Moves per second is way more important than total moves

[tseitsei]

I did some quick solves like this for fun. Feel free to draw your own conclusions.

1st avg5: 47.66s
I used a beginner method
1.cross
2. bottom corners
3. middle edges
4. fruruf
5. beginner corner twist
6. u-perm(s)
7. a-perm(s)
In addition to that I tried to turn quite slowly

The move count of this method turned out to be ~110 moves so my TPS was ~2.3.

2nd avg5: 27.56s
I used the same method described above but now I turned as fast as I could. So my TPS was ~4.

3rd avg5: 22.76s
I used full CFOP but slow turning. CFOP has a move count of about 60 moves so my TPS was ~2.6.


My conclusion:
I could get sub-50 with total beginner method and slow turning (really try it. Below 3 TPS is really quite slow and I believe anyone could do that with minimal practise. I mean if you can do a standard T-perm sub-4.6 that is already >3TPS). So to me that means that eliminating pauses is THE MOST IMPORTANT thing by far. Also note that my solves still have pauses too so by eliminating pauses completely you could get even better times.

I was also able to get 22s avg with only 2.6TPS so TPS really isn't that important until you are sub-20 or sub-15 at least...

 

[mark49152]

@tseitsei, I don't quite follow. Are you saying you deliberately added pauses between the steps in your beginners solve? Are pauses included in your TPS?

Anyway, the reason for the disagreement in this thread all comes down to how pauses are measured and expressed.

To my mind, solvetime = (movecount / TPS) + pauses. Where the unit of pauses is seconds. Fewer seconds paused is an improvement.

@cubo is using a model where solvetime = (movecount / TPS) * pausefactor. In his model, the 18 second solver who pauses for 9 seconds has the same pausefactor as the 100 second solver who pauses for 50 seconds and that represents no improvement.

So we can come up with plenty of examples where in the first model, and intuitively, reducing pauses is the main contributor to improvement in solve times, but when expressed as a pausefactor in the second model it isn't.

Obviously my position is that I don't agree with his model. For @cubo and anyone else who chooses to follow the pausefactor model, I can't fault his arithmetic and agree that this notional pausefactor has a smaller impact than TPS in the example he gave.

 

[tseitsei]

@tseitsei, I don't quite follow. Are you saying you deliberately added pauses between the steps in your beginners solve? Are pauses included in your TPS?

Anyway, the reason for the disagreement in this thread all comes down to how pauses are measured and expressed.

To my mind, solvetime = (movecount / TPS) + pauses. Where the unit of pauses is seconds. Fewer seconds paused is an improvement.

I didn't deliberately add any pauses. I tried to do as smooth solves as I could every time. I only altered my turning speed and method (only altered method between 2nd and 3rd avg).
And yes all the pauses that were still left (since my lookahead isn't perfect) are included in my TPS reading.

My point is that even while turning slowly and using a very simple and inefficient method I was able to achieve sub-50 times and while turning slowly and using a better method (CFOP) I could achieve 22s times. AND to add to that my solves still had some pauses (since my lookahead isn't perfect) so IF I was able to completely eliminate pauses I could achieve sub-20 times with quite slow turning speed.

So IMO eliminating pauses is much more important than TPS if you still average 20+ seconds.

And yes solvetime = (movecount / TPS) + pauses but most people don't really realize how big parts of their solves really are just pauses. If you eliminate all pauses you can achieve reasonable times even with quite lousy TPS.

I hope that you can understand what I'm trying to say now

 

[Rubix Cubix]

I think this is an interesting video that helps to prove the point that a fast TPS can be more effective than move count. As he manages to get sub-20 using the beginner method.

 

[mark49152]

I hope that you can understand what I'm trying to say now

Yes. You mentioned pauses so I thought maybe you added some. For what it's worth, I think beginners pause in ways that it's hard to even imagine once you're experienced. I remember trying to do F2L, spotting a corner then spending 5+ seconds searching for the matching edge. These days, I just seem to automatically know where the edge is.

 

[tseitsei]

I think this is an interesting video that helps to prove the point that a fast TPS can be more effective than move count. As he manages to get sub-20 using the beginner method.

Yep. But having no pauses is even more important than either of those. You dont really see him pausing during those solves now do you?

Yes. You mentioned pauses so I thought maybe you added some. For what it's worth, I think beginners pause in ways that it's hard to even imagine once you're experienced. I remember trying to do F2L, spotting a corner then spending 5+ seconds searching for the matching edge. These days, I just seem to automatically know where the edge is.

Yes! and that is exactly why eliminating pauses is SO important. You can use an insane amount of time just pausing...

 

[cubo]

The reason I asked earlier where you were going with this is because I don't understand the purpose or value of your argument. You seem determined to prove and hammer home this TPS-is-most-important point, which seems a useless conclusion derived from over-simplification and dubious assumptions. It's an interesting discussion, which I enjoyed at first, and there has been some good info and advice posted by others, but why is this TPS point so important? As has been said many times, it's really not as simple as that.

Hey Mark,

My purpose was to start a discussion based on a thought experiment. So in terms of that, it's succeeded

Its value as an experiment is, I believe, in calling attention to the role of TPS.

I admit that calling TPS "most important" is what seems to have provoked the strongest reactions, but it is a valid claim providing people understand that it is specific to the parameters established by the thought experiment and has never been about me telling people how to get better in general. You can criticise the parameters chosen, but not the results drawn from them, mathematically speaking.

As I have already said, but I'll repeat, despite TPS improvement clearly being a crucial part of overall time improvement, it may be something a cuber should not ever specifically try to improve, and in fact (as many people are keen to remind me), at least at some points in a cubers improvement, it may be more effective to deliberately reduce your TPS. This is the "slow to go fast" mantra I keep hearing. I've never disagreed with this.

In terms of taking issues with my experiment, I think the main outstanding question is the amount of pausing involved at various developmental stages (this is something I will investigate further).

I have certainly enjoyed the stimulating discussion and has given me lots of further food for thought.

Thanks for being part of that.

Would you (or any other person in 90 seconds or slower) be willing to record a video of 5 solves? I'd like to try count the moves and pauses.

Hey Alpha, definitely keen to get more data on pausing. But perhaps the data is already available somewhere? A single sample from me wouldn't prove much.

Your TPS theory makes the false assumption that the TPS of a beginner is dependent on how fast this solver is able to perform algs.

Actually "how fast you perform algs" is the definition of TPS. Turns don't happen while pausing

TPS is mainly determined by how fast you can find your pieces and work out how to insert them.

I believe what you've just described is look ahead, if done during algs, or pausing, if done between them. And although there is clearly a relationship between these and TPS, they are categorically different.

 

[JanW]

Actually "how fast you perform algs" is the definition of TPS. Turns don't happen while pausing

I believe what you've just described is look ahead, if done during algs, or pausing, if done between them. And although there is clearly a relationship between these and TPS, they are categorically different.

You missed my point there. The point is that TPS is irrelevant as long as you don't know what you are supposed to turn. A beginner can be capable of quite high TPS, but cannot use this speed. To get faster, you learn look ahead to eliminate pauses and through this increase your overall TPS.

I hope @MarcelP doesn't mind me using his 4 year old solve as an example, it's just because he is the only person I know of who has both 90 and 12 second solves on youtube to compare improvement.

Have a look at this 90 second solve and you should see that TPS is not the bottleneck:

Cross: 14 moves, about 14 seconds, 1 TPS. With pauses between just about every single move, it's quite impossible to measure any value for TPS here.

F2L: about 44 moves, 50 seconds, <1 TPS. Again so much pauses it's hard to give any value to TPS. I mean, second F2L pair is formed in the upper layer when he starts looking for it, but what should be a 4 move insertion takes 7 seconds. How do you measure TPS for that?

LL: about 50 moves, 30 seconds, 1.67 TPS. Since this is the part where alg drilling and improving TPS has the greatest effect, I looked at this part at half speed to see that there was about 14 seconds of pausing and 16 seconds of turning the cube. That would make about 3.1 TPS. (This alone should tell you that eliminating pauses is the most important. Pauses can be just about completely eliminated, especially at 3 TPS, to reduce the time by 14 seconds. Doubling TPS to a very good 6.2 TPS only cuts 8 seconds.)

Next, here's same person 4 years later solving in 12 seconds:

He did a reconstruction of that solve in Older cuber discussions, it's 67 moves, 5.5 TPS. TPS is obviously much faster, but pausing has been reduced by a much greater factor. Hard to tell how much could be counted as pausing without counting frames.

4 years ago his TPS during last layer was about 3, and he used 50 moves. In the 12 second solve it's 26 moves. The time from finishing F2L to solved is about 4.7 seconds. Looks like about 0.7 seconds of this is recognition, so 0.7 seconds pausing and 4 seconds solving, 6.5 TPS.

Now we have some actual numbers to compare.

Total time spent on LL improved by a factor of 6.38 from 30 seconds to 4.7 seconds.
TPS, improved from 3.1 to 6.5, improvement factor 2.09
Movecount improved from 50 to 26, improvement factor 1.92
Pausing reduced from 14 seconds to 0.7 seconds, improvement factor 20

Improving from 90 seconds to 12 seconds, TPS improved a bit more than movecount. Though it's very close to a tie and far from TPS being "way more important" than movecount. And both TPS and Movecount mean nothing if you don't improve lookahead to remove those pauses.

Edit: fixed the post, had some numbers wrong at first.

Edit again... Marcel's reconstruction had the wrong movecount, which explains how I counted wrong twice. The real movecount for last layer is 25, here are the true numbers:

Total time spent on LL improved by a factor of 6.38 from 30 seconds to 4.7 seconds.
TPS, improved from 3.125 to 6.25, improvement factor 2.0
Movecount improved from 50 to 25, improvement factor 2.0
Pausing reduced from 14 seconds to 0.7 seconds, improvement factor 20

It is in fact exactly a tie between TPS and movecount.

 

[tseitsei]

That last post by JanW is awesome and pretty much finishes this thread perfectly right there...

 

[mark49152]

What do you mean by "competent"?

I didn't answer this and would like to.

In my view, the early stages of improvement are just about learning to solve the puzzle well. A lot of that is about basic technique, basic efficiency, not making mistakes, recognition, and developing familiarity with the puzzle. In terms of our metrics, that translates mostly to pause reduction and move count. You could improve like this for say a month, and then look back and feel that you are not really "going faster", despite what the timer says, but that solving the puzzle is just easier.

At some point, you get to a level where you have a good solving rhythm, you know the cube and your cases and algs well, and solving the cube feels easy and fluid, but you're just not getting faster. You find that you really have to push to get faster, whether that means turning faster or concentrating on lookahead, or learning new algs, etc. Improvement is no longer about solving becoming easier, it's about pushing to go faster. Pushing means you have to deliberately work at it.

Obviously in practice it's not so black and white as that and there's no fixed point where competence is achieved and speed training starts. It's a gradual transition. I would say it's mostly competence down to about 30-40 seconds, and mostly pushing speed below 20-25 seconds.

I started cubing in 2012 and have kept detailed logs of my performance since then, including splits, with measurements like cross+1 and last pair+LL so that I have some measurements of pauses as well. This morning I found some time to go through those numbers and make some calculations about my own improvement. I don't have videos from that time, unfortunately.

I started timing myself at around 70 seconds and in the last couple of weeks of 2012 I dropped from 70 to 50 seconds very quickly, which I believe is just competence (as above) and not worth analysing. At the end of 2013 I was at 28.5 seconds average of 50, and end of 2014, 19.7 seconds.

At 50 seconds, I was already using 3LLL and had learned good solutions for cross and F2L cases, so my move count was about 70 on average. That's based on measurements and notes from the time, not guesswork. My maximum TPS was 2.4, measured from PLL drills, and pauses accounted for about 21.1 seconds of the total solve. How I calculated pauses is a long story that I don't have time for in this post, sorry. Maybe later.

At 28.5 seconds, average TPS was 4, pauses 12.2 seconds, and I knew about half of OLL so I estimate move count at 65.

At 19.7 seconds, full OLL so 60 moves, TPS 4.7, and pauses 7 seconds. That 7 seconds sounds high and I will go look at some videos to see if that's really true, but it wouldn't surprise me. Because of the way I calculated it, dips in TPS due to e.g. looking ahead during F2L would also be accounted for as pauses rather than lower TPS.

 

[shadowslice e]

Yes I know what you mean ... but the alternatives "most significant", "biggest impact" etc don't seem better.

Again: my observation is NOT about saying "this means you must focus on TPS above all else". That would be prescriptive, which as a beginner I don't feel qualified to be. It may actually be that you don't need to focus on TPS at all as you progress. I simply don't feel qualified to comment on that. Telling people how to get better is NOT my point here.

Rather, I'm simply observing and describing the mathematics involved in moving between two realistic scenarios and pointing out that, overall, TPS contributes most (i.e. is most significant, important, whatevs ) in the overall time improvement between those two scenarios.

If that's what you're doing, then I think a better title for this thread would be: "Tps improves the most in transition from beginner to world standard" or similar. I'm sure you could think of a better title in the same vein.

 

[cubo]

Hey @JanW, yes I did miss your point I think, my apologies.

We are talking about different ways to measure TPS. The two ways it can be done are:

1. TPS = total move count / total time. e.g. 100 move solve in 100 secs, 50% pausing, is TPS of 1. That's how I calculated TPS in the OP (although I didn't mention pausing because I hadn't considered it until Mark raised it). This approach essentially "absorbs" any pausing into the TPS measure.
   
2. TPS = total move count / (total time minus pausing). e.g. 100 move solve in 100 secs, 50% pausing, is TPS of 2. That's how I've been calculating TPS since introducing pausing into the mix. This approach strictly separates pausing from TPS, as per my last comment about "turns don't happen during pausing".

Both are valid approaches. Main thing is to be clear which we are using.

I'm short on time now, will respond properly to your post about Marcel's times later.

 

[cubo]

Hey again @JanW,

So looking at the figures you posted for Marcel:

LL only

• 50 moves in 30 seconds with 14 seconds pausing (47%), to 25 moves in 4.7 seconds with 0.7 seconds pausing (15%).
  
• Move count improved x2 (50 to 25), TPS improved x2.08 (3.125 to 6.5), pausing improved x3.11 (47 to 15)

So what does this all tell us?

It tells us that, for the LL phase, pause reduction was a significantly higher factor than TPS or move count in Marcel's improved times.

As for the whole solve? Well that depends on our estimate of pausing for the whole solve, but if we used the same figures we used for the LL (47% and 15%) ...

Entire solve

• 108 moves in 94 seconds with 47% pausing, to 67 moves in 12 seconds with 15% pausing.
  
• Move count improved x1.61 (108 to 67), TPS improved x3.03 (2.17 to 6.57), pausing improved x3.11 (47 to 15)

This tells us that, over the whole solve, pause reduction and TPS were similar in effect (pause reduction slightly higher) and that each of them was way more important than move reduction.

Considering the winning result for pause reduction in the LL, but the closer result to TPS overall, this suggests TPS was more important than pause reduction as an improvement factor in the F2L.

Very, very interesting!

Hey @mark49152,

Thanks for your thoughts on competence and for sharing your stats.

Going from 50 secs / 70 moves / 21 secs pausing ... to 19.7 secs / 60 moves / 7 secs pausing ... it's VERY clear that move count has not been a big factor in you getting more than twice as fast overall. Likewise, as a percentage your pausing has only moved from 40% to about 35%.

So that leaves ...

 

[JanW]

I realized after I wrote the post above that looking at som "improvement factor" was really bad and doesn't make any sense at all (reducing pauses from 14 to 0.7 seconds is not 10 times better than reducing from 14 to 7 seconds and reducing pauses to 0 is not an infinite improvement).

What you should look at instead is how the reductions affect the time. I doubt the 47% and 15% pausing figures are accurate for the whole solves, but let's assume they are.

94s solve consists of 44 seconds pausing and 50 seconds performing moves.
12s solve consists of 1.8 seconds pausing and 10.2 seconds performing moves.

Improving from 90s to 12s, pauses were reduced by 42.2 seconds and the time spent performing moves was reduced by 39.8 seconds. Eliminating pauses shaved more time off the solve than improving movecount and TPS combined.

 

[mark49152]

Likewise, as a percentage your pausing has only moved from 40% to about 35%.

Yes, except as I have explained many times, it's nonsensical to measure pausing as a percentage. But I might just as well try to convince you the earth is round .

 

[stoic]

Considering the winning result for pause reduction in the LL, but the closer result to TPS overall, this suggests TPS was more important than pause reduction as an improvement factor in the F2L.

At some point you're going to have to admit to a teeny bit of confirmation bias, right?

 

[aybuck37]

I have bad tps and high turn moves. And i have bad lookahead rip

 

[cubo]

I realized after I wrote the post above that looking at som "improvement factor" was really bad and doesn't make any sense at all (reducing pauses from 14 to 0.7 seconds is not 10 times better than reducing from 14 to 7 seconds and reducing pauses to 0 is not an infinite improvement).

What you should look at instead is how the reductions affect the time. I doubt the 47% and 15% pausing figures are accurate for the whole solves, but let's assume they are.

94s solve consists of 44 seconds pausing and 50 seconds performing moves.
12s solve consists of 1.8 seconds pausing and 10.2 seconds performing moves.

Improving from 90s to 12s, pauses were reduced by 42.2 seconds and the time spent performing moves was reduced by 39.8 seconds. Eliminating pauses shaved more time off the solve than improving movecount and TPS combined.

I also realized something after my last post ... but my conclusion went in the opposite direction to yours Allow me to explain.

I agree it's all about time. I also believe (and this is where my approach is different to yourself and mark49152) that the 3 factors (pausing, moves, TPS) are interconnected and influence each other.

So then I asked myself, how do our 3 factors influence time taken to complete a solve?

• Pause factor: a factor equal to [1 divided by 'active' time expressed as a fraction of total time]. A pause factor value of 1 thus indicates no pausing, a 2 indicates 50% pausing (solve takes twice the time due to pausing), a 10 indicates 90% pausing (solve takes 10 times as long due to pausing), etc.
  For example, if a solve takes 90 seconds, 30 seconds of which is pausing, the pause factor is 1/(60/90)=1.5. This tells us the solve took 1.5 times as long as it would have without any pausing.
  
• Move factor: a factor equal to [the number of moves].
  
• TPS factor: a factor equal to [total moves divided by total time multiplied by the pause factor]. This is the second of the two possible approaches mentioned above.

With this formulation, if you double the value of any factor, the total solve time doubles. Likewise, if you halve any factor, the total time halves. Furthermore, if compare the 3 factors between 2 different solves and work out how much each factor changed, you get 3 change factors which, when multiplied together, will equal the total change in time taken between the two solves.

So going back to Marcel and applying our more rigorous method ...

LL solves:

• 1: 50 moves, 30 secs, 14 secs pausing. Pause Factor = 1/(16/30) = 1.875. TPS = 50/30*1.875 = 3.125
  
• 2: 25 moves, 4.7 secs, 0.7 secs pausing. Pause factor = 1/(4/4.7) = 1.175. TPS = 25/4.7*1.175 = 6.25
  
• Moves improved x2 (50/25), TPS improved x2 (6.25/3.125), pausing improved x1.596 (1.875/1.175)
• Total time improvement = 2 x 2 x 1.596 = 30/4.7 = 6.38

For last layer, move reduction and TPS improvement had an equal effect, with both greater than pause reduction.

Whole solves (assuming same pause rates for whole solves as for LL)

• 1: 108 moves, 94 secs, 44 secs pausing. Pause factor = 1/(50/94) = 1.88. TPS = 108/94*1.88 = 2.16
  
• 2: 67 moves, 12 secs, 1.8 secs pausing. Pause factor = 1/(10.2/12) = 1.18. TPS = 67/12*1.18 = 6.57
  
• Moves improved x1.61 (108/67), TPS improved x3.04 (6.57/2.16), pausing improved x1.6 (1.88/1.18)
• Total time improvement = 1.61 x 3.04 x 1.6 = 94/12 = 7.83

As so, comparing the improvement between the whole solves, TPS was almost twice as important as move reduction or pause reduction.

[ Edited to remove unnecessary brackets and double-entry of whole solve.]

Yes, except as I have explained many times, it's nonsensical to measure pausing as a percentage. But I might just as well try to convince you the earth is round .

Why is it so crazy, given that everyone here keeps talking about how strongly TPS and pausing are connected via look ahead? Do you think they are completely independent factors? In other words, do you think Marcel could have simply reduced his pausing from 44 seconds to 1.8 seconds while not improving at all at TPS? I don't believe that's how cubing improvement happens. I think it happens with all 3 factors improving together, and influencing each other.

At some point you're going to have to admit to a teeny bit of confirmation bias, right?

Sure, but don't we all? The best I can do is try to stick to the facts, explain my approach as clearly as I can and be open about my assumptions.

 

[AlphaSheep]

Why is it so crazy, given that everyone here keeps talking about how strongly TPS and pausing are connected via look ahead? Do you think they are completely independent factors? In other words, do you think Marcel could have simply reduced his pausing from 44 seconds to 1.8 seconds while not improving at all at TPS? I don't believe that's how cubing improvement happens. I think it happens with all 3 factors improving together, and influencing each other.

Its crazy because every single fast cuber here had the exact opposite experience. They've had to actively concentrate on and improve each of those seperately because beyond some basic level of competence (around 30-40 seconds), TPS and pausing are very much independent, and as has already been stated, improvement in either one actually hinders improvement in the other. They absolutely do not improve together.

 

[tseitsei]

Amazing! That cubo guy is still arguing about this.

And still coming up with new ways to twist the numbers to "fit" his explanation despite every single advanced cuber telling him otherwise and JanW even explaining everything perfectly in his post...

I'm not even mad. That's amazing