F1 From Counts

Grid A F1 Fraction

Build the F-score fraction from grid A counts.

highlighted = computed this step

Double TP for the numerator

For grid A, two times TP is 2 times 2 = 4.

2⋅2=42\cdot2=4
F1 Score ExactlyExact F1 fractions from two confusion grids.two confusion grids with exact F1 fractionsgrid Agrid A confusion gridactualpred Ppred NPTP=2FN=1NFP=1TN=1precision and recall side labelsratefractionprecision TP/(TP+FP)2/3 = 2/3recall TP/(TP+FN)2/3 = 2/3F1 denominator blocks2TP=4FP=1FN=12TP+FP+FN=6F1=4/6 = 2/3grid Bgrid B confusion gridactualpred Ppred NPTP=1FN=2NFP=0TN=2precision and recall side labelsratefractionprecision TP/(TP+FP)1/1 = 1recall TP/(TP+FN)1/3 = 1/3F1 denominator blocks2TP=2FP=0FN=22TP+FP+FN=4F1=2/4 = 1/2F1 is computed from displayed counts; denominator is 2TP plus FP plus FNdoes not claim: NOT best metric; NOT future performanceNOT accuracy; NOT calibration; NOT fairness; NOT safetyNOT generalization; NOT probability truth

Add the denominator blocks

The denominator is two TP plus FP plus FN: 4 + 1 + 1 = 6.

4+1+1=64 + 1 + 1 = 6
F1 Score ExactlyExact F1 fractions from two confusion grids.two confusion grids with exact F1 fractionsgrid Agrid A confusion gridactualpred Ppred NPTP=2FN=1NFP=1TN=1precision and recall side labelsratefractionprecision TP/(TP+FP)2/3 = 2/3recall TP/(TP+FN)2/3 = 2/3F1 denominator blocks2TP=4FP=1FN=12TP+FP+FN=6F1=4/6 = 2/3grid Bgrid B confusion gridactualpred Ppred NPTP=1FN=2NFP=0TN=2precision and recall side labelsratefractionprecision TP/(TP+FP)1/1 = 1recall TP/(TP+FN)1/3 = 1/3F1 denominator blocks2TP=2FP=0FN=22TP+FP+FN=4F1=2/4 = 1/2F1 is computed from displayed counts; denominator is 2TP plus FP plus FNdoes not claim: NOT best metric; NOT future performanceNOT accuracy; NOT calibration; NOT fairness; NOT safetyNOT generalization; NOT probability truth

Grid A F-score fraction

Grid A gives 4 over 6, which reduces to 2 over 3.

Fone,A=46=23F_{\text{one},A}={4\over6}={2\over3}
F1 Score ExactlyExact F1 fractions from two confusion grids.two confusion grids with exact F1 fractionsgrid Agrid A confusion gridactualpred Ppred NPTP=2FN=1NFP=1TN=1precision and recall side labelsratefractionprecision TP/(TP+FP)2/3 = 2/3recall TP/(TP+FN)2/3 = 2/3F1 denominator blocks2TP=4FP=1FN=12TP+FP+FN=6F1=4/6 = 2/3grid Bgrid B confusion gridactualpred Ppred NPTP=1FN=2NFP=0TN=2precision and recall side labelsratefractionprecision TP/(TP+FP)1/1 = 1recall TP/(TP+FN)1/3 = 1/3F1 denominator blocks2TP=2FP=0FN=22TP+FP+FN=4F1=2/4 = 1/2F1 is computed from displayed counts; denominator is 2TP plus FP plus FNdoes not claim: NOT best metric; NOT future performanceNOT accuracy; NOT calibration; NOT fairness; NOT safetyNOT generalization; NOT probability truth