What sorts of movecounts do you get on average?
I just counted ten solves and the average was 44. However a great advantage of this method is that low-movecount solves (39 or lower) happen remarkably often, around 1 in 6. At the same time there is the occasional 52-54 move solve as well. It is also worth mentioning that I have had several speedsolves at 28-29 moves which is totally unbelievable.
I have done extensive analysis of the statistics to try to understand what is happening. If you consider CFOP F2L, to skip a pair requires two pieces right next to each other to be exactly pre-solved. If just the corner (in the slot) or just the edge (in the slot) is already solved by accident, this gives no advantage and is even considered a disadvantage. When you solve the corners first, the E2L pairs of the second step are random pairs of L/R slice edges and do not need to be next to each other. This means that if you have just one edge pre-solved in the L face, well you already have saved some moves, and if you have two edges solved (either 2 in L, 2 in R, 1 in L and 1 in R) now you skip an entire E2L pair. So in LMCF the chance of skipping an E2L pair is huge. At least half of solves have one edge piece already pre-solved and perhaps 1 in 5 have two edge pieces solved. Since I usually solve 1 edge piece at the same time as the corners, then 1 in 5 solves I only need to do two E2L pairs and then I am already on the last step (solve remaining L/R edge while orienting the midges).
The EGW variant of LMCF (EGW = EG + Waterman) adds the power to solve two edge pieces at the same time as orienting the midges. This adds an even greater statistical bias to lower movement solutions, because in EGW if you have 1 edge pre-solved (which happens 50% of the time), then the steps are:
1. Solve corners + 1 edge piece in 1 look
1b. [1 extra edge is found pre-solved]
2. Solve two E2L pairs (4 edge pieces)
3. Solve last two edge pieces while orienting the midges
4. Permute midges
Step 1 has the same complexity as CFOP PLL and steps 3+4 have the same complexity as CFOP OLL, so it really just comes down to E2L vs. F2L, and both EGW and LMCF the chance of skipping E2L pairs is way higher than skipping F2L pairs in CFOP.
Waterman's extremely low movecounts are real. As I posted in another thread, in the EGW variant, the solve proceeds based on the scramble. If an easy CLL face can be found, then you use block building to build one face minus one edge and basically solve the whole cube with Waterman. More often no easy block build of such a face is possible but rather you can see all the corners + 1 edge in one look, in which case you solve those with EG and proceed with the classic LMCF solution.
In summary I think the EGW and LMCF methods offer equal speed potential as the best CFOP variants but with the added advantage of much higher statistical chance of fast singles.
Edit: An interesting analysis is time ratios. My current global LMCF average is around 16.7 but I am not a fast turner and solving the corners with EG takes me 5 seconds on average. Using the corners as a metric, world class solvers can solve the corners in 2.0 seconds, so I am 2.5 times slower than a world class solver. Applying this to my global LMCF average predicts a fast turning average of 16.7 / 2.5 = 6.68, and my 9.75 full-step single done by a fast turner would convert to 9.75 / 2.5 = 3.90 (full-step!)
