Why nerds are not Jocks....
In a real game of baseball, there are only 2 instances where a runner tries to run the entire 4 bases:
1) a home run, in which case NO ONE is trying to complete the loop as fast as possible, heck its more aptly named the home-not-so-brisk-jog.
2) an inside the park home run. While aptly applied, the number of times this situation is attempted, much less completed is so infinitesimally small, if kinda makes this junk science. Furthermore, this idea assumes that the runner is aware of the necessity of obtaining an inside the park home run path (as opposed to say a straight line single) from the time he leaves the batters box. This is simply never the case, a typical inside the park home run is usually a stand up double or stretched triple and during the base running the runner must make 2-3 judgment calls as to the prospects of reaching the next base successfully and usually occurs through some unforeseeable bounce in the outfield or fielding bordering on an error. Therefore, in all but a fraction of a percent of plays, following this path will actually cost runners time, bases and outs.
Furthermore, in the instance of a single, where from leaving the box the runner understands extra bases will not be an option, the straight line reigns supreme.
The only instance where this applies is when leaving the batters box, where at least a stretched double is assumed. Again providing inside the park home runs occur so infrequently that a four base path should be
completely omitted from calculations because it would disproportionately and adversely effect the 2 and 3 base runs. Basically apply the distance/speed algorithm used here to a triple and again for a double both will end up different from the 4 base version and each other, merge these two paths weighted based on the proportionality of doubles hit to triples hit. Thats is the path to be followed. furthermore, overlay the double and tripple paths ontop of the combined paths to allow the runner to deviate from the combined path at any point during the run to accommodate for an assumed more expected result which can be judged multiple times during the run.
Now that would be applied science.