Moves per second is way more important than total moves

[cubo]

OK so here's my thinking:

• Consider the beginner cuber who averages 100 seconds per solve, taking an average 100 moves.
  
• Now consider a top speed cuber who averages 10 seconds per solve, taking an average 50 moves.

What has contributed to their x10 speed improvement?
The halving in total moves (from 100 to 50) has been a x2 factor, but the improved moves per second (from 1 to 5) is a x5 factor!

I think this simple observation is interesting for a few reasons:

• It indicates that the focus of development should be on more 'fluid' algs using finger tricks to ramp up your speed, rather than learning more efficient but 'difficult' algs, and ultimately -- practice practice practice!
• It also suggests that generally, given a 'fewer but slower' vs 'more but faster' moves scenarios, the latter is a clear preference if lower times are your goal.
  
• A side question it raises regards this trade off: Does 'fewer' moves in fact always involve a speed trade off? Clearly lowering move count helps lower times up to a point, but when does this focus on move efficiency become a diminishing return?
  
• Lastly, it suggests sub-20 times are possible with beginner methods.

Interested in others thoughts on this.

 

[Matt11111]

What you're talking about is actually a measurement that some cubers use. It's called Turns Per Second (TPS). There are some people who will work on improving their TPS while others may spend that same time learning algs.

 

[cubo]

There are some people who will work on improving their TPS while others may spend that same time learning algs.

Hi Matt, thanks! I think you can work on both ... but one will give you much more improvement

 

[Daniel Lin]

you're right-TPS is more important than efficiency for beginners. However once you get to a certain level, the amount of effort you put into efficiency pays off more. World class cubers (like Feliks) are so fast that it's hard for them to improve their TPS/lookahead, so they need to be efficient as well(xcrosses/ F2L tricks)

A side question it raises regards this trade off: Does 'fewer' moves in fact always involve a speed trade off? Clearly lowering move count helps lower times up to a point, but when does this focus on move efficiency become a diminishing return?

By "efficient" we usually mean "speed optimal". If you know ZBLL, the algs are not movecount optimal (usually ~4 more moves on average), but they are speed optimal, so learning them obviously won't make you slower(than with OCLL+PLL).

 

[cubo]

you're right-TPS is more important than efficiency for beginners. However once you get to a certain level, the amount of effort you put into efficiency pays off more. World class cubers (like Feliks) are so fast that it's hard for them to improve their TPS/lookahead, so they need to be efficient as well(xcrosses/ F2L tricks)

Yes agree, to reach world class times you must be fast and efficient. But remember, 99.9% of cubers are not going to reach world class level. I know I'm not

Of course almost every cuber who tries to get faster will make improvements to their move count by learning a few more algs, as well as getting faster with their TPS through practice. For many, that transition will include learning F2L and possibly going from 4LLL to 3-look LL or 2-look LL. My main point is that improving your TPS is significantly more important to lowering your speed than the better algs you are learning. Not saying you shouldn't learn the algs, but just be aware of where the real gains come from.

For me this all comes from soul-searching my Rubik's goals, which are probably much more modest compared to many here, and contemplating the best way to get myself there. And realizing the way (for me) lies in developing hand speed, fluidity & fingertricks, as the most effective way to get faster compared to learning lots of algs. I know this ultimately limits me, but another of my points is that I think it limits me way less than you might think (see my last comment about sub-20 using beginners).

By "efficient" we usually mean "speed optimal". If you know ZBLL, the algs are not movecount optimal (usually ~4 more moves on average), but they are speed optimal, so learning them obviously won't make you slower(than with OCLL+PLL).

Sorry for my bad terminology - I was using "efficient" to purely mean "lower move count" but I understand what you mean that algs can be "speed efficient" yet "move inefficient" - that's what I call 'fluid' algs, the ones that just feel right and you can do faster than others even if it takes a couple of extra moves. I'm all about that.

 

[mark49152]

You haven't accounted for pauses. Time = (move count / TPS) + pauses. In that 100 second beginner solve, they probably aren't moving at all for 70 seconds of it.

You could argue that overall TPS for the solve accounts for pauses, but by TPS people usually mean speed when you are actually moving, and that's a more useful definition because the fact is that increasing finger speed and decreasing pauses are two very different aims involving different techniques and practice.

The consensus seems to be that decreasing pauses is way more important than TPS, hence all the advice on the forums about turning slow and looking ahead.

 

[Ranzha]

Just be fluid
You don't need crosses
You don't need tps
You don't need rotationless F2L or all your PLLs to be sub-1
Just solve yo and you could average 12 like meeeeeeeeeeeee

 

[cubo]

You haven't accounted for pauses. Time = (move count / TPS) + pauses. In that 100 second beginner solve, they probably aren't moving at all for 70 seconds of it.

You could argue that overall TPS for the solve accounts for pauses, but by TPS people usually mean speed when you are actually moving, and that's a more useful definition because the fact is that increasing finger speed and decreasing pauses are two very different aims involving different techniques and practice.

The consensus seems to be that decreasing pauses is way more important than TPS, hence all the advice on the forums about turning slow and looking ahead.

Interesting point, thanks Mark!

I have a few thoughts on this:

That estimate of 70 percent pause for a beginners solve is surely way too high? That would mean they were effectively making 100 turns in 30 seconds, or 3.33 TPS, which is a very fast for a beginner. I would think the inverse is closer to reality: 30 percent pause, 70 percent moving. Even that seems a bit high (on pausing). My pausing feels closer to 20 percent, but I'd need to do some tests to check more closely. In fact I will do that because I'm very curious now.

EVEN SO if it's 20 percent that's still clearly a significant factor I hadn't accounted for in my OP, so thanks again. Let's use that 20% estimate to re-do my example and see what happens:

• Beginner who solves in 100 seconds with 100 moves and 20 seconds of pauses. That now makes a TPS of 1.25 (100/80).
  
• Top speed cuber who solves in 10 secs with 50 moves and 0 second pauses. That makes a TPS of 5 (50/10).
  
• Note: top speed cubers may pause more than this, but this would only strengthen my point so I'm being generous

So now our tweaked breakdown of improvement factors (total x10) is now:

• TPS improvement: x4 (from 1.25 to 5)
  
• Move reduction: x2 (from 100 to 50)
• Pause reduction: x1.25 (from 100 to 80)

As you see, even if we introduce pausing to the mix, TPS still emerges as the most important of our 3 factors, by a wide margin.

 

[shadowslice e]

I'm pretty sure this is exaggerating at least a little bit. Even at non-world class level, I'm pretty sure that efficiency is very important. My average tps is somewhere in the range of 4-5 tps yet I'm verging on sub-11. I would say that my tps is more charicteristic of 15 second solver- where do I get the boost? Efficiency. I probably have the same if not slower tps that @Berd yet am still a fair bit faster now (just as a 3x3x3 comparison). Also note that @Berd is by no means an inefficient solver (at least for a CFOPer and doesn't spam tps either)

This is also similar to the difference between Alex Lau and Feliks Zemdegs (just as a side note, I'm talking about a couple of years ago when Alex actually practised and both averaged 7s). If tps is as important as you are making it, Feliks should have crushed Alex in every way possible turning about 1.5 times as fast. However, Alex was one of the most efficient solvers ever so his lower movecount allowed him to keep pace.

Similarly, in recent years, it seems at a cursory glance that feliks' tps has not increased as dramatically as his averages suggest but his efficiency has increased more in line.

Also, I think you need to define "more important". If you mean that it improves the most, I wouldn't neccesarily disagree with you. However, if you have (for example) feliks do a beginner solve, it would likely take him around 15-20 seconds but if you took Alex doing slow turning, he could likely get faster times than that with far lower tps.

Just as a final point, IMO, lookahead is perhaps the single most important part of speedsolving as it helps you to reduce pauses, increase lookahead and increase efficiency.

 

[AlphaSheep]

Interesting point, thanks Mark!

I have a few thoughts on this:

That estimate of 70 percent pause for a beginners solve is surely way too high? That would mean they were effectively making 100 turns in 30 seconds, or 3.33 TPS, which is a very fast for a beginner. I would think the inverse is closer to reality: 30 percent pause, 70 percent moving. Even that seems a bit high (on pausing). My pausing feels closer to 20 percent, but I'd need to do some tests to check more closely. In fact I will do that because I'm very curious now.

EVEN SO if it's 20 percent that's still clearly a significant factor I hadn't accounted for in my OP, so thanks again. Let's use that 20% estimate to re-do my example and see what happens:

• Beginner who solves in 100 seconds with 100 moves and 20 seconds of pauses. That now makes a TPS of 1.25 (100/80).
  
• Top speed cuber who solves in 10 secs with 50 moves and 0 second pauses. That makes a TPS of 5 (50/10).
  
• Note: top speed cubers may pause more than this, but this would only strengthen my point so I'm being generous

So now our tweaked breakdown of improvement factors (total x10) is now:

• TPS improvement: x4 (from 1.25 to 5)
  
• Move reduction: x2 (from 100 to 50)
• Pause reduction: x1.25 (from 100 to 80)

As you see, even if we introduce pausing to the mix, TPS still emerges as the most important of our 3 factors, by a wide margin.

Seriously, you'd be surprised. There are so many micro pauses you don't even notice.

I film some of my solves now so I can see my pauses. In a 18 second solve, it seems I typically spend about 12 seconds turning and 6 seconds on pauses. That's already over 30%.

When I was averaging around a minute, if I spammed random moves (say R U R' U' over and over) as fast as I could, I could easily reach 5 moves per second. I'm now sub-20 and I can only reach around 7 turns per second. (I know, my turn speed is slower than younger cubers)

I don't know what percentage of my solves were pauses as a beginner, but 70% doesn't sound unreasonable.

 

[mark49152]

That estimate of 70 percent pause for a beginners solve is surely way too high?

As @AlphaSheep said, you'd be surprised. What feels like a tiny pause when you're solving looks much longer if you watch it back in a video.

A couple of years ago we did some experiments in the older cubers' thread. We timed a solve, then practised the same scramble a few times and timed again. The solution remains the same, TPS doesn't get faster, but since we know what cases are coming next, there are way fewer pauses. I don't remember the exact results but roughly we were seeing 20 second initial solves come down to 13-14 seconds, meaning that even at 20 seconds about 30% of time is spent paused. That's also consistent with what I see when I watch videos of my solves.

Remember the "turn slower and look ahead" advice is usually aimed at solvers at about that level. That advice is irrelevant to 100 second solvers. Down to about 30s it's really about basic competence in solving, like not screwing up and not spending several seconds recognising each case.

If anything, I think for a 100 second solver it's probably higher than 70% pauses.

 

[cubo]

Hey @shadowslice e

I'm pretty sure this is exaggerating at least a little bit. Even at non-world class level, I'm pretty sure that efficiency is very important. My average tps is somewhere in the range of 4-5 tps yet I'm verging on sub-11. I would say that my tps is more charicteristic of 15 second solver - where do I get the boost? Efficiency. I probably have the same if not slower tps that @Berd yet am still a fair bit faster now (just as a 3x3x3 comparison). Also note that @Berd is by no means an inefficient solver (at least for a CFOPer and doesn't spam tps either)

What is spam TPS?

On TPS vs efficiency, it's just maths All other things being equal, 20% faster TPS or doing 20% fewer moves will both result in 20% faster times. IN your case, if you have the same TPS as a 15 second solver but do it in 11 seconds, then yes, you must be more efficient (about 27% in fact). This efficiency can only come from fewer moves or fewer pauses between algs.

This is also similar to the difference between Alex Lau and Feliks Zemdegs (just as a side note, I'm talking about a couple of years ago when Alex actually practised and both averaged 7s). If tps is as important as you are making it, Feliks should have crushed Alex in every way possible turning about 1.5 times as fast. However, Alex was one of the most efficient solvers ever so his lower movecount allowed him to keep pace.

Yes sure. If Felix in fact moved 1.5 times as fast as Alex, then Alex must have been correspondingly more efficient. It's a direct trade off. But this doesn't alter my point that overall, there is 'more' of TPS improvement to trade off. TPS can make a bigger impact because you can improve your TPS way more than you improve your move efficiency. From 100 moves in 100 seconds you can only get about 60% more move efficient (from 100 to a 40-move solve) but you can get 500%+ more efficient by improving your TPS (from 1 to 5+).

Also, I think you need to define "more important". If you mean that it improves the most, I wouldn't neccesarily disagree with you.

Yes, I mean that, on the journey from 100-second beginner to 10-second advanced cuber, it is TPS which mathematically makes the biggest contribution to your improvement (in clocking faster times).

Seriously, you'd be surprised. There are so many micro pauses you don't even notice.

I film some of my solves now so I can see my pauses. In a 18 second solve, it seems I typically spend about 12 seconds turning and 6 seconds on pauses. That's already over 30%.

I have just spent some time experimenting, and although I am MUCH slower than you, I also estimate around 30% pausing.

Note: I only count pausing between algs. I think that pausing during algs is too hard to measure, and also I believe, pretty minimal even at my relatively poor quality level. For me, pausing during algs, if any, is simply part of your TPS.

When I was averaging around a minute, if I spammed random moves (say R U R' U' over and over) as fast as I could, I could easily reach 5 moves per second.

What is spamming moves? Remember the key stat is not your max speed possible, it's your average over the whole solve -- surely as a beginner you were not averaging 5 moves per second for a one minute solve? That would mean you were making 300 moves in your solve!!!

I don't know what percentage of my solves were pauses as a beginner, but 70% doesn't sound unreasonable.

I am beginner and, other than perhaps literally my first few solves, have never taken that much pausing. I chose a '100-second beginner' as my start point because this person has already passed the absolutely basic stage of working out how to solve the cube and so on, where inspection times may indeed be very long.

As @AlphaSheep said, you'd be surprised. What feels like a tiny pause when you're solving looks much longer if you watch it back in a video.

A couple of years ago we did some experiments in the older cubers' thread. We timed a solve, then practised the same scramble a few times and timed again. The solution remains the same, TPS doesn't get faster, but since we know what cases are coming next, there are way fewer pauses. I don't remember the exact results but roughly we were seeing 20 second initial solves come down to 13-14 seconds, meaning that even at 20 seconds about 30% of time is spent paused. That's also consistent with what I see when I watch videos of my solves.

Sure, 30% is consistent with what Alpha has also mentioned, and what I've estimated my own pausing at. That's why I find the 70% figure so hard to believe.

Down to about 30s it's really about basic competence in solving, like not screwing up and not spending several seconds recognising each case.

If "not screwing up" means minimising accidental move blowouts, and "recognising each case" means pausing, you are clearly forgetting something ... TPS Please correct my maths if I am wrong.

If anything, I think for a 100 second solver it's probably higher than 70% pauses.

Remember, this means a beginner is doing 100 moves in lless than 30 seconds with an average TPS of over 3.3! I find that very unlikely.

 

[PenguinsDontFly]

Just be fluid
You don't need crosses
You don't need tps
You don't need rotationless F2L or all your PLLs to be sub-1
Just solve yo and you could average 12 like meeeeeeeeeeeee

Fluidity is gj
Never build crosses.
Never turn fast.
Never rotate.
Never use PLL.
Just learn roux and you don't need to turn fast because the efficiency does all the work for you. "Kian is slow, but Kian is efficient, so Kian is fast." If I had feliks tps i would almost be sub 6.

 

[mark49152]

I'm not sure where you are going with this...?

There are three variables, not two. Move count, TPS, and pauses. It doesn't make sense to conflate pauses and TPS to give a TPS measure for the whole solve, because that measure doesn't help us understand how to improve.

All three variables are important and you need to improve all three to get fast. It sounds like you're saying TPS is more important than the others, but again it's not helpful to take it in isolation like that.

Typically we improve through phases. When very slow, we make big early gains by reducing pauses. Then we learn better F2L/B and more alg sets and become more move efficient. TPS improves gradually all the time. Once you know a good amount of algs and get to around 20s, improvement becomes harder because TPS takes longer to improve and reducing pauses means looking ahead rather than just shortening recognition further. The variables start to conflict with each other because pushing TPS too hard makes look ahead more difficult.

So it's complicated and saying TPS is the most important thing over-simplifies the process.

Also, 70% is just a guess, but 2-3 TPS is really not an unreasonable assumption for a beginner when doing sunes or F2L inserts, etc. The fact is, at 100 seconds the cuber is doing more searching than turning, and that's where those big early improvements are made. At that speed, I'm not sure it really makes much sense to analyse performance anyway. Improvement above 40-50s really is more about becoming competent than becoming fast.

 

[biscuit]

There's no point comparing 100 second solvers to world <10 second solvers. At that level yes, TPS is more important. But only because TPS includes pauses. When you're that new, increasing TPS doesn't mean speeding up how fast you turn, but how frequently you turn.

And another really important factor is, as Mark said, that faster turning makes for harder lookahead, which is EVERYTHING. Look ahead is, without a shadow of a doubt, the most important thing in any current speedsolving method.

 

[Escher]

All three variables are important and you need to improve all three to get fast. It sounds like you're saying TPS is more important than the others, but again it's not helpful to take it in isolation like that.

Typically we improve through phases. When very slow, we make big early gains by reducing pauses. Then we learn better F2L/B and more alg sets and become more move efficient. TPS improves gradually all the time. Once you know a good amount of algs and get to around 20s, improvement becomes harder because TPS takes longer to improve and reducing pauses means looking ahead rather than just shortening recognition further. The variables start to conflict with each other because pushing TPS too hard makes look ahead more difficult.

So it's complicated and saying TPS is the most important thing over-simplifies the process.

Agreed.

I have a pretty good in-solve turning speed (not as fast as others at those RUR'U' exercises for example but I've never practised them), and I did a bunch of timed f2l solves the other day, I'm ~5.00 flat average at the moment. I did a few reconstructions and I'm tending towards high 20/low 30 for the majority of f2ls, which would mean I have a tps during f2l of around 6. Doesn't really tell you that much though, does it?

There is a categorical, and very important difference between turning speed and 'tps', a shorthand we use for moves/time. There are plenty of solvers about 2 seconds slower than I am that are capable of faster burst, and some that pause less than me. Min-maxing the trade-off as accurately as possible is the idea; you're trying to find that crystalline point in your noggin where you can't have both max speed and max lookahead, and force it to let you. It's honestly very hard and some people are simply not as good at it, regardless of practice or learning - they may just be better suited to beat some other task combination problem elsewhere. Compensations for this CAN be made in terms of hitting times, but they're very individual things, not something I'd blindly advise. I made a pretty picture:

Really quickly thrown together but you get the general idea.

Now in terms of actually getting better, priority thinking like the title isn't that useful either. It's not that helpful to say 'x is more important than y' when x and y are over-arching qualities of solving. Making a priority order for your practice is of course good though, once you've made some wider observations: 'I must have paused about 10 times that last solve, maybe more. Although I got a good time, it wasn't a qualitatively good solve, I need to turn a tad slower and concentrate more'.

In terms of your factor comparison (10s vs 100s, 50 moves vs 100), I'm afraid I don't feel like it's valid. Usain Bolt is 10x faster than a toddler, but that doesn't encapsulate anything useful. Clearly 'running faster' is important, but it's not a predicate so much as a judgement.

Edit: Btw, only just noticed you said you were a beginner - it's really cool that you're thinking about stuff like this as a novice. Can't promise I'll respond that quickly but you're welcome to PM me if you ever want some advice on improving.

 

[tseitsei]

Why not both?

 

[SenorJuan]

There's the fourth variable - cube rotations, which are actually time-consuming when you're at an advanced level. But when you're a beginner, they seem to be abundant and almost essential to completing the solve. Rotating just to inspect; doing it because you don't know how to do a move-sequence without rotn; rotating because you're faster with the RU moves than you are with the LU, many more reasons.
And then there's the fifth variable: the inspection process. Eg. CFOP: Beginners work out 2 or 3 edges, advanced solvers get 4 edges and have the first slot sorted out in advance.

It's pretty obvious TPS is mainly why we are seeing todays fast solves. The solve movecount is very similar to what it was 20 years ago, before finger-tricks and decent cubes, but the solve times are down to one third of what they were then.

 

[Ranzha]

Fluidity is gj
Never build crosses.
Never turn fast.
Never rotate.
Never use PLL.
Just learn roux and you don't need to turn fast because the efficiency does all the work for you. "Kian is slow, but Kian is efficient, so Kian is fast." If I had feliks tps i would almost be sub 6.

But I rotate and use PLL
Guess I'll never be fast
(Also I don't use Roux; I can't possibly be fast)

 

[willi pilz]

you're right-TPS is more important than efficiency for beginners. However once you get to a certain level, the amount of effort you put into efficiency pays off more. World class cubers (like Feliks) are so fast that it's hard for them to improve their TPS/lookahead, so they need to be efficient as well(xcrosses/ F2L tricks)

I just want to let you know, that this answer was literally perfect. It was a pleasure to read.