When I first brought up USAMO, I chose to focus on this simply because it was the least identifying of the 4 activities I discussed. Separately, I mentioned that it was one that was completely objective (USAMO qualification is awarded purely on test scores, and makes no judgment about a student’s character, GPA, other test scores, etc. that all impact admissions). I also said that from my observed sample set, that 80% got into at least one HYPSM. An alternate way of looking at this is that, for any particular HYPSM, a student that only had USAMO was more likely to be rejected than accepted.
However other awards such as RSI are based upon holistic criteria. In many ways, the application process looks like a college application. It of course requires GPA and test scores, but it also requires essays and recommendations that, in addition to describing the applicant’s ability, may ask about the applicant’s character, perseverance, teamwork and attitude. And FYI, if a student gets into a program like RSI, you can be sure those same recommenders will be used for college apps since they had to be exceptional.
In your response, you seem wed to the idea that these awards only affect one category, but I think that’s invalid. Rather, the holistic criteria of these elite awards seem to mesh well with the holistic criteria of elite colleges. So while the award itself affects one category (you seem to think that for Harvard it is the EC category, but my limited anecdotal information suggests it is the Academic category), the strong recommendations can affect the Personal category.
As I said before, the Level 9 award resulted in dozens of students getting an average of 3 HYPSM acceptances (with Yale RD and Columbia RD applicants getting likely letters very soon after the award). It’s pretty difficult for your model to explain that given independence, but it is much more easily explained if the criteria for a holistic award affects multiple categories.