Precision depends on the population being measured. This lesson keeps detector behavior fixed and changes only the exact base-rate rows.
Low-positive population
Start with 10 actual positives and 90 actual negatives. The detector catches 8 of the 10 positives and flags 9 of the 90 negatives. Precision is 8/17.
T P = 8 , F N = 2 , F P = 9 , T N = 81 , P = 8 / 17 TP=8,\;FN=2,\;FP=9,\;TN=81,\quad P=8/17 TP = 8 , FN = 2 , FP = 9 , TN = 81 , P = 8/17 Base rate changes precision Exact same-detector comparison. low-positive population output positive negative actual positive negative TP 8 FN 2 FP 9 TN 81 precision=8/17 recall=4/5; FPR=1/10 higher-positive population output positive negative actual positive negative TP 40 FN 10 FP 5 TN 45 precision=8/9 recall=4/5; FPR=1/10 base-rate precision comparison population actual + actual - TP FN FP TN precision recall FPR low-positive population 10 90 8 2 9 81 8/17 4/5 1/10 higher-positive population 50 50 40 10 5 45 8/9 4/5 1/10 same recall and FPR; precision changes with base rate same recall and same false-positive rate; precision changes because the population changed; one pinned slice only; does not prove future performance; NOT training; NOT calibration; NOT generalization threshold fixed first; metric alone is not a claim; NOT training
Higher-positive population
Now use 50 actual positives and 50 actual negatives with the same detector behavior. It catches 40 positives and flags 5 negatives. Precision is 8/9.
T P = 40 , F N = 10 , F P = 5 , T N = 45 , P = 8 / 9 TP=40,\;FN=10,\;FP=5,\;TN=45,\quad P=8/9 TP = 40 , FN = 10 , FP = 5 , TN = 45 , P = 8/9 Base rate changes precision Exact same-detector comparison. low-positive population output positive negative actual positive negative TP 8 FN 2 FP 9 TN 81 precision=8/17 recall=4/5; FPR=1/10 higher-positive population output positive negative actual positive negative TP 40 FN 10 FP 5 TN 45 precision=8/9 recall=4/5; FPR=1/10 base-rate precision comparison population actual + actual - TP FN FP TN precision recall FPR low-positive population 10 90 8 2 9 81 8/17 4/5 1/10 higher-positive population 50 50 40 10 5 45 8/9 4/5 1/10 same recall and FPR; precision changes with base rate same recall and same false-positive rate; precision changes because the population changed; one pinned slice only; does not prove future performance; NOT training; NOT calibration; NOT generalization threshold fixed first; metric alone is not a claim; NOT training
Same behavior, different precision
Both rows have recall 4/5 and false-positive rate 1/10. Precision changes from 8/17 to 8/9 because the population changed. This is one pinned slice, not a claim about training, calibration, or generalization.
R = 4 / 5 , F P R = 1 / 10 , P : 8 / 17 → 8 / 9 R=4/5,\quad FPR=1/10,\quad P:\ 8/17\to8/9 R = 4/5 , FPR = 1/10 , P : 8/17 → 8/9 Base rate changes precision Exact same-detector comparison. low-positive population output positive negative actual positive negative TP 8 FN 2 FP 9 TN 81 precision=8/17 recall=4/5; FPR=1/10 higher-positive population output positive negative actual positive negative TP 40 FN 10 FP 5 TN 45 precision=8/9 recall=4/5; FPR=1/10 base-rate precision comparison population actual + actual - TP FN FP TN precision recall FPR low-positive population 10 90 8 2 9 81 8/17 4/5 1/10 higher-positive population 50 50 40 10 5 45 8/9 4/5 1/10 same recall and FPR; precision changes with base rate same recall and same false-positive rate; precision changes because the population changed; one pinned slice only; does not prove future performance; NOT training; NOT calibration; NOT generalization threshold fixed first; metric alone is not a claim; NOT training