Egregious Professor of Cruel and Unusual Geography
His predecessor was reduced to a pair of pointy boots with wisps of smoke coming out of them, following a terminal encounter with the wildlife on the God of Evolution's home on Mono Island, not far away from The Last Continent. Well, he evidently wasn't paying attention to the job description, which specified Egregious, Cruel and Unusual. Ridcully uses promotions and status either as weapons to divide the rest of the Faculty and get them squabbling among themselves (rather than entertain any ambitions for the Archchancellorship), or else as a carrot to get somebody else to achieve the desired result. With both of the above policy goals in mind, he took his time in finding a candidate to fill those pointy boots.
Ridcully is a manager dedicated to the carrot-and-stick principle. After terrorising Rincewind into a state of normality with the stick (all the things that can happen to somebody falsely claiming wizardhood when in fact he failed all his exams), he later applies the carrot of promoting Rincewind to professor and Faculty status. It is possible that Ridcully has recognised nobody on the Disc knows more about how cruel and unusual its geography is, and that he has promoted the right man to the job. (It is taken as read that Rincewind, by "performing a service of great value to Wizardry", ie his reluctant visit to the Counterweight continent, his assistance to the Faculty when stranded on Fourecks, and his even more reluctant exploration of Roundworld, has finally achieved full Wizardhood and a honorary degree.) Ridcully therefore succeeded in getting three missions' worth of useful work out of the stick, before finally rewarding Rincewind with what turned out to be a very small and relatively inexpensive carrot. Otherwise, Ridcully is deliberately annoying the rest of the Faculty by promoting somebody thought of as having the innate magical ability of a housebrick. He would also consider this a worthy goal.
It is certain that Rincewind was told his appointment is a honorific only, and he is not to do anything daft like holding lectures or tutorials or talking to students. (This begs a very big question of the rest of the Faculty, who also seek to avoid these things without needing to be ordered not to.) It may also be the case that Ponder Stibbons has now realised he is no longer the least, lowest and most despised junior faculty member. Certainly, his attitude to Rincewind is the easy and relaxed manner (most of the time) of a superior giving instructions to to a subordinate.