you may be right that the idea of random mutation is a bias that is not supported by evidence, but i don't even understand what you mean by saying it doesn't work with statistical science, that it's not plausible, and that it's a dead end assumption.
Merely gilding the lily.
Statistical: We have all seen the math regarding the number of mutations necessary for a simple organism to occur by random selection. The numbers exceed the atoms in the universe.
Plausible: If a simple organism can not exist by random selection in the time frame of the known universe, that hypothesis is implausible.
Dead end assumption: This is the same argument used against ID. Random is a process that can not be tested. Only if the system is systemic can it be tested.
At its root, evolution is based on a closed set of ideas that can not be tested and proven. It is a religious belief, albeit nontheistic, not science.
There!
How's that for stirring the pot?