He invented television, which quickly became very popular on his planet. When his planet was invaded by aliens, the people were too glued to their TVs to stop them. They quickly turned to Professor Baffle for a way to save themselves. He made a device to let them escape to another planet using television waves, but he got the compression algorithm wrong and they were left without bodies.
He was then taken by Mr Grizzfizzle, Cool Cat, Amble the Ugly Doll, and some Magic Mice. They wanted revenge for the destruction of their planet and the loss of their bodies, so they toured The Scorchies Show across the galaxy. They forced Professor Baffle to watch as they hypnotised and destroyed countless planets. One day, the Professor joined in and became "just another Scorchie".
After hundreds of years of scorching planets, the group landed in Earth. During The Scorchies Show season finale, Baffle let the Third Doctor take over his body. He and Jo Grant created a reverse polarity polarity reverser which jammed the Scorchies' activation signal, killing them. After all the other Scorchies died, Jo turned off the polarity reverser, giving Baffle a few extra minutes of life. After talking to the Doctor through the Professor, she left, leaving him to die alone. His final words were:
Lovely Jo. One day, we'll kill the Doctor, and then we'll be coming for you.