In the typical adventure or role-playing game, all the plot events are player-dependent; they don't happen until the player finds them and makes them happen. By using constrained environments, we can make sure that the player finds them in the right order. The problem with a plot consisting entirely of player-dependent events, as I explained in the original lecture, is that it feels mechanistic: the whole world just sits around waiting for the player to do something.
If you make the plot entirely player-independent -- that is, it goes forward no matter what the player does, even if he does nothing at all -- then the player tends to lose the game a lot. He's not where he belongs, or he hasn't done what he needs to do, when the dramatic climax occurs.
The trick in sandbox storytelling is to build the plot with a combination of player-dependent and player-independent events.
Keep things flowing no matter what the player does so the world doesn't seem static, but don't make it flow so fast that the player gets behind and loses the game (unless the plot is about finding a time bomb). Put a moderate degree of pressure on the player to act, but reduce the pressure if the player is on the right track.
In a sandbox, exploration itself can't advance the plot -- so instead, use a combination of the passage of time (that's the pressure) and player activity: meeting people, solving puzzles, making decisions, overcoming challenges. Change up the pace from time to time.
Sometimes James Bond is exploring at his own pace (he's master of the situation) and at other times he's desperately running away from bad guys (they're masters of the situation). Then he gets away from them or shoots them and he becomes master of the situation again. Of course, not every game has to use a lot of pressure. You can let the player have a very relaxed experience if you want to.
One question some designers ask is, "What if the player just goes wandering around and never seems to get on with the story?" The answer is, it depends on what kind of experience you want him to have. It might be okay to just let him wander around. I'd love to explore the countryside in the Far Cry games without getting shot at all the time.
Far Cry 2
On the other hand, if you want to push the player through the story, then you have to ask why he's just wandering around. If he's wandering around because he's lost or confused, that's your fault.
The designer Chris Bateman wrote a chapter called "Keeping the Player on Track" in the book that he edited, Game Writing: Narrative Skills for Videogames. In the chapter he talks about funneling: various tricks for helping the player find the "spine" of the game. In an open world you can't use the landscape to forcibly funnel the player back to the plot, but you can leave various signs and clues around. Get the book for more information.
On the other hand, if the player is just fooling around and you want him to get on with it, that's when you have to increase the pressure with player-independent -- and location-independent -- plot events.
Tabletop RPG game masters are very familiar with this. If the players won't come to the plot, bring the plot to them. If they've been hired to take down a crime boss and instead they're just sitting around the tavern gambling, the crime boss might get wind of their plans and send a gang of thugs to the tavern to squelch the expedition before it gets started. In the ensuing fight the tavern just happens to catch fire. Even if the party survives, it won't be doing any more drinking in there.
Another question people sometimes ask is, "In an open world, how do you prevent the player from seeing something early that he's not supposed to see until later?" The question is rooted in the assumption that everything that the story needs will be physically present in a static game world from the beginning -- as it usually is in adventure games and Western RPGs, where the story is mapped to locations.
But we're not mapping the story to locations, we're mapping it to time and player activity. The answer is simple: don't put an object in the world until it needs to be there. In the Grand Theft Auto games you can't destroy a car in Mission 1 that will be needed in Mission 3, because the car simply isn't in the game world at all in Mission 1.
You obviously don't want cars suddenly popping into existence in front of the player's eyes, but you can bring a car out of a (formerly) locked garage. The player can't be in more than once place at once, so you can do all kinds of things behind his back.