Kevin P. McVicker: ‘They’re Playing Our Song: A Memoir’ book review

THEY’RE PLAYING OUR SONG: A MEMOIR By Carole Bayer Sager Simon & Schuster, $28, 352 pages Pop music fans may not recognize the name Carole Bayer Sager, but they have heard many of the 400 songs for which she wrote the lyrics. Songs such as “Nobody Does it Better,” “Groovy Kind of Love,” “That’s What Friends…