It would be nice to know in advance, but as has been previously stated, it’s a relatively opaque process, and your methodology will miss potential opportunities.
The alternative is to post your student’s stats, your top line budget number, what they want their experience to be like and have posters give some idea of where your student might be able to meet those requirements.
The other thing to pay attention to are the other schools an institution lists as their peers. Linked below are WPI’s benchmark institutions. You’ll find similar pages for other schools. Our son was awarded $60K at RPI, $80K at WPI, and $100K at Case. Had he ultimately selected WPI, which he almost did, we could have used his peer institution award to at least ask for more merit aid.
https://www.wpi.edu/offices/institutional-research/benchmarking