Board Thread:Manga/@comment-24407809-20160604010805/@comment-27441457-20160604034453

To be honest, the Before the Fall manga is an absolute mess on several accounts (Carlo's rank, Heath's rank, Titan behavior, etc), the exact date of the story being one of them. I just went with the 49th Training Corps detail since it's the most precise piece of evidence that's presented.

While it's true that a Training Corps lasts for 3 years, I think it's safe to say that there's still one new Training Corps every year:

The 104th Training Corps began in the year 847. In the year 850, an instructor says the Titans breached the walls 107 years ago, which would be the year 743 (a date the BTF novel mentions specifically). When you take away 104 years from 847, this also arrives at the year 743. Thus, we can safely say a new Training Corps begins every year.