What do you think is the best way to rank universities participating in a competition if we know for each university the number of recognitions that it's students won. Each university can participate with 3 students, and approximately half of them get a recognition - which can be first (5%), second (15%) or third place (30%).
To be more specific, let's say 5 universities participated in a competition and the first university won 2 first place recognitions and 1 second place recognitions, the second university won 2 third place recognitions, etc... Probably a good way of measuring universities is by the total number of recognitions won, or the number of first place recognitions won, followed by number of second place recognitions won etc.
Now, my question is: How do we rank the quality of education in the universities if we know for each university how many students learn there? I'm asking this because it's probably a good idea to take into account the number of students? One possibility that I was thinking of is to divide the number of achievements with the number of students and use that to compare universities, but the problem here is that each school can participate with only 3 students (probably if the largest university participated with more than 3 students it would have won more recognitions). We can assume that the universities have a lot of students, and that the background of the students enrolled at different universities is the same.
Thank you very much for your time!