The Third Umpire · Lesson 11 — The Two Mistakes ← Course

The two mistakes — false positives and false negatives.

Accuracy lumps every error together. But there are only two ways to be wrong — and they cost very different things.

When the umpire gets a call wrong, it is wrong in one of exactly two ways. It can give OUT when the batter was not out — a wrong dismissal, punishing an innocent batter. Or it can give NOT OUT when the batter was out — a missed dismissal, letting a wicket slip away.

Sort every decision by what the umpire said and what was actually true and you get four boxes: two right, two wrong. That grid is a confusion matrix, and it is the tool the whole rest of this lesson is built on.

Now the technical names — simpler than they sound. Treat a verdict of OUT, the finger going up, as the “positive”. A false positive is then a wrong OUT: the finger went up but the batter was not out — that is the wrong dismissal. A false negative is a missed OUT: the finger stayed down but the batter really was out — that is the missed dismissal. The word false just means the umpire got it wrong; positive or negative says which way the finger went.

Send a set of appeals through the grid and watch the four boxes fill — then see which two are the mistakes.

Sort each appeal by call and by truth
Ten appeals, each landing in one of four boxes.
truly OUT
truly NOT OUT
umpire says
OUT
correct dismissal
0
wrong dismissal
0
false positive · gave OUT, was not out
umpire says
NOT OUT
missed dismissal
0
false negative · gave NOT OUT, was out
correct not-out
0

Two ways to be right, two ways to be wrong.

Every decision lands in one of four boxes, and the diagonal is where the umpire was right. The other two are the mistakes — the false positive (a wrong dismissal) and the false negative (a missed dismissal). Accuracy just sums the diagonal, so a single number hides which of the two you are actually making.

That matters because the two errors rarely cost the same. A wrongly given wicket and a wrongly spared one have very different consequences — so the next step is to measure each on its own, which is exactly what precision and recall do.

Next: the trigger finger →
▸ Go deeper — the four boxes and their real names optional

Positive and negative are just labels

Here “positive” means the thing you are trying to catch — a dismissal, an OUT. A true positive is a real out correctly called; a false positive is a not-out wrongly called out. “Negative” is the other class — NOT OUT — with true and false versions to match. Which class you call “positive” is a choice, and it frames everything after.

The matrix scales up

With two possible calls you get a 2×2 grid. With more categories — out, not-out, no-ball, dead ball — it becomes a larger square, one row and column per class, with the correct calls down the diagonal and every specific confusion off it. The idea is the same at any size.

Why not just accuracy

Accuracy is the diagonal divided by everything. It is a fine headline, but it throws away which errors you are making. Two umpires with identical accuracy can sit in completely different boxes — and the next page shows exactly that.