You have been trying to count the score. It seems that the score is somewhat close. Maybe you're a bit behind. Hard to say, since there are several big points left.
Then, your opponent doesn't defend his group. You think to yourself, "Can I kill it?" You read ahead some sequences - looks... feasible. Maybe. Not quite sure. If you had to guess, let's say you feel there's a X% chance you'd actually kill the group and win the game. But if you go for the kill, it will drive him into your territory - you'll lose the game for sure. On the other hand, you could decide not to try to kill the group. But the game seems really close. If you play normally, and just try to move into the endgame, and finish the game, maybe you estimate the chance of winning is Y%.
How do you make this decision?

Is this simply a matter of trying to kill if X > Y? Followup: How do you assess these probabilities?