Bourjos is in White Sox camp as a non-roster invitee and is batting.313/.340/.521 during Cactus League play. Tilson was supposed to be their starting center fielder but he will miss about a month in the regular season. Bourjos was expected to compete for time in the outfield this season, most likely in a reserve role. The Chicago White Sox are not going to be contenders this season no matter what.
May has certainly earned the job if he does get it.
Bourjos has no long-term future with the White Sox.
NumberFire's algorithms now project Bourjos to hit.236 with 5 home runs, 17 RBI's and 5 stolen bases across 207 plate appearances in 2017.
For Tampa Bay, Bourjos gives them, as previously mentioned, a seasoned veteran. He has a lifetime average of.243 with 37 homers and 149 RBIs.
Peter Bourjos was simply a body to fill centerfield until Tilson became healthy, so the trade opened up more opportunities for Chicago's prospects while giving Tampa Bay depth.