Suppose $A_{n}$ denotes the set of all humans alive at the beginning of the year $n$. Therefore $A_{2018}$ has about 7.4 billion members, while $A_{0}$ has, let's assume, 200 million members. A person $x$ in the set $A_{0}$ has $k_x$ descendants in $A_{2018}$.
If we want to calculate the average $k$, i.e. the average number of descendants that a member from $A_{0}$ has in $A_{2018}$, what data are needed and what assumptions should be made? How to estimate the order of this number?
Note: There are tens of millions of people who claim to be Sayyid (descendant of Muhammad) while the status of being a Sayyid can only be attributed through the patrilineal lineage. I posted a question about the population of Sayyids here.
The average is $$ \frac{\sum_{x \in A_0} k_x}{|A_0|}. $$ But if you have access to the numbers $k_x$, then it seems your question is much more easily answered by the number $k_{\mathrm{Muhammad}}$.