An RA plot, like its cousin, the MA plot, is a re-scaled and (45-degree) rotated version of a simple two-dimensional scatter plot of a versus b where a and b are equal-length vectors of positive measurements.   This rescaling and rotation allows for better visibility and emphasis of important outliers points that vary between the two measurement conditions.  Essentially it is a plot of the log ratio [R] vs the average log [A] of each pairing of the elements of a and b.   Unlike an MA plot, however, because the RA plot takes non-negative integer counts as input, it must employ work-arounds to include mathematically invisible points (such as points where one or both element(s) of the pair is zero).
If we modify our original a (or b) vector via: 
where
then R and A can be defined as:
R, like M, is plotted on the y-axis and represents a log (fold change) ratio between a and b.  A is plotted on the x-axis and represents the average abundance for a coordinate pair. The RA plot provides a quick overview of the distribution and size of a dataset consisting of non-zero counts.