I have 2 daughters who are science scholars.My older one, who just graduated this year, won a full ride scholarship to UR with 2300 SAT(1600 CR+Math), 3.9 U/W GPA, varsity athlete, paid environmental science internship summer before senior year, school/state level science competition winner, 7APS, NMF, good E/Cs, etc. My younger daughter at UR won a full tuition science scholarship with similar stats, 35 ACT one sitting, NMF, similar ECs, had a paid biomedical engineering internship, varsity athlete, science competition winner, etc.
From my (very limited) perspective as a parent, the big UR scholarships seem go to students who demonstrate exceptional talent and commitment in a particular area (science/math/CS, the arts/music/theater, leadership/ service), along with higher than average scores/GPA. All students who apply by Dec. 1st are considered for the Richmond Scholars program. Semi-finalists are selected (approx 400-450) based on the initial applications. Semi-finalists are then invited to submit additional materials and can choose to apply for up to 2 scholarship designations (science, arts, etc.). Finalists are then selected(not sure perhaps 75? not sure what yield is) and interviews are conducted (via skype for last few years).
Since the supplemental materials are not submitted until after semi-finalist status has been earned, admissions uses the main application to screen for and select semi-finalists. I am guessing that test scores and GPA are a significant part of that process, and being well above average is a big plus, but high scores/GPA alone are not enough. All of the UR Scholars I have met are extremely talented and engaged students. Having a hook of some kind, along with talent in the arts, is a likely boost as well. Students can win an arts scholarship, and are required to major or minor in an arts area, but can major in something else/double major, not unusual at UR. The scholarships are also open to international students.
Stats required to win the scholarships are probably going up each year, too. When my older daughter applied to UR for fall 2012 admission, the acceptance rate was 39%. This past year, it was 31%, and average test scores have been rising each year also.