My comments are reasonably provable.
Let's look at the Seina college rankings, for example:
https://scri.siena.edu/wp-content/uploads/2022/06/PDF-Ranking-FINAL-REAL.pdf
They use 20 rankings in this comparison:
Background
Imagination
Integrity
Intelligence
Luck
Willing to take risks
Avoid crucial mistakes
Court appointments
Domestic Accomplishments
Executive Appointments
Foreign Policy accomplishments
Handling of U.S. Economy
Party leadership
Relationship with Congress
Ability to compromise
Communication ability
Executive ability
Leadership ability
Overall ability
https://scri.siena.edu/us-presidents-study/about-the-presidents-study/
They don't tell you what the criteria are for those ratings, just that they are numerical. In other words, it's still just opinion, there really is no quantitative method involved.
And in some categories, they don't make much sense whatsoever, like how do you measure "Luck?" Also, the rating, "overall" if this is a rating category, not some averaging of the other ratings, is a duplicate and should be eliminated.
The categories aren't weighted by importance either, but all given equal importance. For example, three of the first four (leaving out integrity) really don't play into presidential success. Carter, as one example, was quite intelligent that's pretty clear. Didn't make him a better president...
What difference does "background" make? How do you rate that for importance? Does a career politician rate higher than someone coming from the private sector? Why would that hold significance to overall performance as president?
Then look at the results as posted. Why would a president's say, background rating change dramatically from year to year? Shouldn't it stay relatively constant, only moving slightly as new presidents are added to the list. But some of the ratings in this category vary fairly wildly. The same goes for many of the other categories.
You see, without the survey having some quantitative measures in it to justify a rating, the ratings are nothing but ill-informed opinion.