Two approaches are:
Echo $$
Ps
With this you just have to think about what do different shoes do and why? For example, track shoes need to be extremely light to make it so the runners don't need to move excess weight to accelerate faster whereas basketball shoes can be heavier because they need high ankle coverage for more ankle support during moves like the crossover. Then the key factors that I would do personally are: difficulty to produce, benefit to athlete, cost to athlete, weight, and support. My advice would be to systematically go through a bunch of sports and talk about each of their shoes...
