In his MLB career, Gleeson has hit 16 baseballs out of the park while knocking in 154 runs. For his time in baseball, he stepped up to bat 1,472 times and has notched a base hit 336 times. His career slugging percentage is .015 in addition to racking up 499 bases. He has been struck out 147 times and has gotten a free base on 158 attempts at the plate, contributing to a .350 on-base percentage. Gleeson has compiled an average at the plate of .263 for his career in baseball with 195 scored runs and an OPS of .365.
