Deviance R2 is usually considered the proportion of the deviance in the response variable that the model explains.
The higher the deviance R2, the better the model fits your data. Deviance R2 is always between 0% and 100%.
Deviance R2 always increases when you add additional predictors to a model. For example, the best 5-predictor model will always have an R2 that is at least as high as the best 4-predictor model. Therefore, deviance R2 is most useful when you compare models of the same size.
For binary logistic regression, the format of the data affects the deviance R2 value. The deviance R2 is usually higher for data in Event/Trial format. Deviance R2 values are comparable only between models that use the same data format.
Deviance R2 is just one measure of how well the model fits the data. Even when a model has a high R2, you should check the residual plots to assess how well the model fits the data.
You can use a fitted line plot to graphically illustrate different deviance R2 values. The first plot illustrates a model that explains approximately 96% of the deviance in the response. The second plot illustrates a model that explains about 60% of the deviance in the response. The more deviance that a model explains, the closer the data points fall to the curve. Theoretically, if a model could explain 100% of the deviance, the fitted values would always equal the observed values and all of the data points would fall on the curve.