Sentiment Dynamics of Success: Fractal Scaling of Story Arcs Predicts Reader Preferences (2021)

Abstract: e explore the correlation between the sentiment arcs of H. C. Andersen’s fairy tales and their popularity, measured as their average score on the platform GoodReads. Specifically, we do not conceive a story’s overall sentimental trend as predictive per se , but we focus on its coherence and predictability over time as represented by the arc’s Hurst exponent. We find that degrading Hurst values tend to imply degrading quality scores, while a Hurst exponent between .55 and .65 might indicate a “sweet spot” for literary appreciation.

## introduction and related work what determines the perception of literary quality? it can be argued that the feelings expressed by a story play a major role in its experience and assessment, since they activate similar sentiments in the readers' memory @xcite . at the same time, the relationship between a reader and the sentiments expressed by a text is anything but linear: the reader's perception of the sentiments on page depends on their context (the victory of a villain can engender unpleasant feelings, @xcite ), and mechanisms like irony and catharsis can transform the negative feelings expressed by a text into positive feelings for a reader @xcite . ultimately, the intensity and nature of feelings on page does not tell us much about whether a reader will love, hate or remain indifferent towards a story. while it is of great interest to explore the temporal dimension of sentiments in literary texts @xcite , and specific tools have been developed to this aim @xcite , it might not be the explicit sentimental trend of a story which plays a role in its quality, but the distribution and relative change of such sentiments through the story, independently from whether the direction of the narrative's arc is closer to a comedy or to a tragedy. we use nonlinear adapting filtering and fractal analysis to assess the inner coherence of a story arc and the auto-correlation in the sentiment dynamics at different time-scales, as measured through the hurst exponent @xcite . we then explore the correlation between such value and perceived literary quality. we propose h. c. andersen's fairy tales as an ideal test case for our hypothesis: andersen's tales tend to have relatively simple narratives, making it easier for us to explain their arcs and their level of predictability; they are well known and widely read in contemporary english, allowing us to retrieve the average rating from many readers (in the most popular cases, tens of thousands of readers); and to use state-of-the-art sentiment analysis tools. lastly, some stories are short, which is a disadvantage when producing sentiment arcs, but is also a significant advantage when interpreting our results since we can re-read full stories in a short time and be assured of the quality of the computed arcs, making it much easier to explore the underlying causes of sentimental curves and their resulting hurst exponents. while deciding whether a story's segment is happy or sad is a complex matter of interpretation, we can measure the sentimental value of the components from which such interpretations derive: the average positive or negative value of its words or sentences. during the last two decades, sentiment analysis has generated a large number of resources to infer the kind and intensity of the sentiment expressed by a text, at the word (mohammad and turney, 2013), phrase @xcite , sentence @xcite or overall text level @xcite . wordlevel resources, which are mainly constituted of manually or semi-automatically annotated lexica @xcite , are popular in literary senti-ment analysis @xcite . they provide the highest number of data points for each story, and they keep the inference of the arcs at the simplest possible level, requiring neither rule-based nor pretrained scoring systems. while this is a limitation in the endeavour of inferring the sentiment of a portion of text, since sentiment lexica do not disambiguate the sense of a word in context @xcite and the analysis is limited to the words present in the used lexicon, this approach allows for drawing the succession of the smallest sentimental units of a text, from which human readers themselves draw their inferences. furthermore, using lexica allows for drawing arcs in a transparent way, making it possible for researchers to immediately understand the causes of each score derived from a corpus. finally, we use word-level sentiment arcs and their large-scale human ratings to determine whether the dynamic sentiment evolution and the level of coherence of a story arc at the sentiment level are connected with the perceived quality of the stories. sa lexicon to create the stories' sentiment arcs, we rely on the nrc-vad lexicon (mohammad, 2018), which is composed of almost 20.000 english words annotated for valence, arousal and dominance foot_1 . for this study, we only used valence. ## methods we proceed in three main steps: (i) we convert the stories into raw sentimental arcs through the use of the nrc-vad lexicon (section 3.1); (ii) we compute the story arcs' inner coherence through their hurst coefficient (section 3.2); (iii) we correlate each story's hurst coefficient with its average rating on goodreads (section 4). ## results our final step consisted in correlating each fairy tale's average rating with its average hurst coefficient. we found that there is a small, but significant correlation between the hurst exponent of andersen's tales and their average success on good reads (see figure 3 ). nonetheless, there appears to be a difference in such correlation when we consider the number of ratings each story received. as we discussed before, the statistical value of those ratings can change: obscure stories can have less than ten different raters, while the most known fairy tales can be rated by tens of thousands of readers. many of andersen's stories are not well known to the larger public, and thus received a relatively small number of reviews. based on the average number of ratings of each story, we recomputed the correlation strength for only those tales that received more than 30 different scores, which excluded around half of our corpus, leaving 63 tales in the corpus. this threshold allowed us to keep only stories that had a significant amount of individual annotations, without excessively reducing the size of our dataset. the result was a much stronger correlation, and a more significant p-value (see figure 4 ). in figure 4 : correlation between hurst exponent and average rating for tales having more than 30 ratings with some titles in evidence. most of the very popular stories fall on the upper right corner, while tales like the butterfly, based on a simple repetition of the same dynamic, fall more to the left. also notice how without the outlier the darning needle, the correlation of the remaining data points would be even steeper. all tales popular tales corr. p value corr. p value pearson .19 .03 .4 .001 spearmann .18 .04 .35 .005 kendall tau .12 .03 .23 .009 distance corr. ## conclusions and future work the main finding of this paper is that there is a correlation between a story's sentimental coherence and its perceived quality. with all the necessary caveats, we find that such correlation is an interesting result and advocates for a more extensive use of multifractal theory in the study of sentimental arcs in literature. the emotional coherence of a story, as represented by the average hurst exponent of the sentiment arc, explains a part of its perceived quality as measured by its average rating on a general audience website. furthermore, stories with more ratings tend to show a stronger correlation between these two measures, which might mean that the weaker correlations we recorded for the less known stories might be due to an insufficiently large pool of raters (thus having a less robust score). it is interesting to notice that stories with many ratings also tend to have higher ratings on average: this further shows how, at least for fairy tales, fame and popularity tend to go together. while it proved surprisingly predictive, reducing a story arc to one overall hurst coefficient means losing important information in terms of how coherence is distributed through the narrative. exploring the temporal variation of this coefficient at different time scales of a story might reveal further insights into the sentiment dynamics of a good narrative evolution. another aspect for further exploration is evaluating alternative ways of scoring the sentiments in a text. particularly, when applied to longer stories, adopting a sentence-level approach could help accounting for the context that indeed affects the sentiment interpretation. furthermore, instead of sentiment analysis, moving to an emotion analysis might allow for more detailed insights about an optimal narrative development. however, already the present results suggest that there exists a desir-able ratio of coherence and unpredictability in the sentiment arcs that contribute to the appreciation of a story.