In statistics, a natural initial estimate for a random variable $Z$, is its conditional mean with some given random variable $X$ that is, $\mathbb{E}\left(Z|X\right)$.
With regard to why this is a "good enough" estimate, I am not sure what to make of the following- whether it is complete or even correct: $$\mathbb{E}\left[\mathbb{E}\left(Z|X\right)\right]=\mathbb{E}\left(Z\right)$$ This is equivalent to saying that $\mathbb{E}\left(Z|X\right)$ is an unbiased estimate of $\mathbb{E}\left(Z\right)$.
This is called the law of total expectation. It is correct (provided $\Bbb E(Z)$ is defined).