Bully Score: Metrics and Methodologies

• Bully Score is a family of quantitative constructs that operationalize the severity, persistence, and dynamics of bullying behavior across diverse digital and experimental settings.
• Methodologies include network analysis, probabilistic classification, additive scoring of message content, and behavioral metrics that adjust for context-specific features.
• The interpretation varies by analysis unit—session, user, message, or participant—making cross-study comparisons challenging and context-dependent.

Bully Score denotes a family of quantitative constructs used to operationalize bullying-related behavior, severity, or persistence. In the literature considered here, the term is not standardized across domains. In one network-science formulation, it is the “net malice introduced by bullies as they attack victims (attacks minus pushback)” within an annotated Instagram session graph (Sikdar et al., 19 Dec 2025). In a repeated-game driving study, it is an opportunity-normalized rate at which a human exploits bullying opportunities against an autonomous vehicle (Cooper et al., 2019). In participant–vocabulary consistency, the learned user parameter $b_i$ functions as a bully score over directed social interactions (Raisi et al., 2016). Closely related scoring schemes include a message-level cyberbullying score in in-game chat (Murnion et al., 2019) and a probability-based user-level bullying propensity derived from supervised Twitter classification (Chatzakou et al., 2017). A separate severity-detection study integrates user-specific psychological, demographic, and behavioral attributes, but the available source does not provide an exact bully-score definition (Prama et al., 4 Mar 2025).

1. Terminological scope and measurement targets

The literature suggests that “Bully Score” is best understood as a family resemblance term rather than a single canonical metric. The scored object varies substantially: an entire interaction session, an individual user, a single message, or a participant observed over repeated episodes. The algebra also varies: weighted degree differences, regularized latent variables, rule-based additive scores, or posterior class probabilities. This suggests that direct numerical comparison across studies is usually not meaningful without reconstructing the underlying unit of analysis and sign convention.

Context	Scored entity	Quantity
Instagram cyberbullying network analysis	Session	Average weighted out-degree minus in-degree over bully-role nodes
Autonomous driving repeated game	Participant	Proportion of bullying opportunities exploited
Participant–vocabulary consistency	User	Latent bully score $b_i$
In-game chat moderation	Message	Additive cyberbullying score $CS(m)$

A further terminological complication is that some papers use adjacent but not identical nomenclature. The in-game chat study explicitly names its metric the “Cyberbullying Score” or $CS$ (Murnion et al., 2019), while the Twitter study is summarized in a guide that defines a continuous bully score as a class probability consistent with the reported classifier outputs (Chatzakou et al., 2017). The severity-detection submission emphasizes three severity classes—Not Bullying, Mild Bullying, and Severe Bullying—rather than a scalar bully score (Prama et al., 4 Mar 2025).

2. Session-graph bully score in Instagram cyberbullying networks

The most explicit graph-theoretic definition appears in “Network Analysis of Cyberbullying Interactions on Instagram,” which represents each cyberbullying session $S$ by a directed, weighted graph

$\mathcal{G}=\langle V, E, \kappa, \rho\rangle,$

where $V$ is the set of nodes, $E\subseteq V\times V$ the directed edges, $\kappa:E\mapsto\mathbb{R}^+$ the positive edge weights, and $\rho:V\mapsto L$ the cyberbullying role labels (Sikdar et al., 19 Dec 2025). The role labels include Bully, Bully Assistant, Main Victim, Aggressive Victim, Non-Aggressive Victim, Aggressive Defender, and Non-Aggressive Defender. The analysis aggregates these into

$b_i$0

$b_i$1

and

$b_i$2

Using weighted in- and out-degrees, the paper defines

$b_i$3

and

$b_i$4

Under this construction, a bully’s outgoing attacks are edges from bully or bully-assistant nodes to victim nodes, weighted by comment severity. Incoming pushback against bullies comes from Aggressive Defenders and Aggressive Victims, also severity-weighted; Non-Aggressive Defender confrontations contribute low-weight pushback with weight $b_i$5. A positive Bully Score therefore indicates that attacks outweigh pushback, whereas a negative Bully Score indicates that pushback outweighs attacks.

The session graphs are built chronologically from comments. The graph is initialized with a node for the Main Victim, and comments are processed from oldest to newest. A node represents a user-role pair, so the same user may appear multiple times if that user assumes multiple roles. If an edge already exists between the same pair of nodes, its weight is incremented rather than creating a parallel edge. Bullies and bully assistants add edges to all victim nodes with weight equal to comment severity. Aggressive Defenders both support victims and push back against bullies with severity-weighted edges. Non-Aggressive Defenders either confront bullies or support victims with weight $b_i$6. Aggressive Victims counter-attack bullies with severity-weighted edges. Main Victims and Non-Aggressive Victims do not add edges on their own.

Severity is numerically mapped as non-bullying or mild $b_i$7, moderate $b_i$8, and severe $b_i$9; for each comment, the edge weight $CS(m)$0 is the mean severity across the majority annotators. This is not a lexical toxicity score inferred from text alone; it is a graph quantity induced by annotated interaction roles and severity-weighted exchanges.

3. Annotation pipeline and empirical distributional behavior

The Instagram study extends the dataset of Hosseinmardi et al. (2015), which originally contained $CS(m)$1 sessions and $CS(m)$2 comments (Sikdar et al., 19 Dec 2025). The authors selected $CS(m)$3 sessions with $CS(m)$4 comments for which the majority of the five original annotators agreed that the session contained cyberbullying. Sessions where Main Victim $CS(m)$5 Other were then filtered out, yielding $CS(m)$6 sessions for network analysis. Comments were annotated on Amazon Mechanical Turk by Master workers, five annotators per comment, after anonymization and with attention checks. For each comment, annotators labeled whether it is bullying, the author’s role, severity, and topic, and a session-level Main Victim was chosen.

The preprocessing pipeline discards minority labels for the “is bullying” decision and then applies majority vote for role assignment. Because $CS(m)$7 of comments had role ties, a role tie-breaking heuristic was used. Passive Bystander comments were discarded from network analysis because they represented non-participation in the bullying discourse. The resulting corpus is structurally dense: across the $CS(m)$8 analyzed sessions, the median number of nodes is $CS(m)$9 and the mean is $CS$0 with $CS$1 CI $CS$2; the median number of edges is $CS$3 and the mean is $CS$4 with $CS$5 CI $CS$6.

Role prevalence is strongly asymmetric. Bully appears in $CS$7 sessions ($CS$8), Bully Assistant in $CS$9 ($S$0), Aggressive Victim in $S$1 ($S$2), Non-Aggressive Victim in $S$3 ($S$4), Aggressive Defender in $S$5 ($S$6), Non-Aggressive Defender—Support of the Victim in $S$7 ($S$8), and Non-Aggressive Defender—Direct to the Bully in $S$9 ($\mathcal{G}=\langle V, E, \kappa, \rho\rangle,$0). Passive Bystander appears in $\mathcal{G}=\langle V, E, \kappa, \rho\rangle,$1 sessions ($\mathcal{G}=\langle V, E, \kappa, \rho\rangle,$2) but is removed from the graph analysis. Mean victim nodes per session are $\mathcal{G}=\langle V, E, \kappa, \rho\rangle,$3 with $\mathcal{G}=\langle V, E, \kappa, \rho\rangle,$4 CI $\mathcal{G}=\langle V, E, \kappa, \rho\rangle,$5, whereas mean bully nodes per session are $\mathcal{G}=\langle V, E, \kappa, \rho\rangle,$6 with $\mathcal{G}=\langle V, E, \kappa, \rho\rangle,$7 CI $\mathcal{G}=\langle V, E, \kappa, \rho\rangle,$8.

The Bully Score distribution exhibits a slight right skew. Its median is $\mathcal{G}=\langle V, E, \kappa, \rho\rangle,$9, its mean is $V$0, and the $V$1 CI for the mean is $V$2 (Sikdar et al., 19 Dec 2025). Positive Bully Scores occur in $V$3 of sessions ($V$4), while negative Bully Scores occur in $V$5 ($V$6). The same study reports that a majority of cyberbullying sessions have negative Victim Scores, meaning that attacks outweigh support for victims, and that Victim Score shows greater variability than Bully Score, with a long left tail. Interpreted behaviorally, positive Bully Scores correspond to sessions in which outgoing aggression from bullies exceeds incoming pushback; negative values correspond to sessions in which defenders or aggressive victims impose stronger net counter-pressure.

4. Motif structure, quadrants, and behavioral interpretation

To connect score values with mesoscale structure, the Instagram analysis aggregates roles into Victim, Bully, and Defender, buckets edge weights into light $V$7 and heavy $V$8, and uses FANMOD via igraph to enumerate connected induced $V$9- and $E\subseteq V\times V$0-node motifs (Sikdar et al., 19 Dec 2025). Two prevalence measures are defined:

$E\subseteq V\times V$1

and

$E\subseteq V\times V$2

where $E\subseteq V\times V$3 counts motif occurrences and $E\subseteq V\times V$4 is the set of distinct motifs in session $E\subseteq V\times V$5.

Globally, the most prevalent motifs are star-shaped mobbing structures. The top motif, $E\subseteq V\times V$6, consists of three bullies lightly attacking one victim and has $E\subseteq V\times V$7 and $E\subseteq V\times V$8. Variants with heavier attack edges remain prominent: $E\subseteq V\times V$9 has two light and one heavy bully edge to a victim with $\kappa:E\mapsto\mathbb{R}^+$0, while $\kappa:E\mapsto\mathbb{R}^+$1 has two heavy and one light bully edge to a victim with $\kappa:E\mapsto\mathbb{R}^+$2. Defender presence is also recurrent: $\kappa:E\mapsto\mathbb{R}^+$3, in which one defender lightly pushes back against three bullies, has $\kappa:E\mapsto\mathbb{R}^+$4, and $\kappa:E\mapsto\mathbb{R}^+$5, a balanced standoff where two defenders lightly confront two bullies, has $\kappa:E\mapsto\mathbb{R}^+$6. The paper interprets this as evidence that bullying mitigation is a recurring structural feature even in sessions whose net balance still favors bullies.

The joint analysis of Bully Score and Victim Score partitions sessions into four quadrants. Quadrant IV, defined by Bully Score $\kappa:E\mapsto\mathbb{R}^+$7 and Victim Score $\kappa:E\mapsto\mathbb{R}^+$8, contains $\kappa:E\mapsto\mathbb{R}^+$9 of sessions and is dominated by mobbing stars with escalating heavy-edge variants; this is the structural signature of bully-dominant sessions. Quadrant II, defined by Bully Score $\rho:V\mapsto L$0 and Victim Score $\rho:V\mapsto L$1, contains $\rho:V\mapsto L$2 of sessions and is characterized by strong defender clustering around victims or bullies. In that regime, defenders increase bullies’ weighted in-degree and can drive the Bully Score negative. Quadrant I, with both scores nonnegative, contains only $\rho:V\mapsto L$3 of sessions and reflects evenly matched exchanges with mostly light defense. Quadrant III, with both scores negative, contains $\rho:V\mapsto L$4 of sessions and reflects back-and-forth escalation: bullies face pushback, but victims still absorb sustained incoming attacks.

A concrete worked session clarifies the mechanics. In the example session, two bullies attack the Main Victim with weights $\rho:V\mapsto L$5 and $\rho:V\mapsto L$6, two Aggressive Defenders then appear with weights $\rho:V\mapsto L$7 and $\rho:V\mapsto L$8 and both support the victim while pushing back at the two bullies, and an Aggressive Victim adds additional pushback with weight $\rho:V\mapsto L$9 to each bully (Sikdar et al., 19 Dec 2025). The resulting scores are Bully Score $b_i$00 and Victim Score $b_i$01. This is a Quadrant II session: defenders dominate, bullies receive net pushback, and the victim side has net support.

5. Alternative operationalizations at the user, message, and participant levels

Outside session-graph analysis, the same broad idea is instantiated in several distinct ways. In the participant–vocabulary consistency framework of Raisi and Huang, each user $b_i$02 has a bully score $b_i$03, each user also has a victim score $b_i$04, and each vocabulary feature $b_i$05 has a bullying-indicator score $b_i$06 (Raisi et al., 2016). For each directed message $b_i$07, the social bullying score is $b_i$08, and the model minimizes the regularized inconsistency objective

$b_i$09

subject to $b_i$10 for seed features. The bully score here is neither a count nor a probability; it is a latent parameter learned by alternating least squares from sender–receiver structure and vocabulary co-occurrence.

In the World of Tanks chat study, the relevant construct is the message-level Cyberbullying Score

$b_i$11

where $b_i$12 indicates positivity, $b_i$13 negativity, $b_i$14 “NoobRelated,” $b_i$15 bad language or filtered text, $b_i$16 racism, $b_i$17 specific targeting, and $b_i$18 is a repetition escalation term for the author’s negative messages within the match (Murnion et al., 2019). Excluding repetition, the score ranges from $b_i$19 to $b_i$20, and the paper uses the decision rule $b_i$21 for bullying. This formulation makes the link between targeting, repetition, and severity explicit.

A probability-based user-level construction appears in the Twitter study “Mean Birds.” The reported methodology uses $b_i$22 features across text-, user-, and network-based categories, evaluates several supervised learners, and finds Random Forest to perform best, with over $b_i$23 AUC on a corpus of $b_i$24M tweets posted over $b_i$25 months (Chatzakou et al., 2017). In a formulation aligned with that methodology, the continuous bully score is the model-estimated bully probability,

$b_i$26

with optional rescaling to $b_i$27–$b_i$28. In that setup, the score is fundamentally probabilistic rather than structural or rule-based.

The autonomous-driving study defines a different participant-level bully score over repeated episodes of social negotiation on a one-lane bridge. With episode-level bullying indicator $b_i$29 and opportunity indicator $b_i$30, the participant bully score is

$b_i$31

Here, $b_i$32 if the human forces the autonomous vehicle to back off despite the vehicle having right of way, or if the human blocks the vehicle from finishing within the $b_i$33-second round time limit; otherwise $b_i$34 (Cooper et al., 2019). This is a persistence-of-opportunism metric rather than a content-severity metric. In the reported experiment, among participants who bullied at least once, the persistence rate was $b_i$35 in the control group and $b_i$36 in the experimental group, with Fisher Exact Test $b_i$37.

6. Explainability, user-specific severity, and methodological caveats

The 2025 study “AI Enabled User-Specific Cyberbullying Severity Detection with Explainability” pushes the measurement problem toward individualized severity assessment rather than a generic scalar bully score (Prama et al., 4 Mar 2025). It proposes an LSTM-based model trained using $b_i$38 features that combine emotional, topical, and word2vec representations of social media comments with user-level attributes. The user-specific attributes explicitly include psychological factors such as self-esteem, anxiety, and depression; online behavior such as internet usage and disciplinary history; and demographic attributes such as race, gender, and ethnicity. It also introduces a re-labeling technique that categorizes comments into Not Bullying, Mild Bullying, and Severe Bullying while considering user-specific factors. The reported performance is an accuracy of $b_i$39 and an $b_i$40-score of $b_i$41, and the model uses SHAP and LIME to interpret decision-making. The reported findings indicate that, beyond hate comments, victims belonging to specific racial and gender groups are more frequently targeted and exhibit higher incidences of depression, disciplinary issues, and low self-esteem, and that individuals with a prior history of bullying are at greater risk of becoming victims of cyberbullying.

At the same time, the available source for that study is a submission cover letter rather than the full manuscript, and it explicitly does not provide the exact definition of the “bully score,” the feature list beyond the high-level description, the thresholds or formulas for re-labeling, the exact architecture, the training splits, or the SHAP/LIME configuration (Prama et al., 4 Mar 2025). This highlights a broader methodological issue visible across the literature: bully-score constructs are highly sensitive to annotation design, aggregation level, and domain assumptions. A session-level score can be positive even when defenders are present; a user-level latent score can be high because of repeated sender–receiver consistency with bullying vocabulary; a message-level additive score can be driven by profanity, racism, targeting, and repetition; and a participant-level behavioral score can register bullying in the absence of any text at all.

A common misconception is therefore that “Bully Score” names a single interchangeable scalar. The surveyed work suggests otherwise. In practice, the term designates a measurement strategy whose semantics depend on whether the primary object is a graph session, a user, a message, or an interactive episode. The substantive interpretation of magnitude, sign, and threshold follows from that design choice rather than from the label alone.