I am the president of the Science Bowl Club at my school and am trying to find a mathematically optimal way to pick the best 5 team members for the state competition.
For those who do not know what Science Bowl is, it is a buzzer based competition where teams go head on in questions for math, physics, biology, and chemistry. Usually we have each team member get really good at one subject.
My Model
I am running a tryout procedure:
- Day 1: Read 3 packets (60 questions) and track the number of buzzes a person makes in a certain category, call this variable $x$.
- Day 2: Same as day 1
- Day 3: Hand out a written test of 50 questions and track how many questions a person answers in a certain subject, call this variable $y$.
Now I perform a weighted average on these two variables $x$ and $y$. Each person will have four scores, $f_{\text{math}}, f_{\text{physics}}, f_{\text{biology}}, f_{\text{chemistry}}$, where $$f(x, y) = 0.7 x + 0.3 y.$$ The weighting here is subjective based on what I think is more important. The person with the highest $f$ score in a certain category will make the team.
Problems With My Model
- A person could be well-versed in many subjects, but may not necessarily be the best. This person could be better fit for the team as they are able to answer many types of questions compared to just one subject specific person.
- In the case where two people have very similar $f$ scores, it will be hard to determine who will make the team. This model will only work if the $f$ score is drastically different.
Are There Better Models?
As I have a pretty big sample size (about 100 questions), I could perform some type of statistical analysis, but I am not sure on what exactly. In the end I can only guess what the best team is, that is the most statistics can give us, but I wonder if there is a way that can make the difference in abilities more clear.