In The Way of Kings, the death quotes have years they were recorded in, such as 1171. The Gregorian calendar is based on the birth of Jesus as year one A.D. What event is the calendar on Roshar based on, if any?
please tag spoilers
We do not yet know the occasion that started the common calendar. It's been confirmed that it is none of the major historical events that we know of, and nobody has asked Brandon directly (the only question (2018-11-17) was answered "I would need to look it up" and it hasn't been asked again since).
We do know that the calendar is a Vorin convention that has been widely adopted, though with different names for days/weeks/months (presuming that's what he means by "different numbering conventions"):
Skype Q&A 2018-10-08:
Jofwu: Is the current year number (1174) just a Vorin convention, or is everyone on Roshar using the same calendar?
Brandon Sanderson: It is a Vorin convention, but the Vorin convention has been adopted by a lot of cultures.
Ravi: Just like our Gregorian?
Brandon Sanderson: Yeah. But there are different numbering conventions.