The Video Assistant · 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 VAR gets a call wrong, it is wrong in one of exactly two ways. It can rule NO GOAL when the goal was good — a wrong call, chalking off a goal that should have stood. Or it can let the GOAL stand when it should not have counted — a missed error, letting an invalid goal slip through.

Sort every decision by what the VAR 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 NO GOAL, the VAR chalking a goal off, as the “positive”. A false positive is then a wrong NO GOAL: the goal was ruled out but it was good — that is the wrong call. A false negative is a missed NO GOAL: the goal was allowed but it should not have counted — that is the missed error. The word false just means the VAR got it wrong; positive or negative says whether it ruled the goal out or let it stand.

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 NO GOAL
truly a GOAL
VAR says
NO GOAL
correct call
0
wrong call
0
false positive · ruled out a good goal
VAR says
GOAL
missed error
0
false negative · let a bad goal stand
correct goal
0

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

Every decision lands in one of four boxes. The diagonal is where the VAR was right. The other two are the mistakes: a false positive — a wrong call, NO GOAL given when the goal was good — and a false negative — a missed error, GOAL given when it should not have counted. One number — accuracy — just adds up the diagonal and hides which mistake is happening.

That matters because the two errors rarely cost the same. A good goal wrongly chalked off and a bad goal wrongly allowed 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 goal that should not count, a NO GOAL. A true positive is a bad goal correctly ruled out; a false positive is a good goal wrongly ruled out. “Negative” is the other class — GOAL — 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 — goal, offside, handball, foul in the build-up — 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 officials with identical accuracy can sit in completely different boxes — and the next page shows exactly that.