# When should we use the segregated as opposed to the aggregated data?

In the book "Causal Inference In Statistics" by Pearl et al., there is the following problem (study question 1.2.2.)

A baseball batter Tim has a better batting average than his teammate Frank. However, someone notices that Frank has a better batting average than Tim against both right-handed and left-handed pitchers. How can this happen? (Present your answer in a table.)

This is basically an example of the Simpson's paradox. The following table of proportions is used in the solution

And, apparently, the "casual story" would be

• left-handed batters, on average, hit better than their right-handed counterparts
• Frank met significantly more left-handed than Tim

And the solution is then "left-handed batters is a common cause of meeting the player and failure", thus we should look at the segregated data, that is, we should compare Frank and Time with left-hand and right-hand batters separately.

I am not fully understanding this "causal story". It is clear that Frank met more left-handed than Tim, according to the table. But how can we solve this problem if we do not know that "left-handed batters, on average, hit better than their right-handed counterparts". Where does this information come from? Or is this just a supposition in order to draw a conclusion? For example, could we have supposed that right-handed batters are better than left-handed? Then what? Furthermore, how can we come up with these tables?

In general, how do we know whether to draw some conclusions based on the segregated or aggregated data?