In my senior year of high school, I completed a graduation project on an optimization problem, which was to find the general shape of the fastest base running path from home to second base on a baseball field.
I solved the problem by making an assumption that the fastest way to get to second base for an individual is similar to the fastest way for another individual. In other words, everyone’s fastest path is similar in shape. One of the articles I consulted (see citation below) makes the same assumption, saying that “slow runners should follow the same route as fast ones.” This assumption was made so that I only need to find my own fastest path to answer my topic question.
Note that my topic was focused only from home to second base because base runners advance two bases at a time more often than three or four and the fastest path from a base to an adjacent one is just a straight line.
Carozza, D., Johnson, S. and Morgan, F. “Baserunner’s Optimal Path.” Math Intelligencer 32, no. 4 (2010): 10-15. https://doi.org/10.1007/s00283-009-9106-2.