Close the boundary around exact precision and recall bookkeeping.
Compare the two thresholds
Threshold 1/2 gives precision and recall both 2/3. Threshold 5/6 gives precision 1 and recall 1/3.
t = 1 / 2 : 2 / 3 , t = 5 / 6 : 1 and 1 / 3 t=1/2:\ 2/3,\quad t=5/6:\ 1\text{ and }1/3 t = 1/2 : 2/3 , t = 5/6 : 1 and 1/3 Precision and Recall Exactly Exact precision and recall denominators for two thresholds. same scored rows with precision and recall denominators threshold 1/2 score line, threshold 1/2 0 1 t=1/2 A 5/6 B 2/3 C 1/2 D 1/3 E 1/6 predictions at 1/2 row y score pred A 1 5/6 1 B 0 2/3 1 C 1 1/2 1 D 0 1/3 0 E 1 1/6 0 confusion and denominators at 1/2 item exact value TP 2 FP 1 FN 1 TN 1 precision denominator TP+FP 3 precision 2/3 recall denominator TP+FN 3 recall 2/3 threshold 5/6 score line, threshold 5/6 0 1 t=5/6 A 5/6 B 2/3 C 1/2 D 1/3 E 1/6 predictions at 5/6 row y score pred A 1 5/6 1 B 0 2/3 0 C 1 1/2 0 D 0 1/3 0 E 1 1/6 0 confusion and denominators at 5/6 item exact value TP 1 FP 0 FN 2 TN 2 precision denominator TP+FP 1 precision 1 recall denominator TP+FN 3 recall 1/3 same rows; precision uses TP plus FP; recall uses TP plus FN does not claim: NOT best metric; NOT threshold policy NOT future performance; NOT accuracy; NOT calibration NOT fairness; NOT safety; NOT generalization; NOT probability truth
No metric winner claim
This is exact rate arithmetic under two stated thresholds. It does not choose a metric winner.
exact rate arithmetic only \text{exact rate arithmetic only} exact rate arithmetic only Precision and Recall Exactly Exact precision and recall denominators for two thresholds. same scored rows with precision and recall denominators threshold 1/2 score line, threshold 1/2 0 1 t=1/2 A 5/6 B 2/3 C 1/2 D 1/3 E 1/6 predictions at 1/2 row y score pred A 1 5/6 1 B 0 2/3 1 C 1 1/2 1 D 0 1/3 0 E 1 1/6 0 confusion and denominators at 1/2 item exact value TP 2 FP 1 FN 1 TN 1 precision denominator TP+FP 3 precision 2/3 recall denominator TP+FN 3 recall 2/3 threshold 5/6 score line, threshold 5/6 0 1 t=5/6 A 5/6 B 2/3 C 1/2 D 1/3 E 1/6 predictions at 5/6 row y score pred A 1 5/6 1 B 0 2/3 0 C 1 1/2 0 D 0 1/3 0 E 1 1/6 0 confusion and denominators at 5/6 item exact value TP 1 FP 0 FN 2 TN 2 precision denominator TP+FP 1 precision 1 recall denominator TP+FN 3 recall 1/3 same rows; precision uses TP plus FP; recall uses TP plus FN does not claim: NOT best metric; NOT threshold policy NOT future performance; NOT accuracy; NOT calibration NOT fairness; NOT safety; NOT generalization; NOT probability truth
The honest boundary
This is exact precision and recall bookkeeping only; it does not claim: NOT best metric; NOT threshold policy; NOT future performance; NOT accuracy; NOT calibration; NOT fairness; NOT safety; NOT generalization; NOT probability truth.
same rows; exact denominators \text{same rows; exact denominators} same rows; exact denominators Precision and Recall Exactly Exact precision and recall denominators for two thresholds. same scored rows with precision and recall denominators threshold 1/2 score line, threshold 1/2 0 1 t=1/2 A 5/6 B 2/3 C 1/2 D 1/3 E 1/6 predictions at 1/2 row y score pred A 1 5/6 1 B 0 2/3 1 C 1 1/2 1 D 0 1/3 0 E 1 1/6 0 confusion and denominators at 1/2 item exact value TP 2 FP 1 FN 1 TN 1 precision denominator TP+FP 3 precision 2/3 recall denominator TP+FN 3 recall 2/3 threshold 5/6 score line, threshold 5/6 0 1 t=5/6 A 5/6 B 2/3 C 1/2 D 1/3 E 1/6 predictions at 5/6 row y score pred A 1 5/6 1 B 0 2/3 0 C 1 1/2 0 D 0 1/3 0 E 1 1/6 0 confusion and denominators at 5/6 item exact value TP 1 FP 0 FN 2 TN 2 precision denominator TP+FP 1 precision 1 recall denominator TP+FN 3 recall 1/3 same rows; precision uses TP plus FP; recall uses TP plus FN does not claim: NOT best metric; NOT threshold policy NOT future performance; NOT accuracy; NOT calibration NOT fairness; NOT safety; NOT generalization; NOT probability truth