Can we do anything to make it more precise?
There are some posts on complexity measures, which make note of a) degrees of freedom, b) free variables, ways of penalizing them, and how to calculate these measures. They probably rely on formalization though.
Links: Model Comparison Sequence, What are principled ways for penalising complexity in practice?*, Complexity Penalties in Statistical Learning,
*This might be someone asking the same question as you. While the other links might hold an answer, this one has multiple.
There are some posts on complexity measures, which make note of a) degrees of freedom, b) free variables, ways of penalizing them, and how to calculate these measures. They probably rely on formalization though.
Links: Model Comparison Sequence, What are principled ways for penalising complexity in practice?*, Complexity Penalties in Statistical Learning,
*This might be someone asking the same question as you. While the other links might hold an answer, this one has multiple.