# Relative Solve Times for 2x2x2 - 7x7x7

#### Logiqx

##### Member
Latest update (2020-02-13)

SQL - https://github.com/Logiqx/wca-stats/blob/master/sql/misc/relative_solve_times.sql

Original Post

I wondered if there might be a rule of thumb which can be used to calculate comparable solve times (e.g. 4x4x4 vs 3x3x3, 5x5x5 vs 4x4x4, etc). I decided to see what I could find out using the WCA data and I've producing the graph below using peoples best average in each event.

The horizontal axis splits everyone into "vigintiles" (20 groups, 5% in each) based on their ranking for a particular puzzle. For example: The green line (4x4x4 vs 3x3x3) tells us the top 5% in the 4x4x4 rankings take 4 times longer to solve a 4x4x4 than they do a 3x3x3, based on their best average for each event. Conversely the slowest 5% have a 4x4x4 average which is almost 7 times their 3x3x3 average.

Aiming for the ratio towards the left hand side seems like a good goal for people looking to improve at a specific event.

Here are some high-level ratios across the categories (2x2x2/3x3x3, 4x4x4/3x3x3, 5x5x5/4x4x4, 6x6x6/5x5x5, 7x7x7/6x6x6):

Min: 0.30, 4.04, 1.86, 1.98, 1.43
IQM: 0.39, 4.89, 2.03, 2.18, 1.57
Mean: 0.41, 5.01, 2.07, 2.20, 1.57
Max: 0.60, 6.79, 2.51, 2.58, 1.73

I've found this graph quite interesting so I figured one or two of you might like it as well!

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#### Logiqx

##### Member
Relative Solve Times vs Standard Puzzles

Moving on from the original idea, I thought I'd also have a look at events such as one-handed, feet and blindfold. This chart compares OH / Feet / BLD times against the standard events.

Like the original chart (2x2x2-7x7x7), I've used peoples best average from the WCA data. For BLD events where averages aren't available (4x4 + 5x5), I've compared BLD single and sighted average.

Here are the high-level ratios across all of the categories (OH, Feet, 3x3 BLD, 4x4 BLD, 5x5 BLD):

Min: 1.62, 3.84, 3.03, 3.84, 3.56
IQM: 2.26, 10.81, 11.42, 12.22, 11.30
Mean: 2.36, 11.29, 12.11, 13.10, 13.09
Max: 4.04, 19.61, 24.28, 32.89, 37.24

Feet and BLD shows similar trends. The journey from novice to pro (right to left) is significant mountain to climb... thanks for the metaphor Noah.

#### mark49152

##### Super Moderator
Staff member
This is interesting, I'm surprised there have been no replies before.

Looking at 3x3 versus 4x4, I assume the vigintile is based on 4x4 ranking? So it might be reasonable to assume that those who focus on 4x4 are towards the left of the graph and those who neglect it or focus on 3x3 are towards the right of the graph. A good place to aim for a typical ratio without bias to either would be the middle, or a factor of 5x.

I've been wondering what my target should be for 4x4 and this answers it. My target for 3x3 is sub-20, so my target for 4x4 should be sub-1:40.

It's interesting how the 4x4/3x3 line is steeper than the others. I assume that means there's a lot of people who do 4x4 but who don't train it as hard as they train 3x3, which makes sense. On the other hand, those that do 5x5 tend to also do similarly well at 4x4 hence the narrower range of ratios.

It would be interesting to see lines based on the other vigintile - i.e. 4x4/5x5 as well as 5x5/4x4. I guess it wouldn't be a simple inverse since it would use a different ranking. Perhaps show the same line, 5x5/4x4, but for both 4x4 and 5x5 rankings, and see how they differ.

#### Logiqx

##### Member
Looking at 3x3 versus 4x4, I assume the vigintile is based on 4x4 ranking?
Correct. The 4x4x4 / 3x3x3 vigintiles are based on 4x4x4 rankings.

So it might be reasonable to assume that those who focus on 4x4 are towards the left of the graph and those who neglect it or focus on 3x3 are towards the right of the graph. A good place to aim for a typical ratio without bias to either would be the middle, or a factor of 5x.
That's a good way of viewing it. There are definitely some highly ranked 4x4x4 people who aren't so highly ranked at 3x3x3. However... some people towards the left of the graph are also very good at 3x3x3 (e.g. Felix). It would appear that 5x is fairly "normal" and a reasonable target for most people with plenty of room for further improvement.

https://www.worldcubeassociation.org/results/events.php?eventId=444&regionId=&years=&show=100+Persons&average=Average

It would be interesting to see lines based on the other vigintile - i.e. 4x4/5x5 as well as 5x5/4x4. I guess it wouldn't be a simple inverse since it would use a different ranking. Perhaps show the same line, 5x5/4x4, but for both 4x4 and 5x5 rankings, and see how they differ.
I'll dig out my original workings later this week to and see how that looks.

#### mark49152

##### Super Moderator
Staff member
I was curious how these stats related to relative sizes of cubes, so did the following calcs of pieces solved per unit time. The unit of time is one 3x3 solve, with factors for other order cubes estimated from the graph. I did not count fixed centres.

2x2: 8/0.33 = 24
3x3: 20
4x4: 56/4.5 = 14
5x5: 92/9 = 10.2
6x6: 152/18 = 8.4
7x7: 212/27 = 7.9

I was a bit surprised the slope wasn't steeper. Seems remarkable that on a 7x7 the pieces are solved as fast as one-third the rate of 2x2.

#### goodatthis

##### Member
Looks to me like I have "world class" relative solve times. My relativity factors (correct term?)

2x2/3x3: 0.32
4x4/3x3: 4.12
5x5/4x4: 1.85
6x6/5x5: 2.07
7x7/6x6: 1.38

what at this tells me is that I need to practice 4x4 and 6x6 more

#### lerenard

##### Member
Would someone be willing to expand this to include more events? I would like to have a better idea of what my FMC results mean, and soon I'll be getting a pyraminx. I understand if it would be a lot of work, I just don't know how to do anything like this myself.

#### mark49152

##### Super Moderator
Staff member
Here are some high-level ratios across the categories (2x2x2/3x3x3, 4x4x4/3x3x3, 5x5x5/4x4x4, 6x6x6/5x5x5, 7x7x7/6x6x6):

Min: 0.30, 4.04, 1.86, 1.98, 1.43
IQM: 0.39, 4.89, 2.03, 2.18, 1.57
Mean: 0.41, 5.01, 2.07, 2.20, 1.57
Max: 0.60, 6.79, 2.51, 2.58, 1.73
I through I'd check this thread again to see how my times compare. I am uncannily close to the IQM for 2x2 and 4x4 - 0.38 and 4.82 respectively.

I officially suck at 5x5 - 2.31.

#### One Wheel

##### Member
This is a slightly different angle, but the same idea. I took PB averages (except 4x4BLD, 5x5BLD, and FMC, which are single, single, and Ao3, respectively) and took the time (or moves for FMC) that fell at every 5%. The ratio at the bottom is 95th percentile divided by 5th percentile, to weed out the incredibly talented and unusually lackadaisical, and then give an idea of just how competitive the remaining 90% of competitors are. I think it is interesting that the lowest ratios are for big cubes: it would seem that mostly people who are reasonably serious about cubing will attempt big cubes. Perhaps there is a significant talent gap for blind solving?

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#### mark49152

##### Super Moderator
Staff member
@One Wheel : Interesting, but I think 3BLD should be single too, since that's what competitors are ranked on during comp. Single and mean are kind of in conflict, since trying to get a fast single increases risk of a DNF mean.

#### Logiqx

##### Member
This is a slightly different angle, but the same idea. I took PB averages (except 4x4BLD, 5x5BLD, and FMC, which are single, single, and Ao3, respectively) and took the time (or moves for FMC) that fell at every 5%. The ratio at the bottom is 95th percentile divided by 5th percentile, to weed out the incredibly talented and unusually lackadaisical, and then give an idea of just how competitive the remaining 90% of competitors are. I think it is interesting that the lowest ratios are for big cubes: it would seem that mostly people who are reasonably serious about cubing will attempt big cubes. Perhaps there is a significant talent gap for blind solving?
Thanks for sharing. With regards your ratios it is with noting that some events have more challenging cut offs and therefore anyone getting an average is by definition good at the event.

This can be clearly demonstrated with a simple example. Someone mid-way in the 3x3 rankings (30.9s) and someone midway in the 5x5 rankings (2:13.5) exhibit a significant skill difference.

It would be crazy to think to look at the 50% results for these events and conclude that 5x5 times are 4.5 * 3x3 times. The original study addressed this by comparing the performances of individuals.

#### One Wheel

##### Member
@One Wheel : Interesting, but I think 3BLD should be single too, since that's what competitors are ranked on during comp.
I can fix that later today.

With regards your ratios it is with noting that some events have more challenging cut offs and therefore anyone getting an average is by definition good at the event.
My hope is that these numbers may eventually help with making cut-off times more cuber-centric. Rather than just using round numbers, like 2:00 for 4x4, 3:00 for 5x5, 4:00 for 6x6, etc., one might make cut-offs of 85th percentile, or 2:06, 3:17, 5:23, etc. Over time that might tend to skew (or correct the current skew) results a little slower, but aside from the relatively minor issue of competition schedules I'm inclined to like that change. The bigger the cube is the more the solve depends on logic rather than memorized algorithms, so in my book more people solving big cubes = better.

#### One Wheel

##### Member
Updated with 3BLD single instead of average.

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#### One Wheel

##### Member
It would be crazy to think to look at the 50% results for these events and conclude that 5x5 times are 4.5 * 3x3 times. The original study addressed this by comparing the performances of individuals.
The intention of this project, unlike the original project in this thread, is less about figuring out relative solve times and more about figuring out roughly where one might rank. If I went to a competition with 100 representative cubers I would probably end up ranked about 65 in 3x3, 85 in 4x4, and somewhere in the bottom 5 in 5x5. That's what I wanted to find out.

#### Logiqx

##### Member
My hope is that these numbers may eventually help with making cut-off times more cuber-centric. Rather than just using round numbers, like 2:00 for 4x4, 3:00 for 5x5, 4:00 for 6x6, etc., one might make cut-offs of 85th percentile, or 2:06, 3:17, 5:23, etc. Over time that might tend to skew (or correct the current skew) results a little slower, but aside from the relatively minor issue of competition schedules I'm inclined to like that change. The bigger the cube is the more the solve depends on logic rather than memorized algorithms, so in my book more people solving big cubes = better.
You also need to consider the competitors who are unable to complete an average if you want to calculate what time a specific percentile tends to achieve. I suspect there are a lot of people how have entered 5x5 upwards who didn't complete an average and they need to be considered the bottom X percent.

As an aside, I know of people who've queried cut-off times (e.g. 2:30 cut-off for 5x5 being tough compared to 1:30 cut-off for 4x4) and the response was that cut-offs are purely for logistical reasons, reducing the length of time required to run the event. The cut-offs aren't chosen to allow X percent of the entrants to do an average.

The intention of this project, unlike the original project in this thread, is less about figuring out relative solve times and more about figuring out roughly where one might rank. If I went to a competition with 100 representative cubers I would probably end up ranked about 65 in 3x3, 85 in 4x4, and somewhere in the bottom 5 in 5x5. That's what I wanted to find out.
You need to consider my point about people with a DNF average. Try running your analysis across the full range of participants but treating DNF average as a large number (e.g. 60 minutes). That way the bottom X percentiles will be attributed to the slow people and the people cable of completing an average will be at the top. This still isn't perfect though because cut-offs vary around the world and at different competitions.

Staff member

#### One Wheel

##### Member
As an aside, I know of people who've queried cut-off times (e.g. 2:30 cut-off for 5x5 being tough compared to 1:30 cut-off for 4x4) and the response was that cut-offs are purely for logistical reasons, reducing the length of time required to run the event. The cut-offs aren't chosen to allow X percent of the entrants to do an average.
Fair enough, but it might be easier to explain X percent. The time limits are very frustrating to me as I try to get into cubing. I've already been forced to skip one competition because I didn't have any chance of making a cut-off (I could have done 2:10, or maybe even 2:00, but not 1:30 for 4x4). As someone who is getting involved in cubing at a relatively late age (29) I doubt I have any chance of ever being anything better than average, which come to think of it most people will never be better than average. I understand focusing an event on people who are better/more talented/more committed, but might it be a better policy to move toward limits on the number of competitors rather than time? This would most likely result in competitions having more local people compete, because it's easier to plan ahead and register early when you don't have to make significant travel plans. Obviously this wouldn't be a good idea for major national and international competitions, but smaller local events should be there to help get people involved, not just serve as proxy competitions between the top few percent of talent.

You need to consider my point about people with a DNF average. Try running your analysis across the full range of participants but treating DNF average as a large number (e.g. 60 minutes). That way the bottom X percentiles will be attributed to the slow people and the people cable of completing an average will be at the top. This still isn't perfect though because cut-offs vary around the world and at different competitions.
You're probably right, that's just a lot more data to work with, and I was having some trouble with the large amount of data I had anyway. It might be better to run the numbers on each person's best competition, and weight incomplete averages as though they included 5 solves of the same average time as the 1 or 2 singles. I don't think it would be too hard to do that, but you're working with a massive dataset.

#### Logiqx

##### Member
@One Wheel: You might like to look at the "Older Cuber" thread where a lot of us oldies hang out. Actually... a lot of us are older than you and the participants in the thread provide inspiration + motivation.

#### mark49152

##### Super Moderator
Staff member
I've already been forced to skip one competition because I didn't have any chance of making a cut-off (I could have done 2:10, or maybe even 2:00, but not 1:30 for 4x4).
I sympathise, because I came on here 5-6 months ago having a good old moan that I was years from reaching the 5x5 soft cut. Then I decided to make it a target, practised 5x5 like crazy to the exclusion of most everything else, and made cut at my next comp a few weeks later. It's not as hard as you think it is - it just takes a bit of determination.

#### One Wheel

##### Member
Then I decided to make it a target, practised 5x5 like crazy to the exclusion of most everything else, and made cut at my next comp a few weeks later.
I learned Yau about 6 or 7 weeks ago, and started practicing 4x4 almost to the exclusion of everything else just over a month ago when I found out about the competition I will miss tomorrow. I haven't recorded DNFs, and I've done a reasonable number of untimed solves, but since I started Yau I have recorded times for 603 4x4 solves. After 50 solves my Ao12 was 3:29, so that's a reasonable approximation of where I started. My pb single in those solves is 1:44.16, and my current Ao100 is 2:17.76. Sure, it's possible to get there, but in the last month I've spent over 27 hours of cumulative solve time on 4x4 alone, probably closer to 30 hours, and I'm nowhere close to 1:30. I'll get there someday, I'm sure, but I'd like to compete sooner rather than later.

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