# Deviance and saturated models

Deviance is defined as $$-2(\log L_0 - \log L_s ),$$
where $L_s$ is the log-likelihood of the saturated model. One definition of a saturated model is "a model with a parameter for every observation so that the data are fitted exactly". How can I "fit exactly" a binary logistic regression $$EY=\frac{1}{1+\exp\{-(b_0+b_1x) \}}$$ (there's one scalar independent variable $x$) to, say, the following dataset: (-5; 0), (2; 1), (4; 0)? Where can one find a rigorous and understandable definition of deviance? Any concrete example of a GLM and the corresponding saturated model would be very welcome.