The information diffusion prediction on social networks aims to predict future recipients of a message, with practical applications in marketing and social media. While different prediction models all claim to perform well, general frameworks for performance evaluation remain limited. Here, we aim to identify a performance characteristic curve for a model, which captures its performance on tasks of different complexity. We propose a metric based on information entropy to quantify the randomness in diffusion data, then identify a scaling pattern between the randomness and the prediction accuracy of the model. Data points in the patterns by different sequence lengths, system sizes, and randomness all collapse into a single curve, capturing a model's inherent capability of making correct predictions against increased uncertainty. Given that this curve has such important properties that it can be used to evaluate the model, we define it as the performance characteristic curve of the model. The validity of the curve is tested by three prediction models in the same family, reaching conclusions in line with existing studies. Also, the curve is successfully applied to evaluate two distinct models from the literature. Our work reveals a pattern underlying the data randomness and prediction accuracy. The performance characteristic curve provides a new way to systematically evaluate models' performance, and sheds light on future studies on other frameworks for model evaluation.

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