Before you can trust a single formula on the parent page Accuracy, Precision, Recall, F1-Score, you must be able to read every symbol in it without a dictionary. This page builds each one from nothing, in the order that lets the next one make sense.
The picture to hold in your head: a sorting machine with two output bins.
Figure s01 — Notice the flow: one thing goes IN, the machine picks ONE bin. The amber bin is "positive", the white bin is "negative". Every example lands in exactly one bin.
Every example that goes in must have a true label (reality) and gets a predicted label (the machine's guess). When we compare the two, four situations can happen — and those four situations are the whole foundation of this topic.
Compare truth (what the thing really is) against the guess (what the machine said). Two questions, each yes/no, give 2×2=4 boxes.
Figure s02 — Notice the layout: columns = what the model predicted, rows = what is actually true. The two cyan boxes on the diagonal are the correct guesses (TP, TN); the two amber boxes off the diagonal are the mistakes (FP, FN). Memorise this grid — it is the confusion matrix.
Read the two-word decoder for the names:
The second word (Positive / Negative) = what the machine guessed.
The first word (True / False) = whether that guess was correct.
So "False Negative" = a negative guess that was wrong = we said "no" but the answer was "yes" = a miss.
Recall Self-check: which box is a missed cancer case?
A patient who has cancer but the model says "healthy" ::: False Negative (guessed negative, wrongly)
The four counts are not loose numbers — they live in a fixed 2×2 table called the Confusion Matrix. By convention we put actual (true) classes down the rows and predicted classes across the columns:
Every metric on the parent page has the shape some total countssome correct counts. So you must be fluent with what a fraction means here, and how the word "rate" is used.
Picture a bar of length b with a coloured chunk of length a; the fraction is how much of the bar is coloured.
Figure s03 — Notice the whole white bar is the denominator (100 predictions) and the cyan chunk is the numerator (93 correct). The fraction is simply how much of the bar is filled: 0.93, or 93%.
The parent page constantly writes things like TP+TN+FP+FN. The plus sign here just means "pile these boxes together and count".
Knowing which sum is a row and which is a column is the single trick that tells precision and recall apart. Recall divides by a row (reality); precision divides by a column (the model's claims).
Recall Self-check: which sum is "everything the model flagged as positive"?
F1 (also written F1) is one number that summarises both P and R. It is defined as their harmonic mean — the special average we build next.
To see why the harmonic mean (and not a plain average) is the right tool, we compare the two.
Figure s04 — Notice how, as recall R shrinks toward 0 (left edge), the cyan arithmetic-mean line stays comfortably near 0.5 while the amber harmonic-mean (F1) line dives toward 0. F1 will not let a great precision hide a terrible recall.
Each box below is a foundation from this page; each arrow means "understand the box the arrow leaves before the box it points to". Read it top-to-bottom: everything funnels down into the parent topic's metrics.
Every arrow means "you must understand the box it leaves before the box it enters". Notice all paths converge on the four outcome counts — that is why we spent the most effort there.
