However, college graduation rates are heavily correlated to incoming student characteristics – more selective colleges have higher graduation rates. So most of the student’s likelihood to graduate (and on time) can be predicted based on the student’s prior academic record. Some other student characteristics can also factor into that, such as how decided s/he is on his/her major (late change of major can delay graduation).
At the margins, there are college treatment effects that can move the needle from the graduation rates expected based on student characteristics. Such things include advising quality and course availability (probably the most overstated problem by students who do not want to take the 8am section of a key prerequisite course). College factors that interact with student characteristics include whether the student’s possible majors have additional competitive admission gates to pass (students who do not pass these gates may be delayed due to switching to another major that they did not previously prepare for) and financial concerns (the college’s price and financial aid generosity versus the parent/student financial resources). Indeed, if everything else is equal, a higher cost college will mean a higher risk of dropping out due to running out of money.