Search / Multiple Choice System evaluation

I have a DB with N items. My system can output an ID for the item or say N/A (not found). What are different ways to evaluate the performance of such system, and what are the characteristics/tradeoffs of these?

PS. Earlier I came with a definition:

Ground truth ↓, Prediction → ID1 N/A
ID2 TP IF ID1 == ID2 ELSE FP FN
N/A FP TN

Would be curious to get some thoughts / feedback on this definition and whether we can base Precision / Recall on this.

Topic metric evaluation information-retrieval search

Category Data Science

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