How important is a good AIME score for college admissions?

I’ve often wondered about AMC/AIME/USAMO (once I heard about those here) and if those would have made my S20’s application more appealing. He’s been on his HS math team all 4 years and (so far) has qualified for state every year, placing at the state level 2 out of their 3 trips to state so far. He’s always been talented in math and was double accelerated, taking math at the high school while in middle school. He’s also on the ACES (Academic Challenge in Engineering and Science) team his junior and senior year. It’s only for juniors and seniors. Last year they qualified for state. This year’s regional competitions for math team and ACES are just underway.

He is our oldest and I had never heard about AMC/AIME/USAMO and I’m disappointed his HS never mentioned anything about further math competitions (or others) outside of the math team. I only heard about them by seeing the acronyms on CC when I joined last year. By then, I assumed it was too late to really pursue anything. I’ve realized his school doesn’t provide much direction for exceptional students, so that’s been pretty disappointing. Partly my fault for I suppose not investigating things, but I wouldn’t have known where to start.

Don’t get me wrong, this kid will be fine wherever he ends up. He’s a high stats kid and has applied to a number of T20 schools for CS, but I can’t help but wonder how some of these “extra” accolades would have helped his application. Because having 36, 1600, NMSF, etc doesn’t distinguish him much from all the other similar kids applying to those top-tier schools! And luckily from CC, I knew that having those stats didn’t make ANYTHING a slam dunk. I can’t help but think some of those other accomplishments might have helped set him apart. So, to answer the OP’s question, I don’t think those accomplishments could hurt!