When people are baffled, these days, they are at a mental loss, unable to work out what is going on - a state of mind that applies as much to frustrated detectives as to crossword-puzzle solvers. It is a sense which developed in the 17th century. In Shakespeare's time, two other meanings were present, now both obsolete. The older sense, from the mid-16th century, was to "disgrace publicly", referring especially to a knight being treated with scorn. This is the meaning we need when Mowbray says to King Richard: "I am disgraced, impeached, and baffled here" (Richard II, I.i.170), or when Falstaff tells Prince Hal to "call me a villain and baffle me" (Henry IV Part 1, I.ii.101). Then, during Shakespeare's lifetime, a more general meaning was emerging - to expose someone or something to ridicule. "How have they baffled thee!" says Olivia to Malvolio, tricked by Sir Toby and his companions (Twelfth Night, V.i.367).
And Pistol says to Falstaff, "shall good news be baffled?" (Henry IV Part 2, V.iii.105) - in other words, treated with contempt.
David Crystal is author, with Ben Crystal, of Shakespeare's Words, published by Penguin