I didn’t think it was possible for an EGOT winner to be an underdog. Mike Nichols had a Grammy when he was 31, a Tony when he was 33, and an Oscar when he was 36. The Emmy didn’t come until he was 70, but to make up for lost time he snatched up two in one year and, shortly thereafter, another two. Contemporary improvisational comedy (i.e., comedy) would not be the same without him, nor would Broadway theater, and he directed at least one film people will still be talking about — maybe celebrating, maybe scorning, but certainly talking about — in half a century.