When doing FM solves, in the back of your mind you're always thinking about move efficiency - ie: how much closer does each move take you to your goal. I believe the moves made during EOLine do a lot more to help the rest of the solve than the equivalent number of moves used during the Fridrich cross. EO helps you during F2L, with move ergonomics and lookahead. It also helps you on LL by pre-orientation of the LL edges, leading to easier/more efficient LL options.
It seems that ZZ should be better than Fridrich
in theory, but we've yet to see that proved in practice. All the more reason to learn it, and learn it good
In FM, you try to orient pieces independently. Your moves should solve a section of a cube. Orientation doesn't solve a piece, unless it's already permutated, and you usually don't "pure" orient pieces. What you should do in FM is to permute in the correct orientation from any starting orientation. So with ZZ, it doesn't help your moves, it
restricts them. I'm not saying Fridrich is better at FM. It has restrictions too. Freestyle block-building gives less restrictions to these 'methods'. Of course, FM is different than speed.
I wasn't suggesting that you should use EO in FM solves, I was just hi-lighting the principal of move efficiency. Although orientation doesn't solve a piece, it does bring it closer to its goal state. You are correct that both edge orientation and the cross introduce restrictions, but I question whether the restrictions introduced by EOLine are worse than the restrictions introduced by the Cross. Although I don't have comprehensive statistics on this, I'm inclined to believe that the restrictions introduced by EOLine have a less significant effect on move count.
The following stats show the optimal move-count of a colour neutral cross and a colour neutral EOLine, followed by the number of moves required to complete the cube using the Kociemba algorithm. It suggests that although EOLine has a slightly higher move count, it results in a lower move-count for completion of the cube.
Compiled using
http://laire.dy.fi/jarcs/
Cross | EOLine | Scramble
-------+--------+----------
4 + 24 | 5 + 20 | U' B' D L2 D R' L2 U R F2 U L' B2 L F2 D2 B F2 R F L' F L' R' B2
5 + 23 | 5 + 21 | U B2 R2 D' R2 U' L2 F R2 B2 D2 L2 F' R' L B D' U' F' D' B2 F L2 R B
5 + 19 | 4 + 20 | F L2 R' F R B L F' B2 U2 R' L2 D' R2 B2 R' L B2 U F L' F' L U R2
5 + 23 | 5 + 18 | D' U' L F2 L F' D2 F2 U' R2 U R' D' R' U D' L2 B2 U F2 B' U B D2 L
3 + 21 | 5 + 21 | R F' L' F' U' D L R2 B2 R' B2 U2 D2 B2 L2 D2 B' R' D' R2 D2 L' U R B
4 + 23 | 4 + 22 | D' L' D' L2 R2 D B R2 D2 B2 D' U' B F2 R2 F' D' B2 L' U R2 D' B' F D
5 + 20 | 5 + 20 | B' L2 D R' L2 F2 R F' R F' U2 F2 R' L' D' B' R' B2 U' B' D' B2 L2 F2 R2
4 + 21 | 4 + 20 | L2 R2 B2 R F R2 B U2 L2 F D' L2 U2 F2 R' B R B' R2 L2 U2 R2 D2 R' L2
3 + 21 | 4 + 19 | D2 U' R U' R2 U2 L2 U B' U2 F2 D' B' L B2 F2 U' B' U2 B' R' B D R2 F2
5 + 24 | 4 + 20 | R2 D F2 R L' B' D' B2 R' L2 F B2 U F' B2 R' U' F D R D2 L U B' R
Avg for Cross = 4.3 + 21.9 = 26.2
Avg for EOLine = 4.5 + 20.1 = 24.6
I'm not calling this proof because only 10 runs were used, and use of the Kociemba algorithm may introduce bias towards pre-orientation of edges. It would however be nice to get some hard statistics on this!
I agree with MistArts, and that is why I said a couple days ago in this thread that the downside to the ZZ method is a slightly higher move count than Petrus; this is because ZZ restricts the cube group earlier than Petrus.
With Petrus a good solver can complete F2L with less moves then Fridrich/ZZ F2L, but this requires a lot of mental effort to do. In a speedsolving context it would be more useful to compare the average move count of a Petrus speed-solver, than the optimal move count. With both Fridrich and ZZ it is plausible for a speedsolver to consistently achieve an optimal move-count for each stage, but I'm not sure if the same can be said for Petrus.
... actually, does anyone know whether optimal petrus + EO is less moves than optimal EOLine + 1x2x3 + 1x2x3??
