There are several algorithms for efficient scalar multiplication of an arbitrary point P(x,y) by some positive integer k in elliptic curves defined over $F_{p}$ or $F_{2^{m}}$.
The scalar multiplication deals with point doubling (adding P(x,y) to itself) and point addition(adding two different points (P(x,y), Q(X,Y)). These point doubling and additions, fundamentally, further deal with additions, squaring, multiplications and inversion operations.
My question here is that though there are considerable addition and squaring operations involved in scalar point multiplication, ( for example, a single point addition requires 8 additions, 1 squaring, two multiplications and one inversion ) why is the inversion multiplication ratio (I/M) is of special interest for researchers in performance evaluation of different algorithms for scalar point multiplication ?
I do understand that the inversion and multiplication operations are dominant in elliptic curve arithmetic, but aren't these addition and squaring operations, not dominant enough to be considered ?
I would encourage the readers to go through the table 3.13, page no. 145 in this book so that you may get a clear idea of my question. Please have a look at the last 2 columns titled "EC operations" and "field operations" in this table.