The criteria for the PCR Scholar are identical to the four that are used for the Rhodes Scholarship, covering academic achievement, participation in sports, personal character, leadership and community service. PCR scholars include Struan Jacobs, Karl Popper and Peter Klein.
Given the requirement for academic component the scholarship is awarded to university graduates but the level of achievement required is not high enough to preclude some unlikely winners such as Ross Campbell who was stunned to achieve the award. He suspected a clerical error because he was short on sports and community service as well. There is an interview in the Hazel de Berg collection but the link fails. This is more fun than the interview. [Warning, he does not sound like a Rhodes Scholar]. You could say if Ross Campbell could win it, practically anyone could.
Recall that in Barassi’s time only about 2% of people went to uni, a couple of decades later he probably would have gone and achieved a respectable degree to teach Physical Education. On the other criteria he looks good, you have to give some points for growing up in Tasmania and coming to the rescue (aged in his 70s) when he saw a girl being monstered in the street.
Much the same applies to Bradman with the advantage that he was more obviously cerebral.
The big problem for the committee is to decide is how much to allow for talents that were not realised for lack of opportunity. And how much weight to assign to the academic component in relation to the other three criteria.