Some method speed definitions:
- Fastest official average-of-5.
- Fastest average-of-100.
- Have 100 kids learn and practice the method for 10000 hours, then have each kid do 100 solves and define the method speed as an average of those 10000 solves.
- Average solve move count (like I did in my diploma thesis, though ideally using all possible scrambles).
- Average solve time using more sophisticated models (including grips like Gripper and recognition).
1. Based on your first definition, the speed of the CFOP method is 6.54. That is the method's speed (that number is a time, by the way, not a speed). What if Feliks breaks this world record at a future comp? Then by your definition, CFOP's speed would then be lower than before. But the speed of CFOP is 6.54! Without changing the method at all, how could its speed possibly change? Answer: it wouldn't. The only thing changing is Feliks' proficiency with the method. If a method itself actually has a speed, then that speed is a property of the method. If you don't change anything about a method, one particular property of it can't spontaneously change.
2. Based on your second definition, the speed of the Roux method is 7.00. That is the method's speed (that number is a time, by the way, not a speed). What if Alex starts practicing hardcore again and breaks this average? Then by your definition, Roux's speed would then be lower than before. But the speed of Roux is 7.00! Without changing the method at all, how could its speed possibly change? Answer: it wouldn't. The only thing changing is Alex's proficiency with the method. If a method itself actually has a speed, then that speed is a property of the method. If you don't change anything about a method, one particular property of it can't spontaneously change.
3. Say this experiment was carried out for CFOP, and the average ended up being 7.00 flat, with the fastest person's avg100 being 6.66 (made-up numbers, no statistical calculations made here). By your third definition, the speed of CFOP is 7.00. That is the method's speed (that number is a time, by the way, not a speed). But the fastest person in that group of 100 actually averages faster than that. How is it possible to use a method and be faster than what the method's speed is? How can you say that "the speed of the CFOP method is 7.00" if there is actually a person averaging below 7.00 over a whole lot of solves?
4. Okay, hold up. Your first definition states that CFOP is faster than all other methods. Your second definition states that Roux is faster than all other methods. Your fourth definition says that, for example, Heise is faster than both CFOP and Roux. But these statements are all mutually exclusive. It's also pretty much guaranteed that the kind of model proposed in your fifth definition would declare a different "Fastest" method than your fourth definition does, since an extremely low movecount method will inherently have bad grips (as compared to CFOP/Roux) and recognition. And if this sophisticated model did in fact declare the same "Fastest" method as any of your other four definitions, I
strongly doubt it would also come up with the same specific number as did the other definition. Therefore, all five of your definitions for the speed of a method are mutually exclusive. So which, if any, is actually correct? (The answer of course, is none, since they aren't even giving speeds, but rather other quantities such as time or number of moves, but moving on).
A method does not have a speed as an inherent property of it. Something like the kind of model mentioned in your fifth definition would indeed make it possible to compare two methods to each other and say definitively "the CFOP method is better for human speedcubing than the Dan Brown method," but it would not let you say "the speed of the CFOP method is x.yz." For that kind of model to even output a specific number at all, it would have to include such factors as turnspeed. Well, that's a factor that depends both on the cuber's experience/current ability, and the qualities of the cube they are using. And both of these can get better over time as a cuber gets better and as cubes get better. So if you want the model to say "the speed of CFOP is x.yz," where will you get specific numbers to represent these factors? How can you say unarbitrarily "the best turnspeed achievable with the best cube that could be produced in the future is xx.xx"? Furthermore, even if you can answer that question, that is still looking specifically at
human capability, which is separate from
the properties of a method.