There is another scenario which leads to the second installment in a series being the best.

A developer makes a game with a new IP. They have a creative vision of what they want the game to be, but because of deadlines, delays, budgets, etc. they are forced to skip some of the things they wanted to do with the game. It may also be buggy and/or unbalanced. Nevertheless, the game does well enough to warrant a sequel.

This time around, they have a working base, so they don't have to start from scratch. This enables them to implement all the things they had originally intended, and so the second game ends up becoming what the first game should have been. This is of course a bigger success, so it's sequel time again.

Now however, they are outside the scope of what they wanted to do in the first place, but since you can't make a sequel identical to its predecessor, they have to come up with some changes, regardless of whether they fit the game or not. Often they don't, because they are "tacked onto" an already finished design, and so from the third game onwards, the series goes downhill, or takes a different direction than the first games. Taking a different direction altogether may be the way to go, since it may gain the series new fans to replace the ones who abandon it because it's "not what it used to be".

I find there are a lot of game series where my favorite installment is the second one. A few examples:
Civilization
Heroes of Might and Magic
The Settlers