The grey edge: how grey system theory redefines online advertising performance metrics

Purpose This study aims to explore the application of grey system theory in evaluating the effectiveness of online advertising, with a primary focus on key performance indicators such as cost per mille (CPM), cost per click (CPC) and click-through rate (CTR). By addressing the challenges associated with incomplete data and small sample sizes, this study seeks to offer data-driven insights for marketing practitioners. Design/methodology/approach This study employs grey relational analysis (GRA) and grey clustering analysis (GCA) on real-world advertising data collected from Facebook’s advertising platform. To enhance objectivity in indicator evaluation, the entropy weight method (EWM) is adopted to determine the weights of each metric based on their degree of variation. These weights were subsequently incorporated into the GRA process to improve analytical precision. The dataset includes advertising performance metrics from campaigns across multiple industries, such as e-commerce, digital gaming and real estate. GRA is used to assess the degree of association among metrics, whereas GCA facilitates the clustering of advertisement performance. Findings The results demonstrate that grey system theory effectively reveals the correlations among CPM, CPC and CTR, thereby enabling advertisers to identify high-performing strategies. Notably, advertisements that emphasize price discounts tend to achieve higher performance scores. However, the GCA results also indicated that superior performance was not consistently attained, potentially due to variability in ad creatives or the limited sample base. Originality/value This study extends the application of grey system theory to the domain of digital advertising by integrating it with real-world campaign data. This study contributes to the theoretical foundation of advertising performance evaluation and offers a flexible analytical framework for uncovering performance-related patterns across diverse advertising materials. These findings provide actionable insights for practitioners aiming to optimize digital marketing strategies in increasingly dynamic and competitive contexts.