Let $f:X\to \mathbf{P}^1$ be a simple cover of the Riemann sphere. This means that $f$ is a branched cover, and that each fibre has at least $\deg f-1$ points in it.
Is it true that the number of ramification points is $(\deg f -1) \cdot \# B$, where $\#B$ is the number of branch points in $\mathbf{P}^1$?
If you label the branch points $b_1,\ldots,b_r$, is there a natural way to label the set of ramification points?