It’s a good question. I think test taking is very individualized. S22 didn’t do really well on the SAT (1200) but he didn’t prepare at all and his math was much weaker than his English. He didn’t feel like prepping and retaking so he went TO (no top 50s or anything like that) - could he have gotten his score up to the mid 1300s? Probably. But what would that prove about him as a student? He did do well on his AP exams last year and typically tests well on big exams like midterms (including multiple choice tests) so he doesn’t have real test anxiety. Could be the format of the SAT or the time constraints. In any case, I valued TO for him as it freed him from hours spent prepping during a time that was already stressful with college apps. To me that was the advantage - not the opportunity to apply to more reach schools.
It is important to consider what criteria is being used to admit test optional applicants and how selective the college is. For example, most colleges in the United States admit the majority of applicants. Many have near open admissions. I think less selective colleges are the ones where you are most likely to find kids who are not adequately qualified for admission, like you describe. This forum instead tends to focus on more selective colleges that use a wide variety of criteria in admission decisions for test optional applicants – transcript, course rigor, which classes had non-A grades and how relevant they are to planned major, LORs, essays, ECs/awards, interview, etc. I think it’s unlikely that a kid performing at the 10th grade level would not be flagged in any of the criteria that is considered at such highly selective colleges.
Regarding your original question, the 2014 version of the previously referenced NACAC study at https://www.iacac.org/wp-content/uploads/2014/05/H59-Defining-Promise.pdf goes in to more detail about publics. Some numbers are below for 6 publics including Washington Stat and, 2 flagships. Also note that the non-submitter/submitter follows the same demographic pattern that occurred at Bates and nearly all other colleges.
Demographics
URM: Non-Submitter = 24%, Submitter = 12%
First Gen: Non-Submitter = 32%, Submitter = 22%
Pell: Non-Submitter = 27%, Submitter = 15%
Female: Non-Submitter = 60%, Submitter = 45%Before College
HS GPA: Non-Submitter = 3.40, Submitter = 3.12
SAT: Non-Submitter = 1037, Submitter = 1130During College
STEM Major: Non-Submitter = 51%, Submitter = 53%
Cum GPA: Non-Submitter = 2.78, Submitter = 2.62
Graduation Rate: Non-Submitter = 67%, Submitter = 63%
Many of the publics above had auto admit criteria for high grades/rank rather than traditional test optional, which fits with why the GPA is notably higher for non-submitters than submitters. This might be an example of what is expected to happen if there are notably higher GPA/rank expectations for non-submitters than submitters, which may be true at some public colleges.
However, I suspect what you are more interested is in the group they call “minority serving institutions”, which had many kids scoring as low as 600/1600. This group of colleges also appears to have unselective admissions, so the non-submitters have lower HS grades as well as lower scores.
Before College
HS GPA: Non-Submitter = 2.61, Submitter = 3.00
SAT: Non-Submitter = 791, Submitter = 974During College
STEM Major: Non-Submitter = 5%, Submitter = 11%
Cum GPA: Non-Submitter = 2.31, Submitter = 2.66
Graduation Rate: Non-Submitter = 24%, Submitter = 37%
Given that the non-submitters had both lower grades and scores, it may be more meaningful to breakdown outcomes by stat group rather than give averages, like they do on the following page.
Non-submitter with…
3.5+ HS GPA + 658/1600 SAT – 3.44 Cum GPA, 65% Grad Rate
3.0-3.5 HS GPA + 713/1600 SAT – 3.38 Cum GPA, 43% Grad Rate
2.5-3.0 HS GPA + 697/1600 SAT – 3.17 Cum GPA, 30% Grad RateSubmitter with…
3.5+ HS GPA + 1101/1600 SAT – 3.51 Cum GPA, 53% Grad Rate
3.0-3.5 HS GPA + 971/1600 SAT – 3.22 Cum GPA, 40% Grad Rate
2.5-3.0 HS GPA + 944/1600 SAT – 3.15 Cum GPA, 32% Grad Rate
There are some more selective MSIs, such as UCSB and UCI (both now test blind, though typical SAT scores before were a lot higher than 600).