The balanced rate averages the actual positive side and actual negative side. This lesson starts from the hidden-miss grid so both denominators stay visible.
Start with the same grid
Use the hidden-miss grid again: TP=0, FN=2, FP=0, and TN=8. The plain overall correct-row rate is still 4/5.
accuracy = 0 + 8 10 = 4 / 5 \operatorname{accuracy}={0\mathbin{+}8\over10}=4/5 accuracy = 10 0 + 8 = 4/5 Balanced accuracy keeps both sides Exact recalls from both actual-class sides. missed positives grid output positive negative actual positive negative TP 0 FN 2 FP 0 TN 8 accuracy=4/5 positive recall=0 one displayed grid only; does not prove future performance or training behavior balanced accuracy table row exact fraction value plain accuracy (TP+TN)/total=(0+8)/10 4/5 positive recall TP/(TP+FN)=0/2 0 negative recall TN/(TN+FP)=8/8 1 balanced accuracy (0+1)/2 1/2 balanced accuracy keeps both actual-class sides visible balanced accuracy averages positive recall and negative recall for one displayed grid; counts stay visible; NOT training; NOT generalization threshold fixed first; metric alone is not a claim; NOT training
Read the positive side
The balanced rate keeps the actual positive side visible. Positive recall is TP divided by TP+FN, so here it is 0 out of 2 actual positives.
recall + = 0 2 = 0 \operatorname{recall}_{+}={0\over2}=0 recall + = 2 0 = 0 Balanced accuracy keeps both sides Exact recalls from both actual-class sides. missed positives grid output positive negative actual positive negative TP 0 FN 2 FP 0 TN 8 accuracy=4/5 positive recall=0 one displayed grid only; does not prove future performance or training behavior balanced accuracy table row exact fraction value plain accuracy (TP+TN)/total=(0+8)/10 4/5 positive recall TP/(TP+FN)=0/2 0 negative recall TN/(TN+FP)=8/8 1 balanced accuracy (0+1)/2 1/2 balanced accuracy keeps both actual-class sides visible balanced accuracy averages positive recall and negative recall for one displayed grid; counts stay visible; NOT training; NOT generalization threshold fixed first; metric alone is not a claim; NOT training
Read the negative side
Then read the actual negative side. Negative recall, also called specificity, is TN divided by TN+FP. In this grid it is 1.
recall − = 8 8 = 1 \operatorname{recall}_{-}={8\over8}=1 recall − = 8 8 = 1 Balanced accuracy keeps both sides Exact recalls from both actual-class sides. missed positives grid output positive negative actual positive negative TP 0 FN 2 FP 0 TN 8 accuracy=4/5 positive recall=0 one displayed grid only; does not prove future performance or training behavior balanced accuracy table row exact fraction value plain accuracy (TP+TN)/total=(0+8)/10 4/5 positive recall TP/(TP+FN)=0/2 0 negative recall TN/(TN+FP)=8/8 1 balanced accuracy (0+1)/2 1/2 balanced accuracy keeps both actual-class sides visible balanced accuracy averages positive recall and negative recall for one displayed grid; counts stay visible; NOT training; NOT generalization threshold fixed first; metric alone is not a claim; NOT training
Average both sides
The balanced rate averages those two class-side recalls: 0 and 1. The result is 1/2. The counts stay visible; this is one displayed grid only.
balanced accuracy = 0 + 1 2 = 1 / 2 \operatorname{balanced\ accuracy}={0\mathbin{+}1\over2}=1/2 balanced accuracy = 2 0 + 1 = 1/2 Balanced accuracy keeps both sides Exact recalls from both actual-class sides. missed positives grid output positive negative actual positive negative TP 0 FN 2 FP 0 TN 8 accuracy=4/5 positive recall=0 one displayed grid only; does not prove future performance or training behavior balanced accuracy table row exact fraction value plain accuracy (TP+TN)/total=(0+8)/10 4/5 positive recall TP/(TP+FN)=0/2 0 negative recall TN/(TN+FP)=8/8 1 balanced accuracy (0+1)/2 1/2 balanced accuracy keeps both actual-class sides visible balanced accuracy averages positive recall and negative recall for one displayed grid; counts stay visible; NOT training; NOT generalization threshold fixed first; metric alone is not a claim; NOT training