My eldest son, who went through the graduate school process says that the written statement is a big part of it all. Anybody can crunch the numbers in terms of GPA, class rank, etc but if you can pull at an academic’s heartstrings a little with the written statement, it gives you an edge. Worth putting time into and even having a pro help edit it, if necessary.
I think, as RJM alludes to, being on the Baseball team is a pretty big edge, but the above is some extra perspective from a non athlete who got his grad degree