
It depends on you that you aim the shown times or you just treat them as references.


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## kotarot (Feb 10, 2015)

StachuK1992 said:


> Neat!
> Any way you could use all of the user's times in the estimates, rather than just 1 event?
> 
> Edit: my want might not be obvious.
> ...



Nice idea!
This might be my next work.


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## kotarot (Feb 10, 2015)

okayama said:


> Quick question about the records:
> 
> single for fmc/333bld/444bld/555bld/mbld, and average/mean for the rest?
> Or single for only 444bld/555bld/mbld?



"single for fmc/333bld/444bld/555bld/mbld, and average/mean for the rest" is true.

I basically wanted to use "average" if possible.
Although, the number of average data in fmc/333bf is too small to use for statistics.


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## okayama (Feb 10, 2015)

kotarot said:


> "single for fmc/333bld/444bld/555bld/mbld, and average/mean for the rest" is true.
> 
> I basically wanted to use "average" if possible.
> Although, the number of average data in fmc/333bf is too small to use for statistics.



I see, thanks!  It would be nice if that is explained in the page (e.g. in "Notes").


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## kotarot (Feb 10, 2015)

okayama said:


> I see, thanks!  It would be nice if that is explained in the page (e.g. in "Notes").



Thanks for your advice and I added it in the notes.


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## cmhardw (Feb 10, 2015)

Wow, if I understand correctly then I am really bad at 3x3 for my level of skill at BLD.

Inputting my WCAID I am:
62.5% faster than the predicted 3BLD
63.9% faster than the predicted 4BLD
47.5% faster than the predicted 5BLD

If I were 63% faster on the 5BLD (for consistency's sake) that would be a time of 8:58.84 on 5BLD. That seems a little fast to me, but not out of my reach. This gives me a goal to strive for on 5BLD 

Thanks for making this site!


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## ottozing (Feb 10, 2015)

According to this, my skewb times should be over 10 seconds slower.

Dank.


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## Kit Clement (Feb 10, 2015)

As a statistician, using simple linear regression for (in most cases) data with increasing variation is really making me uncomfortable.  Results would be much better with a GLM or even just log transformations on the variables.


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## Laura O (Feb 10, 2015)

Well, "correlation does not imply causation", so I don't like that the results are called "objectives".

But I'm quite confident that I can meet most of the objectives: being 20 seconds slower in 4x4, 30 in 5x5, 1 in 2x2, 2 minutes in 3BLD, 7 seconds in OH, 21 moves in FMC, 5 seconds in Megaminx, 6 seconds in Pyraminx, 30 in Square-1, 18 in Clock, 30 in 6x6 and 13 in 7x7 won't be that hard.


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## tseitsei (Feb 10, 2015)

Funniest results:

event time given by program real time how many % faster the real time is
3BLD 3:42.47 36.99 83%
4BLD 13:02.79 4:15.07 67%
5BLD 24:31.21 15:00.00 39%
Pyra 13.30 5.79 56%
MBLD 3.17 cubes 9 cubes(my official MBLD sucks) but still 183% more cubes than predicted 

If I count my MBLD with 20/23 which I should be AT LEAST able to do at my next comp I would get 436% more cubes than predicted...

But then again those are the only events that I practise. In all other categories (except 2x2) I lose to my predicted times.

Interesting program...


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## TDM (Feb 10, 2015)

3x3, the only event I practise, is apparently my worst event other than bigcubes/mega...


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## kotarot (Feb 10, 2015)

Kit Clement said:


> As a statistician, using simple linear regression for (in most cases) data with increasing variation is really making me uncomfortable.  Results would be much better with a GLM or even just log transformations on the variables.



I intuitively know simple linear regression is not suitable for most of the combinations of events.
I used linear regression just because it's the simplest one that I know.

So the problem is, the variables are not normally distributed?
I'll try Poisson regression instead.

Anyway, I'm very glad to hear your opinion because I'm usually in computer science field not in statistics field.


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## kotarot (Feb 10, 2015)

Laura O said:


> Well, "correlation does not imply causation", so I don't like that the results are called "objectives".



That's true...
but the basic idea is that fast cubers in a event who can turn faces faster and know more algorithms, etc..., must have solve fast in other events.
Causations depend on that expectation.

In the first place, only a few combinations of events have well correlation...


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## AlphaSheep (Feb 10, 2015)

Laura O said:


> Well, "correlation does not imply causation", so I don't like that the results are called "objectives".



I really like that they're called objectives because, to me at least, it doesn't imply any direct correlation between the events. It simply says that if you average x in 3x3, then you should aim to average less than y in 4x4 to be faster than a typical cuber with your 3x3 speed.

I can't think of a better name. Any other name like "expected times" or anything along those lines would have been a terrible choice of name, because they imply stronger correlations between times, whereas there is actually only a slight correlation.


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## Laura O (Feb 10, 2015)

kotarot said:


> That's true...
> but the basic idea is that fast cubers in a event who can turn faces faster and know more algorithms, etc..., must have solve fast in other events.
> Causations depend on that expectation.



Sure, I know what the idea behind this is and I like those statistics, but I don't like how they are actually interpreted.

Another way to describe objectives would be to look at the results of competitors at your level (e.g. +/- 1%) and then get the minimum result of every event of them. That's actually what I would call "objective" - at least a way more motivating one.


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## lerenard (Feb 10, 2015)

It seems like basically everyone has better times than the program expects. Perhaps this is because most people practice 3x3 more than other events? Maybe you should do something like find the competitors 3x3 speed as a percentile of all competitors and then use that percentile to find the corresponding times in other events? Idk


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## the super cuber (Feb 10, 2015)

if i enter my 3x3 time as 2.00 sec it gives pyraminx expected time as 9.29 sec, why is that? many people are sub 9 in pyra but no one is even close to 2 sec in 3x3.

can someone explain this?


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## AlphaSheep (Feb 10, 2015)

the super cuber said:


> if i enter my 3x3 time as 2.00 sec it gives pyraminx expected time as 9.29 sec, why is that? many people are sub 9 in pyra but no one is even close to 2 sec in 3x3.
> 
> can someone explain this?


It's just a quirk of the straight line fitted to the data, which is 0.31X + 8.67. Pyraminx is very easy, so it's easy to be, say, sub-20 even if you're a 60 second solver on 3x3, which skews the higher end downward. Then at the lower end, I guess it is skewed upwards by people who are fast at 3x3 but who have never bothered getting faster at pyraminx.

What's even funnier is that some people (Feliks *cough*) should be faster at one-handed than at two handed. In fact, anyone faster than 4.52 seconds on 3x3 will get a negative time for one-handed.


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## qqwref (Feb 10, 2015)

Some of these results are incredibly bad. No matter how fast you are at 3x3x3, it'll never give you results better than 1:31 BLD, 8.70 pyraminx, 24.20 square-1, 19.38 clock, 9.60 skewb, 9:36 4BLD, 20:24 5BLD, and 4.18 cubes multi. The results I listed vary from noobish to decent but not great (other results are very good, as they should be for someone who gets 0.10 second times on 3x3x3).

Straight regression lines are really not a good fit for this type of data. In fact, even a more complicated curve would be a very poor fit. Different people have different amounts of skill on different events, and that skill doesn't automatically transfer over. So a better 3x3x3 time (for instance) doesn't lead to a much better time at other events. So the given times don't really correspond to anything, especially in the outlying regions where most experienced cubers are. It would be better to use the WCA ranks, and compare (say) top 5% in 3x3x3 to top 5% in other events - that way the times on other events would require very roughly the same skill as it took to get the time you input at the top.


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## Ollie (Feb 10, 2015)

My expected 4BLD time is 1:18.77 when I use Multiple Blindfolded as my base event. wut

edit: and my 3BLD is -99.81s


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## Kit Clement (Feb 11, 2015)

Here's the problem with the data -- the variance is obviously increasing as times get larger (for most relationships). This is very clear for the example of 3x3 vs. 4x4:



To reduce this, as I mentioned before, we can take logarithms of the data. The variance increase is so strong here, I actually found that taking the log twice worked well.



Conveniently, this also fixes the strong right skew of the data, and makes it much closer to normal. Still a bit off, but it's not as important as the variance.

We can now fit a linear model to the loglog data. 


```
Call:
lm(formula = X333loglog ~ X444loglog, data = x3x4)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.41500 -0.04422  0.00383  0.04860  0.32557 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) -0.657522   0.009407   -69.9   <2e-16 ***
X444loglog   1.126283   0.006288   179.1   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
```

How do we interpret these coefficients now? We can see our model as such:

Pred. 3x3x3 times = exp{exp{-0.658 + 1.126*log{log{4x4x4 time}}}}

As you can see, this fits the data much better:



This won't work for every pair of events (MBLD is especially hard to model) but should work much better for events that have this kind of pattern.


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## YouCubing (Jul 26, 2015)

I put in my 3x3 global average of 34.99. I had some fun looking at the average predictions, and then... 6x6. My global average is 8:16.63 on 6x6 (Yes, I am a nub. I know.) But the website predicted my global average to be 8:16.64. Gj.


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## RedTopCuber (May 3, 2018)

The site doesn't work


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## Underwatercuber (May 3, 2018)

tigermaxi said:


> The site doesn't work


Probably due to the fact that it’s 3 years old and they probably haven’t done maintenance on it in a while


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