This diagram, left out of the book, tracks how many songs were written in each of the LM classes over the length of the Beatles' recording career. It clearly shows at least three interesting things.
First, Lennon and McCartney continued to write "nose-to-nose" until the very end (green line).
Second, they accelerated their individual writing much more relative to collaborating (top two lines).
Third, it is crystal clear that, likely due to their competitive natures, they worked very hard to keep up with each other, ultimately posting almost identical totals on an ongoing basis.