Thank you for the most interesting thread in the game!!
You have given a fantastic effort and I love it.
I want to tell you that I used your rating formula to create a simple XML rating tool that I use now for evaluating players before purchasing them.
It is very useful although it is clear that the formula is not perfect, since players' basic rating does not always fit their "declared" position.
I call basic rating to the rating a player has, based on his skills, before combining in the stamina, game shape and experience.
What I found is that a player entitled a POWER FORWARD might have according to his given skills a better rating as a CENTER.
This means that the formula is not identical to the one used by the engine when deciding about the position-title of the player.
Still, this is a great tool, effective and very practical.
I use my XML rating tool regularly now to evaluate players on the transfer list and the results are very satisfying.
I can also say (from the short period of time I am doing it) that you provided me another way to validate the importance of wide range of qualities. Players with high rating for the neighboring positions (or even for all positions) turn out to be better players with better results, than players with one fantastic rating for only a specific position.
I also use it to decide on the specific line-up for a specific game. I combine the game-shape factor in with the formula: BR (basic rating) multiplied by the GS, then divided by 10. I think it is not far, but I'm not completely happy with it and think it might still credit GS too much .
I avoid combining the stamina in, since I typically give free hand to the coach, and I think that if the players' stamina is beyond a basic minimal level, less stamina will result in less minutes instead of lower ratings.
I also did not find the way to treat experience. I suspect that experience is not individual, which means – experience, especially in the ending minutes of each period will have an impact on the final result - winning or losing. This might be calculated as the sum of the experience on the field at a certain moment, but it might also be according to the maximal experience of a certain player (one player with high experience and 4 other players with no experience at all, might be better than 5 with medium experience).
Anyway I suspect that experience will improve the team's results not necessarily the team's specific ratings, and will have no impact at all on the individual ratings.
One more thing –
I thought it might be useful to you (for making your formula even better) if I indicate the specific deviations I came across. I'll start with the more serious deviations
Best position according to rating: C. Title: PF. Most common. According to my experience – 30-40% of PF. (can give you 4 detailed examples if needed).
Best position according to rating: SG. Title: SF. Common. According to my experience - 10-20% of SF. (can give you 3 detailed examples if needed).
Best position according to rating: SG. Title: PG. (can give you a detailed example if needed)
Best position according to rating: C. Title: PG. (can give you a detailed example if needed).
Best position according to rating: PG. Title: SF.
Best position according to rating: PG. Title: PF. (can give you a detailed example if needed).
As I see it – most accurate ratings are for Centers. Least accurate for both Forward positions.