Scaling laws are predictable relations between the performance of AI systems and various scalable design choices such as model or dataset size. In order to keep predictions interpretable, scaling analysis has traditionally relied on heavy summarisation of both the system design and its performance. We argue this summarisation and aggregation is a major source of predictive inaccuracy and lack of generalisation. With a synthetic example we show how scaling analysis needs to be _instance-based_ to accurately model realistic benchmark behaviour, highlighting the need for richer evaluation datasets and more complex inferential tools, for which we outline an actionable proposal.