As great as Willie Mays was, someone could make an argument for Christy Mathewson as well. Granted, Baseball-Reference.com isn't the beat-all-end-all of argument solvers but still...
Mays: 12 times was the teams best player - went to three World Series - won one.
Mathewson: 10 times was the teams best player - went to five World Series - won one (includes 1904 when there was no World Series but the Giants would have been the N.L. representative).
I still think Mays wins this one but to me it's closer than some may think...