Measuring Narrative
The book Narrative Is Everything has two metrics that the author, Randy Olson suggests using to measure the narrative quality of a text.
Narrative Index
This is the ration of Buts to Ands. Although it's stated as a ratio of word counts, it isn't exactly that straightforward as the actual words and or but might not be used, but it's a rough way to examine long texts (he recommends not using it if there are fewer than 1,000 words).
\[ \textrm{Narrative Index} = \frac{\textit{number of 'buts'}}{\textit{number of ands}} \times 100 \]
The higher the value the better the narrative quality.
And Frequency
This is just a measure of the fraction of the words in a text that are the word and.
\[ \textrm{And Frequency} = \frac{\textit{number of 'ands'}}{\textit{total word count}} \]
Well-edited texts have an And Frequency of about 2.5%.