Analysis paralysis is a rather strange term.
I have a game group that takes a long time for just about any game. Amun Re, which is supposedly 90 minutes, takes 3.5 hours in our group. Puerto Rico for five takes 2.5 hours. Settlers up to 2.
No matter what game we play, I often feel that there is too much thinking going on. This may be because my own moves are usually: roll-pick-go, or the equivalent.
Thinking long and hard can be frustrating to other players.
My friend, on the other hand, is a slow thinker. He will usually sit and think about his turn, shuffling his cards, pointing with his finger at various parts of the board, and then putting his hand on his chin. After he has taken his turn (finally), he will often shake his head and say: wait, can I take that back?
I think I win about as often as he does.
Thinking long and hard doesn't guarantee that you are thinking long and hard about the right things.
I'm used to him, and he's a really good friend, so I don't mind. In fact, if he had to play any shorter, he would find the game frustrating, because he would be unhappy that he wasn't allowed to at least try to find the optimal play.
And that is the crux: his enjoyment out of playing games comes from searching for the optimal play. As long as the game is finished before the night is over, he is not in paralysis, he is playing.
Thinking long and hard is the only way that some people enjoy games.
Chess doesn't give you many options. You only have, at most, 16 pieces to move, and maybe 100 moves to make, most of which are blindingly stupid or fruitless. A game lasts about 20 to 50 moves. Yet each player is given 5 hours to make their moves. Is that analysis paralysis? No, because both players come to the game expecting the game to be a game of optimal play, and they enjoy it that way. You want to play a quick game, play speed chess.
Thinking long and hard is a style of play, no worse and no better than any other style.
I wonder if the same people who don't like long thinking in their games also don't like games that have much thinking at all.
There are some game specific issues to think about when it comes to all this thinking.
Luck: a game with luck naturally has a limit to useful thinking, and that limit is about where your ability to determine the outcome drops below 50%. If you can determine what will happen after an event with 90% accuracy, it is fairly useless to think about anything beyond six events from now.
Width: The wider the tree of useful possibilities, the less useful to think about future turns, since the game is not likely to look much like you anticipated by that time. The number of players multiplies this search tree accordingly.
Thinking long and hard is only useful if the game state is predictable.
Time between turns: as a corollary to the above, you should be spending a whole lot more time thinking about the game when it is not your turn, whenever possible. In games with wide search trees, this may only be possible on the turn before yours, since the game may have changed a whole lot by the time it gets back to you. Narrow search tree = 2 player Scrabble. Wide search tree = 5 player Cosmic Encounter.
Hidden/trackable information: Traumfabrik is a game with "hidden" information, all of which is trackable and known to the players at any time. A person with good memory can drag a game out by tracking exactly who has how many contracts. In fact, a really good memory can do it even without dragging the game out. My advice to you is: don't. The point of hiding the pieces is not to provide extra work to people who have better memory. It is to make that element vaguely knowable but uncertain. Tracking the information goes against the spirit of the game, if the information goes beyond a turn or two's worth.
Thinking long and hard is against the spirit of some games.
That's it. No ending. Just a collection of thoughts.