You don't have to know PhD level statistics. At the very least you should be proficient in the following basics: five figure summaries (what those quartiles, ranges, means and modes all mean) How to calculate ratios What standard deviation means and the relevant formulas (its easier than you think) explanatory and response variables how to interpret scatterplots least squares regression. how to work it out and what means (also, easier than you think) Probabilities, combinations and permutations (very important to know this stuff) data distributions and profiling (the standard distribution curve you see everywhere) As you know, the market is skewed with a fat tail so one way to use this knowledge is to try and model your data into a normally distributed profile and then you have found an edge. This stuff is important to know and it is a lot easier then you are making it out to be. You don't need to be a physicist but you do need to know that basics and how to apply that knowledge in the real world.
Just like seasoned trader might have gut feeling. In the end PhD or hobby statistician developing complex models might not even understand what the modeles are doing or what is the edge. Perhaps it was 10 year work and 5 is forgotten. They might just feed input and evaluate output to improve models without knowing what was found. But they should at least vaguely know how it was found if they developed it, unless it's very flexible system. Then there is no way of knowing easily. NNs for example , how would you debug what hidden info it found to determine features.
Look, I'll comment here again, just because I think you're trying to add value to ET and are referencing some important stuff. I already said, it's the ideas that are important. So you should understand all the stuff from intro courses, and I mean really understand it. Random variables and transformations are intro topics in probability theory, but shit gets real when you actually try to learn this stuff. You will never master that topic without serious study - and even then the Ph.D stuff will be out of reach. And in my opinion, the Ph.D stuff is the real edge. I'll just give you a couple examples that really opened my eyes to how foolish and naive most people's understanding of this shit is. Doubly stochastic process (model's with random parameters) Self referential process (parameters are functions of the realized process) Trying to get the qualifications to work on this stuff in an academy is strictly Ph.D, and yet these are some of the most important ideas I have ever learned. A rigorous technical treatment would require a level of expertise that is essentially not worth obtaining (due to opportunity costs). Really understanding the probability transform (you don't), and how even slightly altering the model basically makes completely invalid the entirety of parameter estimation was mind blowing. Anyway, the market is driven by robot and algo trading now. And they're using quant shit like lag polynomials, fractional differencing, and hardcore predator/prey type models.