I think that is a critical question to answer. As someone who is on the statistical side of the house, I have a particular train of thought about this:

The obvious answer is that statistics on its own is not interested in causes; it is only interested in the preponderance of a pattern, because math is a language of pattern exploitation. Domains on the other hand couldn't care less about the preponderance of a pattern, but realistically only care about causes. They care about patterns insofar as they ought to highlight causal relationships because a pattern shouldn't be a coincidence intuitively.

The adage of "correlation does not imply causation" is at the heart of that dichotomy. I always extend that statement when I teach in that area to be that "correlation does not imply causation, but causation almost certainly implies correlation." This is a logical problem that people have with interpretation is they want the second part, but are left with only the first. Regressive statistics by itself does not posit causal relationships - it is not designed for that. The underlying assumption is a mathematical and coldly calculated one that gives the illusion of it intuitively. Probabilism is realistically the way that you can have the discussion of the causal correlation. That's why it is important in my book. Otherwise, you are left with saying: "They're correlated; but I have to stop there"

Article Probabilistic Causation

I got some new info ... Thanks to your discussion Olatunji Shobande

Because causes raise the probabilities of their effects, all else being equal

Kindly check https://link.springer.com/content/pdf/10.1007%2F978-1-4899-2370-7_30.pdf

Also check https://personal.lse.ac.uk/gyenisb/physcity/pdf/Salmon1980.pdf

“Probabilistic Causation” designates a group of theories that aim to characterize the relationship between cause and effect using the tools of probability theory. The central idea behind these theories is that causes change the probabilities of their effects. Which is why we need to focus it.

In probabilistic approaches to causation, causal relata are represented by events or random variables in a probability space. Since the formalism requires us to make use of negation, conjunction, and disjunction, the relata must be entities (or be accurately represented by entities) to which these operations can be meaningfully applied.

Reference :

https://plato.stanford.edu/entries/causation-probabilistic/