At the end of the day, you win the game if you have more points. A caveat to this is that, if your group is weak, you cannot efficiently make points - your opponent can attack and get better exchanges. Note that you can also get points in the center. So if you aren't making a lot of points on the side, playing toward the center may very well be getting more points.
$$c
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . O . B . . . O . . O . . |
$$ | . . . , . O . . . , . . . . . X . . . |
$$ | . . X . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . O . . . . . . . . . . O X X X . . |
$$ | . X O . . . . . . . . . . . O . O X . |
$$ | . X O . . . . . . . . . . O . . O X . |
$$ | . . X O . . . . . . . . . . . . X . . |
$$ | . . X O . . . . . , . . . . . X . . . |
$$ | . . X O . . . . . O . . . X . . . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . X . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
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[go]$$c
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . O . B . . . O . . O . . |
$$ | . . . , . O . . . , . . . . . X . . . |
$$ | . . X . . . . . . . . . . . . . . O . |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . O . . . . . . . . . . O X X X . . |
$$ | . X O . . . . . . . . . . . O . O X . |
$$ | . X O . . . . . . . . . . O . . O X . |
$$ | . . X O . . . . . . . . . . . . X . . |
$$ | . . X O . . . . . , . . . . . X . . . |
$$ | . . X O . . . . . O . . . X . . . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . X . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
Above, the marked black stone is weak. If black doesn't do anything, white can get lots of points by attacking it.
If black jumps to the side, the group is still weak, and can still be easily attacked later. For example, even if white just splits black, the black stones are still weak:
$$c
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . O . B . B . O . . O . . |
$$ | . . . , . O . . . , . . . . . X . . . |
$$ | . . X . . . . . . . . . . W . . . O . |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . O . . . . . . . . . . O X X X . . |
$$ | . X O . . . . . . . . . . . O . O X . |
$$ | . X O . . . . . . . . . . O . . O X . |
$$ | . . X O . . . . . . . . . . . . X . . |
$$ | . . X O . . . . . , . . . . . X . . . |
$$ | . . X O . . . . . O . . . X . . . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . X . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
- Click Here To Show Diagram Code
[go]$$c
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . O . B . B . O . . O . . |
$$ | . . . , . O . . . , . . . . . X . . . |
$$ | . . X . . . . . . . . . . W . . . O . |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . O . . . . . . . . . . O X X X . . |
$$ | . X O . . . . . . . . . . . O . O X . |
$$ | . X O . . . . . . . . . . O . . O X . |
$$ | . . X O . . . . . . . . . . . . X . . |
$$ | . . X O . . . . . , . . . . . X . . . |
$$ | . . X O . . . . . O . . . X . . . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . X . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
However black jumps out, white will be more efficient - black is just jumping out without getting points, in order to save his group. White continues to get points in the center by attacking.
Stepping backwards, if black just jumps out:
$$c
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . O . X . . . O . . O . . |
$$ | . . . , . O . . . , . . . . . X . . . |
$$ | . . X . . . . a . B . c . . . . . O . |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . . . . b . . . . . . X . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . O . . . . . . . . . . O X X X . . |
$$ | . X O . . . . . . . . . . . O . O X . |
$$ | . X O . . . . . . . . . . O . . O X . |
$$ | . . X O . . . . . . . . . . . . X . . |
$$ | . . X O . . . . . , . . . . . X . . . |
$$ | . . X O . . . . . O . . . X . . . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . X . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+
- Click Here To Show Diagram Code
[go]$$c
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . O . X . . . O . . O . . |
$$ | . . . , . O . . . , . . . . . X . . . |
$$ | . . X . . . . a . B . c . . . . . O . |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . . . . b . . . . . . X . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
$$ | . . . , . . . . . , . . . . X , . . . |
$$ | . . . . . . . . . . . . . . . . O . . |
$$ | . . O . . . . . . . . . . O X X X . . |
$$ | . X O . . . . . . . . . . . O . O X . |
$$ | . X O . . . . . . . . . . O . . O X . |
$$ | . . X O . . . . . . . . . . . . X . . |
$$ | . . X O . . . . . , . . . . . X . . . |
$$ | . . X O . . . . . O . . . X . . . . . |
$$ | . X O O . . . . . . . . . . . . . . . |
$$ | . X . . . . . . . . . . . . . . . . . |
$$ +---------------------------------------+[/go]
There are many directions for black to escape to after this. So it's hard (for me) to think of an effective attack on black. For example, even if I play a stone in the a, b, or c area, black may not even answer. There are so many areas for black to move in the center.
I'll probably tenuki now and see if there's a better time later to revisit attacking. So black effectively avoided a strong attack with just one move. Extending to the side induces white to split black, which is something white wanted to do anyway.
---
But, this is not a DEFINITE rule. Sometimes jumping out may not have a lot of benefit.
Let's say the board is like this:
$$c
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . O . X . . . O . . O . . |
$$ | . . . , . O . . . , . . . . . X . . . |
$$ | . . X . . . W . . . . . . W . . . O . |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . W . W . W . W . . . X . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
- Click Here To Show Diagram Code
[go]$$c
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . O . X . . . O . . O . . |
$$ | . . . , . O . . . , . . . . . X . . . |
$$ | . . X . . . W . . . . . . W . . . O . |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . W . W . W . W . . . X . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |[/go]
In this case, black doesn't really avoid an attack by jumping out. Just jumping almost wastes a move. Since escaping doesn't help here, making a base is probably better - it's a tough situation for black since there are many white stones in the area, but trying to use forcing moves to make a base could be effective. I'm not sure if it's definitely possible to live in an area like in this example, but supposing it's necessary, this may be a case where trying to get two eyes by whatever means possible may be pragmatic.
Maybe I'd start by attaching.
$$c
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . O . X . . B O . . O . . |
$$ | . . . , . O . . . , . . . . . X . . . |
$$ | . . X . . . W . . . . . . W . . . O . |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . W . W . W . W . . . X . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |
- Click Here To Show Diagram Code
[go]$$c
$$ +---------------------------------------+
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . O . . . |
$$ | . . . O . . . O . X . . B O . . O . . |
$$ | . . . , . O . . . , . . . . . X . . . |
$$ | . . X . . . W . . . . . . W . . . O . |
$$ | . . . . . . . . . . . . . . . . X O . |
$$ | . . . . . . W . W . W . W . . . X . . |
$$ | . . X . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . X . . |[/go]
Seems tough.
But anyway, in this kind of scenario, jumping out may not be helpful even though the top part of the board is the same. The example may not be the best if black ends up dying anyway, but my point is, sometimes living inside is still a better option than jumping, when life is necessary.