The title means in effect a "little baron" (17, 43, 165, 229, 266). Quoting J.C.G. George Esq. FSA (Scot), Garioch Pursuivant of Arms (123): "In the United Kingdom a baronet ranks above a knight and below a baron. Unlike a knight his title is hereditary but although he is of the nobility he has no seat in the House of Lords. The rank was officially instituted in 1611 when … thirteen knights and five esquires were created Baronets."
Some students of the Savoy operas have noted that Sir Roderic Murgatroyd was the 21st Baronet of Ruddigore. That made Robin the 22nd and Sir Despard the 23rd. Since the time frame from first to last baronet could not have exceeded 194 years (i.e., 1611, when the rank was established, until 1805), the average incumbency works out to be less than a decade. That seems unrealistically short to some persnickety critics. George (123) defends Gilbert. He observes that there were 22 Popes during the period 1605-1830, much like the period in question. He adds, "Nor is it a question of generations. Brothers and/or cousins of the same generation can, and not infrequently do, succeed to titles held by senior members of the same generation." To this I can add the further observation that the travails of the Murgatroyd Baronetcy were enough to drive any man to an early grave -- or to an escape like that of Robin's. If you are willing to believe that ancestors can step out of picture frames, you can easily believe there were 23 baronets in 200 years.