The decision about whether to submit SAT scores is basically a math problem. The issue is that we generally don't have all the data we'd need to solve the problem, so we have to make some educated guesses and assumptions.
My assumptions:
- People who do well on the test all submit their scores
- Many people who do poorly on the test will not submit their scores
- Those who do better on the test will also be higher achievers over all. There will obviously be many, many exceptions in both directions, but generally speaking, there are going to be big differences in the groups averages of kids getting 1500s vs. 1300s vs. 1100s across everything - grades, awards, extracurricular accomplishments, essay quality, etc.
If you agree with those assumptions, then the takeaway is that the overall pool of candidates who submit SATs is going to be much stronger than those who don't submit SATs.
A few years ago, someone posted data on a number of colleges showing the school's acceptance rate for candidates who submitted SATs vs. those who didn't submit SAT's.
There was one school (Vanderbilt I think) where there was almost no difference - like 7% for no-test candidates and 6% for test candidates. That's insane. It means that they're taking almost as many of the kids who averaged something like 1500 on the SAT as those who probably averaged like 1200-1300. For someone applying there, it probably only makes sense to submit a score if your kid is in the high 1500s.
Other schools had more reasonable ratios (maybe accepting at 1.5x to 2x the rate for those who submit scores). In that scenario, i think you submit if you're at or above the median acceptance score and probably don't if you're below it.
If the ratio gets up to 2.5x+ then you probably should submit as long as you're in the range that has any shot at all at being accepted.