Heartbeat counting score ($A=1-\mathrm{mean}(|N-C|/N)$)

A common score compares reported counts $C_j$ with recorded counts $N_j>0$ over $m$ intervals: $A=m^{-1}{\sum }_{j=1}^m(1-|N_j-C_j|/N_j)$. The absolute error is normalized by the recorded count. Equal reports give $A=1$, but the score does not identify the reporting strategy. The unclipped expression is at most one and can be negative for sufficiently large overcounts.

Two strategies can generate the same observations: a person detects every beat, or a person estimates the count from an expected heart rate and the interval. Whenever the estimate equals the actual count, both produce $C=N$ and score $1$. The score alone therefore lacks identifiability for the latent detection strategy. This logical counterexample does not say that all high-scoring participants use estimation.