EU3 had 1453 as the originally start date and then it was moved to 1399 with the last expansions it had. It fit well with the theme of Early Modern Period colonization and empires as many historians place 1453 as the end of the Middle Ages with the fall of Byzantium (or successor state of the Western Roman Empire). Some place it at 1492 with the discovery of the New World for symbolic purposes, other historians round the date to 1500 for simplicity. The 1399 date allows more playtime and also the availability to play as Byzantium but it seems to be a bit to far back for a Europe of consolidated powers to form. The developers later regretted having 1399 as the start date.
EU4 starts in 1444. It's a balanced start because it takes place after the Battle of Varna which separates the personal union of Poland and Hungary. Having a Poland-Hungary in the early game could be lethal because it is in an area that is surrounded by much weaker powers. It also offers the option to play Byzantium, although historically, Constantinople fell 9 years later.
When deciding on a start date, certain factors influence the decision:
1) Balance of regional powers, especially in Europe where most players tend to play.
2) Early enough to maximize gameplay time, though this can fluctuate with the end date being changed.
3) Enough time to consolidate "continental homelands" before the colonial period.
4) Late enough to reduce a Balkanized Europe and to allow the AI to enable the creation of strong regional powers.
5) Late enough that there is at least some resemblance to historical or plausible outcomes up until the mid game.
6) For some players, the existence of the Byzantines is important, so anything after 1453 is unfavorable to them.
In my personal opinion, I like to see solid numbers or symbolic years. For me, 1444 is a spontaneous year that just happens to be ideal due to the outcome of the Battle of Varna and large consolidations of land for regional powers in Europe.
I would personally prefer to see 1448 to 1848 which allows a full and exact 400 years of gameplay. It still allows for the existence of Byzantium and it ends on the symbolic date of 1848 which is the Springtime of Nations or when nationalism in Europe finally reached its high point. It also grants more time to colonize more of Asia and Africa. It is unfortunate that the game ends in 1821 when most of Asia and Africa is historically barely even touched yet.
Some reasons why 1448 is not a bad idea. In 1445, Portugal sets up a Feitoria in Arguin which would help gear Portugal for a Africa trade hub start. In 1448, the Kalmar Union is dissolved, leaving Denmark, Norway, and Sweden as independent nations (although some might dislike this).
If we want to move back in time and avoid having the Poland-Hungary behemoth, we'd have to go before 1440. We could always have 1436 as the start date so it slides in with Victoria's start date of 1836. Lithuania is in the middle of a civil war with one side backed by the Teutonic Knights and the other backed by Poland. This could have interesting effects on what goes on in Eastern Europe as the game progresses. The Hussite Wars end and the rebellion in Sweden is put down.
Any other opinions on start and end dates?