Well, the concept of the Scapegoat has been around for ages, and before christianity invaded the pagan religions, even.
The people of a community would “volunteer” a scapegoat who would take all the “sins” of the tribe and be sacrificed to the deities of the community. Or professional scapegoats lived as outcasts with the sins, and gifts (hence one could earn a living as a scapegoat..kind of), of the community and travel from tribe to tribe offering this service.
So in christianity, Jesus the Christ, acts as a scapegoat. But, because he lives eternally with his father in imortality, he is only out the days of suffering and loss of human mortality (no great loss if one is to believe in heaven). In fact, many christians can hardly wait to get there. So, indeed, one may ask, “Where is the sacrifice?”
Mortal scapegoats realized a true sacrifice…death or absolute shunning of all society. Immortal scapegoats, like Jesus, however…what did he really lose? And what did his father who offered him up, lose?
So whether one splits hairs or not, the circumstance of the christian scapegoat’s sacrifice is not much, when compared to the scapegoats of mortal circumstance.