The Third Umpire · Lesson 11 — The Trigger Finger ← Course

The trigger finger — precision and recall.

Two umpires, the same accuracy, opposite habits. One number can't tell them apart. Two sharper ones can.

The confusion matrix gives you two questions far sharper than accuracy. Precision asks: when the umpire raises the finger, how often is it truly out? — of all its OUT calls, the share that were right. Recall asks: of all the real dismissals, how many did it actually catch?

They are not the same, and a model can be strong at one and weak at the other. Here are two umpires judging the same twenty appeals. Both score 70% accuracy — identical. Yet one is trigger-happy and one is cautious, and precision and recall pull them apart at a glance.

High precision means few wrong dismissals — you can trust an OUT call. High recall means few missed edges — real wickets rarely slip by. As you will see, each umpire has bought one by giving up the other.

Switch between the two umpires and watch accuracy hold at 70% while precision and recall trade places.

truly OUT
truly NOT OUT
said OUT
correct dismissal
0
wrong dismissal
0
said NOT OUT
missed dismissal
0
correct not-out
0
Accuracy same for both70%
Precision of its OUT calls, how many were right0%
Recall of real outs, how many it caught0%

Precision and recall see what accuracy hides.

Same 70% accuracy, opposite umpires. Precision rewards not crying wolf; recall rewards letting none slip. The trigger-happy umpire wins recall and loses precision; the cautious one does the exact reverse — and accuracy, identical for both, never saw the difference.

So report both, never accuracy alone. A single number can look healthy while the model is quietly making the one mistake that matters to you. Which of the two you should favour — precision or recall — is the last question of this lesson.

Next: the balance →
▸ Go deeper — the formulas, in plain terms optional

Precision and recall as fractions

precision = TP / (TP + FP) — correct dismissals out of every wicket given. It reads only the top row of the matrix: of the times the finger went up, how many were right. recall = TP / (TP + FN) — correct dismissals out of every real out. It reads only the left column: of the true dismissals, how many were caught.

Each ignores one mistake

Precision never looks at missed dismissals (false negatives); recall never looks at wrong dismissals (false positives). That is precisely why you need both — each is blind to the error the other watches.

Other names

Recall is also called sensitivity or the true positive rate. And all of this hangs on which class you call “positive”: here it is OUT, so precision and recall are about catching dismissals, not not-outs.