=Paper=
{{Paper
|id=Vol-3290/short_paper9235
|storemode=property
|title=Correlations between GoodReads Appreciation and the Sentiment
Arc Fractality of the Grimm brothers' Fairy Tales
|pdfUrl=https://ceur-ws.org/Vol-3290/short_paper9235.pdf
|volume=Vol-3290
|authors=Yuri Bizzoni,Mads Rosendahl Thomsen,Ida Marie S. Lassen,Kristoffer Nielbo
|dblpUrl=https://dblp.org/rec/conf/chr/BizzoniTLN22
}}
==Correlations between GoodReads Appreciation and the Sentiment
Arc Fractality of the Grimm brothers' Fairy Tales==
https://ceur-ws.org/Vol-3290/short_paper9235.pdf
Correlations between GoodReads Appreciation and
the Sentiment Arc Fractality of the Grimm brothers’
Fairy Tales
Yuri Bizzoni1 , Mads Rosendahl Thomsen2 , Ida Marie S. Lassen1 and
Kristo昀昀er Nielbo3
1
Center for Humanities Computing Aarhus, Aarhus University, Jens Chr. Skous Vej 4, Building 1483,DK-8000 Aarhus
C
2
School of Communication and Culture - Comparative Literature, Aarhus University, Langelandsgade 139, Building
1580, DK-8000 Aarhus C
3
Center for Humanities Computing Aarhus & Interacting Minds Centre, Aarhus University, Jens Chr. Skous Vej 4,
Building 1483, 3rd 昀氀oor, DK-8000 Aarhus C
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
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 com-
plex operations on textual data have given rise not only to an explosion of tools for the ex-
ploratory analysis of literary collections [9], but also to new hypotheses in literary and aes-
thetic studies, all the while making existing complex hypotheses relatively easier to test [34,
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 regular-
ities 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.
CHR 2022: Computational Humanities Research Conference, December 12 – 14, 2022, Antwerp, Belgium
£ yuri.bizzoni@cc.au.dk (Y. Bizzoni); madsrt@cc.au.dk (M. R. Thomsen); idamarie@cas.au.dk (I. M. S. Lassen);
kln@cas.au.dk (K. Nielbo)
ȉ 0000-0002-6981-7903 (Y. Bizzoni); 0000-0002-4975-6752 (M. R. Thomsen); 0000-0001-6905-5665 (I. M. S. Lassen);
0000-0002-5116-5070 (K. Nielbo)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
374
One growingly popular object of research falling in the second category is the concept of
literary quality [43]. Making use of large-scale quantitative means, several works have tried
to de昀椀ne and study literary quality, focusing on di昀昀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 as GoodReads [26] as a way to approximate the ‘mean per-
ceived quality” of a text. Platforms like GoodReads 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 scores [42]. Usually these studies do
not take into account the average number of raters in order to avoid completely con昀氀ating per-
ceived 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 qual-
ity 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 shapes [36].
A relatively prominent line of research has looked into the sentimental and emotional aspect
of literary texts [24, 25], as well as renown movies scripts or song lyrics [8], following the idea
that the emotions expressed in texts, as drawn through sentiment analysis resources [3, 1, 23,
30] and emotion recognition tools [2, 10] working at the word [31, 32, 22] or paragraph level
[27, 44], might play a fundamental role in readers’ engagement and response [15].
This line of research seems to have returned some promising results [40], and o昀琀en these
studies focus on the cultural context of narratives in general, linking their sentimental or emo-
tional values to social or historical changes in the broadest sense [41, 17, 4].
Finally, some studies have recently linked the linear and temporal dimension of texts with
375
that of fractal analysis, the ensemble of techniques to assess the fractal characteristics of an
object and assign a fractal dimension to a dataset [13, 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 Redies [33] looked into the fractality of shallow
stylometric features such as TTR and POS-R, while Hu, Liu, Thomsen, Gao, and Nielbo [21]
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 translation of The 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 re-
ceived 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 website [38].
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 such as Ra-
punzel, Hansel and Gretel, and Red Riding Hood. It also contains several titles that are relatively
less widespread, such as Clever Hans, The Salad or The Turnip. Most titles of these selections
are nonetheless read enough to have earned more than ten di昀昀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 lexicon [31], one of the
most popular word-based sentiment resources in computational linguistics [32]. 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
376
Figure 1: Number of GoodReads ratings (on the x axis) plotted against the average rating score (on the
y axis) for our selection of Grimm fairy tales. A growing number of ratings seems to overall correspond
to a higher average rating: more appreciated stories tend to become also more popular.
Figure 2: Number of GoodReads ratings (on the x axis) plotted against the Hurst exponent (on the y
axis) for our selection of Grimm fairy tales.
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 coher-
ence. The Hurst exponent, �㔻 , 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uctua-
tion patterns at slower time scales [37]. We use Adaptive Fractal Analysis (AFA) to estimate
the Hurst exponent [18]. AFA is based on a nonlinear adaptive multi-scale decomposition algo-
rithm [18]. The 昀椀rst step of the algorithm involves partitioning an arbitrary time series under
study into overlapping segments of length Ā = 2�㕛 + 1, where neighboring segments overlap
by �㕛 + 1 points. In each segment, the time series is 昀椀tted with the best polynomial of order �㕀,
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 poly-
nomials for the �㕖 − ýℎ and (�㕖 + 1) − ýℎ segments by �㕦 �㕖 (�㕙1 ) and �㕦 (�㕖+1) (�㕙2 ), respectively, where
377
�㕙1 , �㕙2 = 1, ⋯ , 2�㕛 + 1, we de昀椀ne the 昀椀tting for the overlapped region as
�㕦 (�㕐) (�㕙) = Ā1 �㕦 (�㕖) (�㕙 + �㕛) + Ā2 �㕦 (�㕖+1) (�㕙), �㕙 = 1, 2, ⋯ , �㕛 + 1
where Ā1 = (1 − �㕙−1
�㕛
) and Ā2 = �㕙−1
�㕛
can be written as (1 − �㕑�㕗 /�㕛) for �㕗 = 1, 2, and where �㕑�㕗
denotes the distances between the point and the centers of �㕦 (�㕖) and �㕦 (�㕖+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 boundary [37].
The global trend thus determined can be used to maximally suppress the e昀昀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)
昀椀t of the overall time series. Note that, even if �㕀 = 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 size Ā, we determine, for the random walk process þ(�㕖),
a global trend ÿ(�㕖), �㕖 = 1, 2, ⋯ , �㕁 , where �㕁 is the length of the walk. The residual of the 昀椀t,
þ(�㕖) − ÿ(�㕖), characterizes 昀氀uctuations around the global trend, and its variance yields the Hurst
parameter �㔻 according to the following scaling equation:
�㕁 1/2
1
�㔹 (Ā) = [ ∑(þ(�㕖) − ÿ(�㕖))2 ] ∼ Ā �㔻
�㕁 �㕖=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 size Ā, we can plot log2 �㔹 (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 �㔻 1 . Accordingly, a �㔻 higher than .5 indicates a degree
of linear coherence (e.g., positive sentiments are followed by positive sentiments), while �㔻
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 Solorio [28], and then for each Hurst
1
Code for computing DFA and AFA is available at https://github.com/knielbo/sa昀케ne
378
Figure 3: Correlation matrix between Hurst exponents and average GoodReads scores. The higher
correlations appear to be between Hurst exponents between 0.55 and 0.6, and avg. ratings between 3.0
and 4.5. The highest correlations seem set between H=0.56 and H=0.58.
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 Thomsen [7].
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 cor-
relation 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 0.5 (p-value: 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
379
Figure 4: Probability of seeing a high scoring vs a non-high scoring fairy tale for di昀昀erent Hurst values.
The probability of a high-scoring tale seems to peak between Hurst=0.56 and Hurst=0.6 circa.
0.45 (p-value: 0.02) for the Hurst interval 0.48-0.58, and of -0.37 (p-value: 0.02) for the interval
0.57-0.75. Following standard boundaries for the strength of linear correlations’ ranges [11], we
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 0.05 2 . 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 ex-
ample, 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 Figure 6, Little Red Riding
Hood/Little Red-Cap (1900 ratings), Hansel and Gretel (2711 ratings), Rapunzel (2303 ratings)
fall on the upper right quadrant, while in Figure 7 Ashputtel, the Grimms’ version of Cinderella
(1706 ratings), King Grisly-Beard (230 ratings), The Travelling Musicians [of Bremen] (479 rat-
ings) 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 like The Fox and the Horse (55 ratings), Sweetheart Roland (88
ratings) or Clever Hans (75 ratings). But independently from the number of ratings, the reader
2
The 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.
380
Figure 5: Correlations between Hurst exponent and average GoodReads rating, breaking point set at
H=0.57.
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 previ-
ous literature on H.C. Andersen [7] 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 read-
ers, 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昀昀erent aspects of the text to one
381
Figure 6: Closer look into the titles in the upward trend part of the plot. Pearson correlation=0.44,
p-value=0.03.
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昀昀ects on readers. If we compare the study from Bizzoni, Peura, Nielbo, and Thom-
sen [7] with our own 昀椀ndings, we see that the most iconic titles from both collections fall in a
similar interval for Hurst scores: The Little Mermaid or The Ugly Duckling for H.C. Andersen,
Red Riding Hood or Hansel 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昀昀er-
ent 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.
382
Figure 7: Closer look into the titles in the downwards trend part of the plot. Pearson correlation=-0.43,
p-value=0.03.
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