Correlations between GoodReads Appreciation and the Sentiment Arc Fractality of the Grimm brothers' Fairy Tales

Abstract

Despite their widespread popularity, fairy tales are o昀琀en overlooked when studying literary quality with quantitative approaches. We present a study on the relation between sentiment fractality and literary appreciation by testing the hypothesis that fairy tales with a good balance between unpredictability and excessive self-similarity in their sentiment narrative arcs tend to be more popular and more appreciated by audiences of readers. In short, we perform a correlation study of the degree of fractality of the fairy tales of the Grimm brothers and their current appreciation as measured by their Goodreads scores. Moreover, we look at the popularity of these fairy tales through time, determining which ones have come to form a strong “internal canon” in the corpus of the authors and which one have fallen into relative obscurity.

Keywords

• eol>computational narratology
• sentiment analysis
• fractal analysis
• literary quality assessment

1. Introduction

In recent years the increase in size of available corpora and the possibility of performing complex operations on textual data have given rise not only to an explosion of tools for the exploratory analysis of literary collectio9n]s, b[ut also to new hypotheses in literary and aesthetic studies, all the while making existing complex hypotheses relatively easier to t3e4st, [ 39 ]. This change in the ways we can study texts has on one hand brought about the possibility of testing for complex patterns in linguistic data, such as the presence of long-ranging regularities and multifactorial structures, de昀椀ning new research questions for the 昀椀eld. On the other hand, it has become possible to study traditional questions with brand new methodologies.

One growingly popular object of research falling in the second category is the concept of literary quality4[ 3 ]. Making use of large-scale quantitative means, several works have tried to de昀椀ne and study literary quality, focusing on di昀erent aspects of literary texts and their contexts [ 14 ]. The riddle of quality is as intriguing as elusive: while large numbers of readers can o昀琀en converge on their overall judgment of a piece of literature, they can o昀琀en be a loss to justify why a di昀erent text, on similar topics or with a similar perspective, fails to produce for them the same experience. At the same time, no single text in the history of literature has attracted unanimous approval, and the reasons that di昀erent readers bring for their judgment of a piece can be both varied and hard to de昀椀ne rigorously.

The 昀椀rst major di昀케culty in this line of research is how to 昀椀nd proxies to represent quality itself: should one do it through prestigious prices, book sales, or crowd voting? While this question has been problematic in any study on quality, it becomes perhaps even more stringent when dealing with quantitative analyses, since it is necessary to 昀椀nd a way to represent it into a number or a boolean value.

It has become relatively common among quantitative studies on literary quality to use large online platforms for readers such GasoodReads [ 26 ] as a way to approximate the ‘mean perceived quality” of a text. Platforms likGeoodReads represent a particularly appealing source of information since they gather data from unconstrained readers, over relatively long spans of time, and can average on large numbers of individual scor4e2s][. Usually these studies do not take into account the average number of raters in order to avoid completely con昀氀ating perceived quality (how much readers liked a book) with popularity (how many readers rated the book). Even so, using scores from a general purpose platform like GoodReads deals with quality as a statistical mean of all raters’ appreciation, which is a democratic but not unproblematic take on concept. Since it allows to take into account the perspective of very di昀erent readers, giving to each the same value, it could be argued that literary quality is a multi-dimensional problem and by using GoodReads scores we are measuring one dimension of it, while other means could be used to compound it with its other aspects.

Beyond the question of how to represent quality, the second main problem in this line of research is to decide which features we should select to explore it.

Some studies have looked into classic stylometric features, while others have tried more sophisticated properties, exploring the semantic and psycholinguistic dimensions of texts.

A set of works has looked speci昀椀cally into the linearity of textual narratives, representing them as series extended through the virtual time of reading (or listening). In such cases, the focus has been on how to best represent such narratives lines or arcs and to de昀椀ne their most typical or relevant shapes3[ 6 ].

A relatively prominent line of research has looked into the sentimental and emotional aspect of literary texts2[ 4, 25 ], as well as renown movies scripts or song lyri8cs],[following the idea that the emotions expressed in texts, as drawn through sentiment analysis resourc3es, 1[ , 23, 30 ] and emotion recognition tools2,[ 10 ] working at the word 3[ 1, 32, 22 ] or paragraph level [ 27, 44 ], might play a fundamental role in readers’ engagement and respon1se5][.

This line of research seems to have returned some promising resul4t0s],[ and o昀琀en these studies focus on the cultural context of narratives in general, linking their sentimental or emotional values to social or historical changes in the broadest sen4s1e, [ 17, 4 ].

Finally, some studies have recently linked the linear and temporal dimension of texts with that of fractal analysis, the ensemble of techniques to assess the fractal characteristics of an object and assign a fractal dimension to a dataset1[ 3, 29, 6, 16 ]. Such studies hypothesize that the quality of literary narratives might be partly due to fractal properties embedded in texts [ 12, 19 ]. For example, Mohseni, Gast, and Redies3[ 3 ] looked into the fractality of shallow stylometric features such as TTR and POS-R, while Hu, Liu, Thomsen, Gao, and Nielb2o1][ explored the self-predictability of a novel’s narrative arc. Following the latter, Bizzoni, Peura, Nielbo, and Thomsen 7[] brought this analysis to the fairy tales of H.C. Andersen, 昀椀nding a positive correlation between the level of fractality in the 昀椀ne-grained sentiment arc of a narrative and its appreciation: on average, fairy tales with more “fractal” sentiment arcs would receive higher scores on GoodReads.

In this work we attempt to take this line of research slightly further, hypothesizing that while the level of fractality might correlate with reader appreciation or perceived literary quality, there most likely is a breaking point or ”sweet spot” a昀琀er which a text’s sentimental fractality stops being a good thing.

To check this hypothesis we reproduce the experimental setting of Bizzoni, Peura, Nielbo, and Thomsen [ 7 ] on a selection of fairy tales from the Grimm brothers, and we test whether (a) a correlation between sentiment fractality and GoodReads scores for the Grimm brothers exists at all; and (b) whether this correlation is linear or follows a rise-and-fall pattern.

2. Data

We followed Taylor and Edwardes’s 2001 English translationThoef Grimms’ Fairy Tales [ 20 ]. We chose this edition simply because it is the most popular on the Gutenberg Project, and that would help us select the fairy tales from the Grimm brothers that are most likely to have received ratings from more than one or two reviewers on GoodReads; this selection is composed of 62 tales. We drew the text from Project Gutenberg’s website38[].

We worked on English both to replicate as close as possible the work of Bizzoni, Peura, Nielbo, and Thomsen 7[] and to have access to some of the most tested resources for Sentiment Analysis.

This selection includes most of the best-known stories from the Grimm brothers suchRaa-s punzel, Hansel and Gretel, and Red Riding Hood. It also contains several titles that are relatively less widespread, such asClever Hans, The Salad orThe Turnip. Most titles of these selections are nonetheless read enough to have earned more than ten di昀erent ratings on GoodReads. As we show in Figure 1, there seems to be a weak correlation between the number of ratings and the average rating of a fairy tale, indicating that the most liked stories are also the ones attracting most votes (link between popularity and appreciation).

3. Method

We performed the sentiment analysis of the fairy tales using the VAD lexico3n1][, one of the most popular word-based sentiment resources in computational linguist3i2c]s.[Since we are working on unusually short pieces of narratives, we drew our sentiment arcs from each word score, without averaging them on sentences or paragraphs. This also allows us to operate at the 昀椀nest grain of sentiment analysis, keeping us at the interface between narrative and style, which is particularly important when working with literary quality.

As suggested by [ 21 ], we use the Hurst exponent to approximate the story arc’s inner coherence. The Hurst exponent, , is a measure of self-similar behavior. In the context of story arcs, self-similarity means that the arc’s 昀氀uctuation patterns at faster time-scales resemble 昀氀uctuation patterns at slower time scales3[ 7 ]. We use Adaptive Fractal Analysis (AFA) to estimate the Hurst exponent [ 18 ]. AFA is based on a nonlinear adaptive multi-scale decomposition algorithm [ 18 ]. The 昀椀rst step of the algorithm involves partitioning an arbitrary time series under study into overlapping segments of lengtĀh = 2 + 1, where neighboring segments overlap by + 1 points. In each segment, the time series is 昀椀tted with the best polynomial of order , obtained by using the standard least-squares regression; the 昀椀tted polynomials in overlapped regions are then combined to yield a single global smooth trend. Denoting the 昀椀tted polynomials for the − ýℎ and ( + 1) − ýℎsegments by ( 1) and ( +1)( 2), respectively, where ( )( ) = Ā1 ( )( + ) + Ā2 ( +1)( ), = 1, 2, ⋯ , + 1 where Ā1 = (1 − −1) and Ā2 = −1 can be written as (1 − / ) for = 1, 2, and where denotes the distances between the point and the centers of ( )and ( +1), respectively. Note that the weights decrease linearly with the distance between the point and the center of the segment. Such a weighting is used to ensure symmetry and e昀ectively eliminate any jumps or discontinuities around the boundaries of neighboring segments. As a result, the global trend is smooth at the non-boundary points, and has the right and le昀琀 derivatives at the boundary37[]. The global trend thus determined can be used to maximally suppress the e昀ect of complex nonlinear trends on the scaling analysis. The parameters of each local 昀椀t is determined by maximizing the goodness of 昀椀t in each segment. The di昀erent polynomials in overlapped part of each segment are combined using Equation 5 so that the global 昀椀t will be the best (smoothest) 椀昀t of the overall time series. Note that, even if = 1 is selected, i.e., the local 昀椀ts are linear, the global trend signal will still be nonlinear. With the above procedure, AFA can be readily described. For an arbitrary window sizĀe, we determine, for the random walk procesþs( ), a global trendÿ ( ), = 1, 2, ⋯ , , where is the length of the walk. The residual of the 昀椀t, þ( ) − ÿ ( ,)characterizes 昀氀uctuations around the global trend, and its variance yields the Hurst parameter according to the following scaling equation: (Ā ) = [ 1 ∑(þ( ) − ÿ ( )2)]1/2 ∼ Ā

=1

By computing the global 昀椀ts, the residual, and the variance between original random walk process and the 昀椀tted trend for each window sizeĀ , we can plot log2 (Ā ) as a function of log2 Ā . The presence of fractal scaling amounts to a linear relation in the plot, with the slope of the relation providing an estimate of 1. Accordingly, a higher than .5 indicates a degree of linear coherence (e.g., positive sentiments are followed by positive sentiments), while lower than .5 indicates a series that tends to revert to the mean (e.g. a positive emotion always follows a negative emotion).

A昀琀er determining the Hurst exponent for each fairy tale, we correlated it with the average scores on Goodreads. To compute the strength of the correlations, we used the most popular metrics: Pearson 5[] and Spearman [ 35 ] correlations. A昀琀er computing them on the whole dataset, we calculated each of these measures on what we considered the possible “upward” and “downward” trends of the data. To choose the breaking point to divide the data between a potentially positive and a potentially negative correlation trend, we computed a correlation matrix between all of the Hurst scores and all of the GoodReads values in our dataset (see Figure 3).

We also computed the probability distribution of seeing a highly rated fairy tale versus the probability of seeing a non-highly rated fairy tale at di昀erent Hurst values (see Figure 4). To do this, we 昀椀rst conventionally set a high rate threshold at 3.5 GoodReads stars, following the practice of Maharjan, Arevalo, Montes, González, and Solor2io8][, and then for each Hurst 1Code for computing DFA and AFA is available at https://github.com/knielbo/sa昀케ne value (H=0.5, H=0.51, and so forth) we computed the probability of seeing a highly rated tale (higher than the threshold) versus the probability of seeing a non-highly rated tale.

Both these tests point to a peaking positive correlation of arc fractality with GoodReads scores between a Hurst exponent of 0.56 and a Hurst exponent of 0.6 circa, which appears in line with the 昀椀ndings of Bizzoni, Peura, Nielbo, and Thomsen7[].

4. Results

Our analysis shows that the correlation between the number of ratings a fairy tale receives and its Hurst exponent, on the other hand, does not appear so obvious (Figure 2). a positive correlation between a tale’s Hurst exponent and its average rating up until a given Hurst value, and a negative correlation a昀琀erward. As we said in Section 3, we de昀椀ned this breaking point both by checking the probabilities of a “high scoring tale” (Figure 3) and by computing the correlation matrix between Hurst exponent and GoodReads’ scores (Figure 4). We found that the point that most clearly divides the positive from the negative correlation in our data appears to be Hurst=0.57, although naturally it is the whole area between H=0.56 and H=0.59 that seems to indicate an inversion in the correlation between these two variables. In this way, we can easily identify two opposing trends in our data, that appear by computing both Pearson’s and Spearman’s correlations. The Pearson correlation is of 0p.-5va(lue: 0.01) for the Hurst interval 0.48-0.58, and of -0.3 (p-value: 0.08) for the interval 0.57-0.75. The Spearman correlation is of 0.45 (p-value: 0.02) for the Hurst interval 0.48-0.58, and of -0.37p-(value: 0.02) for the interval 0.57-0.75. Following standard boundaries for the strength of linear correlations’ ra1n1g]e,sw[e can de昀椀ne all these correlations as moderate or robust. In average, all but the second Pearson correlation have a p-value under the signi昀椀cance threshold of 0.025. In all cases, the negative correlations appear weaker (and less signi昀椀cant) than the positive ones. This seems to con昀椀rm what can also be seen in Figure 5: a昀琀er the “ sweet spot” of arc fractality, the steepness of the trendline is smoother and the link between a fairy tale’s average score and its Hurst exponent decreases. Looking into the individual titles of the fairy tales is also interesting: the stories falling into the “internal canon” of the Grimm brothers seems to form a loose cluster. For example, fairy tales that have the highest number of readers on GoodReads, that have elicited reproductions in movies or cartoons, or that tend to appear most o昀琀en in choice anthologies of the authors appear to cluster at the center of the graph, namely at the high point of GoodReads’ appreciation and fractal equilibrium. As can be seen for example in FigurLeit6t,le Red Riding Hood/Little Red-Cap (1900 ratings), Hansel and Gretel (2711 ratings), Rapunzel (2303 ratings) fall on the upper right quadrant, while in FigurAe s7hputtel, the Grimms’ version ofCinderella (1706 ratings), King Grisly-Beard (230 ratings), The Travelling Musicians [of Bremen] (479 ratings) tend to cluster on the upper le昀琀 quadrant of the graph. At the margins of the plots we can 昀椀nd less widespread pieces likeThe Fox and the Horse (55 ratings), Sweetheart Roland (88 ratings) orClever Hans (75 ratings). But independently from the number of ratings, the reader 2The second Pearson’s p-value is just slightly above the formal threshold of signi昀椀cance. What this indicates, rather than a Yes/No signi昀椀cance output, is that the correlation between Hurst values and readers’ scores becomes less obvious a昀琀er the peak area around H=.57. Both the value and the signi昀椀cance of the negative correlations are weaker than the positive correlations’ ones. will recognize the stories in the center as being among the best known from the authors.

5. Discussion

We have computed a correlation between sentiment arcs’ Hurst exponents and average GoodReads’ scores on a selection of Grimms’ fairy tales, both con昀椀rming the 昀椀ndings of previous literature on H.C. Andersen7][ and validating our hypothesis of the presence of an ideal balance or “sweet spot” between de昀椀cient and excessive fractality. Based on our results, it seems that the correlation between these two variables is positive and increasingly robust up to a certain point, and becomes negative and weaker from that point on wards. The fact that our correlations are never “very strong” (e.g. they are never higher than Pearson=0.5) appears to us as reassuring rather than discouraging. The fractality of a fairy tale’s sentiment arc is not, naturally, the sole cause for its literary quality or popular appreciation, and a large number of factors are likely to in昀氀uence the appreciation of a text - we would not expect very strong correlations from this one feature.

Naturally, our study’s take on literary quality has a number of limitations. The average ratings of GoodReads have the substantial advantage of representing a large number of readers, who annotate a text in completely natural circumstances (e.g. they are not being paid or brought in a lab to do the annotation) over a relatively long span of time. At the same time, like all works using GoodReads scores or similar averages, we are consciously con昀氀ating quality with popularity, a perspective that might contrast with a prestige-driven view of quality, in which a smaller number of experts de昀椀nes the quality of a text. Also, using the simple average of GoodReads reduces judgments that might be related to di昀erent aspects of the text to one single dimension. Although this problem is less severe when we consider a dataset of a single genre, from a small group of authors, it would become increasingly relevant if we were to apply this way of measuring quality to heterogeneous collections of texts.

Overall, our study con昀椀rms the perhaps surprising 昀椀nding that quality (in terms of GoodReads’ scores) and sentiment fractality hold a correlation for literary fairy tales, but adds the insight that such correlation might not be always linear: there could be a “sweet spot” for fractality’s e昀ects on readers. If we compare the study from Bizzoni, Peura, Nielbo, and Thomsen [ 7 ] with our own 昀椀ndings, we see that the most iconic titles from both collections fall in a similar interval for Hurst scoreTsh: e Little Mermaid orThe Ugly Duckling for H.C. Andersen, Red Riding Hood orHansel and Gretel for the Grimm brothers are between H=0.55 and H=0.60 approximately.

In future, we will try to test other quality “proxies” (prestigious awards, established canons) and to expand our feature set beyond sentiment arcs. It is reasonable to assume that di昀erent stylistic characteristics complement each other. It would also be interesting to attempt to predict the popularity of a text through automatic classi昀椀cation. Overall, sentiment fractality appears to be a promising feature to further our understanding of literary quality. [24]

M. Walsh and M. Antoniak. “The Goodreads ‘Classics’: A Computational Study of Readers, Amazon, and Crowdsourced Amateur Criticism”. IJno:urnal of Cultural Analytics 4 (2021), pp. 243–287.

M. Wilkens. “Canons, close reading, and the evolution of method”. IDne:bates in the digital humanities (2012), pp. 249–58.

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