Solving the cube as a craft has evolved over the past 40 years and as people have studied and trained to solve it ever faster, a body of knowledge has started to take shape. The past 10 years have seen the time necessary to solve the cube plunge to a handful of seconds, while the amount of know-how has skyrocketed. A body of data has started to form, as databases of algorithms, but also reconstructions of eminent solves have been gathered into repositories for the cubing community. Foremost among these, www.speedcubedb.com now comprises thousands of algorithms for many puzzles and events, and several thousands of solves by the fastest cubers in the world.
This work, and this article would not have seen light were it
not for the herculean work of a number of people in the cubing
community, it is worth mentioning 3 of them. Heading the solve
reconstruction effort, Stuart Clark not only
reconstructs the vast majority of all new solves, to the tune of
hundreds of solves per month, but he manages and nudges
the main efforts of the reconstruction community. The
torchbearer mantle was passed onto him by the original
reconstruction god, Brest, who single-handedly
reconned half of the four thousands solves available at the time
of this writing. Closing this holy triumvirate is Gil
Zussman, who not only created, designed and coded speedcubedb.com
(both formidable feats of technological craftiness) but
developed a plethora of tools for solve reconstruction, alg
discovery and management, that make the life of speedcubers the
world over so much easier and better.
And finally thanks to Anto, Ben, Feliks and Phillip for going over a pre-read of this and for their insightful feedback.
When we combine the solve time with the turns per second (TPS) of the solver, and the number of moves to solve the cube, we're struck by two things: While there is a relatively linear relationship between times and TPS until we hit about 8 seconds, the times hit a wall even though very-high TPS can still happen. Conversely, while the average number of moves per solve decreases slowly until about the same time, it takes a sharp downward turn for the faster solves. So far so good. However, when we look at solve moves vs TPS we realise that there are very few solves that have both very low moves and very high tps, whereas there are many more that have only one of them. This suggests that – for the time being – it is not really possible to find efficient solutions while going very fast.
It is rare to have clear-cut answers, for once this looks like one. Solves with cross rotations are 5.5x slower than crosses with equivalent move-count that increase the complexity of the movement set (n-gen). This is likely due to the fact that inspection allows to prepare and adjust to the more complex fingertricks necessary to operate on several cube axes.
The opposite is true for f2l, where the much higher tps (2/3 faster than cross tps on average) means that spamming low-gen moves whilst incurring rotations is a successful strategy, regardless of whether we move from 2-gen to 3 or from 3 to 4.
The desire for no-rotation methods (which made sense when fingetricks were vastly more limited by cube hardware, and TPS was by necessity much lower) might not be that relevant anymore.
The Back-Right slot is the most used for the first f2l pair, and it's usage is more frequent the faster the solve. Last slot tends to end on Front-Right more than half of the time, but Back-Right is also an option that gets some usage. That is not to say that the other slots aren't used at all, they still account for between 1/6 and 1/4 of slot usages. But the habit of slotting things in the back still comes out as a winning one.
95% of pair insertions use standard RU/LU insertions, foregoing
the more complex FRUF or wide-move insertions (slice-move inserts
didn't even make the graph, but you can find them below). This has
some validity – wide-move insertions are slower than the others –
but not only, as F-based ones are just as fast if not slightly
faster, than vanilla. They're just not used much.
Keyhole (the fastest insert on average) is very rare, and appears mostly for the first couple of pairs, while edge-controlling F inserts (e.g. sledge) appear mostly (and unsurprisingly) for last pair.
The relatively recent improvements in cube hardware technology, have made the execution of non-M slice viable during solves, and their usage has gain some traction, especially in the younger community. Whilst we know that M slices have their place in a solve (the fastest OLL and PLL algs demonstrate this easily), the same is not clear for S and E slices. When solvers utilise them in any step except OLL, those steps will be significantly slower than when using their outer-layer variant.
With that being said, our data reflects the performance of current top-level solvers, who have learned their ropes in an earlier less slice-heavy era. It might be that with time the advantages given by these "new" moves (previously less viable due to hardware limitations) might come to the fore. However, the fact that S moves have quickly found their place in OLL but not in others indicates that if they presented a stark improvement on alternative moves those might have come to light already. The prominence of "simple works better" instances especially in f2l would suggest slices might not be the way to go for at least some of the cfop phases.
Oll executions require a rather wide range of time in general, but it true that the median execution for Dot OLLs is slightly slower than other OLLs (by about 0.16sec). This doesn't seem to affect solves overall: the median solve containing a Dot OLL sits evenly in-between solves with OCLL and those with other cases. What's more, any attempt to influence EO through last slot will lose you more time than the expected gain in time. So just learn good algs, and don't worry about dot OLLs.