Four Ways to Choose a Classification Cutoff Give Three Answers
Updated October 2026
A score is not a decision. Four common ways of choosing the cutoff give three different answers on the same data. A teaching example, not a screening tool.
Four usual ways of choosing a cutoff give three different cutoffs on the same measurement. On 569 breast fine-needle-aspirate samples, flagging a sample as malignant when its mean nucleus radius is at or above a cutoff, best F1 and Youden's J both pick 15.05, a precision target of 0.80 picks 14.25, and a recall target of 0.80 picks 14.60. Moving between them trades missed cases against false alarms: at 15.05, 51 of the 212 malignant samples are missed. This is a teaching example of choosing a cutoff, not a screening tool, and no cutoff here is the right one.
The data and the score
The data are 569 samples, 212 malignant (37.3%) and 357 benign, with 456 distinct mean-radius values. The score is the mean nucleus radius. We declared it in advance, as the first listed feature, and did not choose it for how well it separates the two classes.
Data: Wolberg, Mangasarian, Street and Street (1993), Breast Cancer Wisconsin (Diagnostic), UCI Machine Learning Repository, DOI 10.24432/C5DW2B (CC BY 4.0). Changes: we reduced the data to two columns, the diagnosis as 1 or 0 and the mean radius, and did not alter the values.
Throughout, a positive is a malignant sample. A missed sample is a malignant one below the cutoff. A false alarm is a benign one at or above it.
What a cutoff does
A cutoff splits the samples in two. Any sample whose mean radius is at or above the cutoff is flagged, and the rest are not. Every distinct observed radius is a candidate cutoff.
At the cutoff 15.05, the counts are:
| Flagged | Not flagged | |
|---|---|---|
| Malignant (212) | 161 | 51 |
| Benign (357) | 11 | 346 |
So 161 malignant samples are caught and 51 are missed, while 11 benign samples are false alarms and 346 are correctly left alone. Precision is 0.936, recall is 0.759, and specificity is 0.969.
Our plain-word definitions, not the key's: precision is the share of flagged samples that are malignant; recall is the share of malignant samples that are flagged; specificity is the share of benign samples left unflagged. F1 combines precision and recall into one number.
Four ways to choose
The free tool offers four criteria. No costs are set, and the targets are the tool's defaults.
- Best F1: the cutoff with the highest F1.
- Youden's J: the cutoff with the highest J, which is recall plus specificity minus 1.
- Precision target: the highest recall among cutoffs with precision at least 0.80.
- Recall target: the highest precision among cutoffs with recall at least 0.80.
Ties go to the highest cutoff.
| Measure | Best F1 and Youden's J | Precision at least 0.80 | Recall at least 0.80 |
|---|---|---|---|
| Cutoff | 15.05 | 14.25 | 14.60 |
| Precision | 0.936 | 0.802 | 0.850 |
| Recall | 0.759 | 0.840 | 0.802 |
| F1 | 0.839 | 0.820 | 0.825 |
| Specificity | 0.969 | 0.877 | 0.916 |
| Missed | 51 | 34 | 42 |
| False alarms | 11 | 44 | 30 |
Youden's J at its cutoff is 0.729, and F1 at the best-F1 cutoff is 0.839. Best F1 and Youden's J pick the same cutoff here, so four ways give three distinct cutoffs.
Why they differ
Each criterion asks a different question. Moving the cutoff down, from 15.05 to 14.25, misses fewer malignant samples (34 instead of 51) and raises more false alarms (44 instead of 11). Moving it up does the reverse. The four criteria sit at different points on that trade.
The key sets no costs. Nothing here says that a missed sample costs more than a false alarm, or the other way round, so no one cutoff wins. Which one is better depends on which mistake you can afford, and that is a decision outside the data. A default cutoff is not a decision rule.
What this does not tell you
- The figures are optimistic. Every cutoff is chosen and scored on the same 569 samples, so the figures are optimistic about new samples.
- It is one measurement and one data set. Mean radius is one of many measurements, and this is one data set.
- It is not a screening tool or advice. This is a teaching example of choosing a cutoff. It makes no clinical claim and gives no medical advice.
Run it on your own file
You need an actual yes or no column and a score column, where a higher score means more likely yes. The free tool does not fit a model; it takes your score as given. Set costs if you know them. Run the free threshold optimizer on your own file. For the general idea, see our practical guide to classification thresholds.
Questions people ask
What is a cutoff?
A value of the score. Samples at or above it are flagged, and the rest are not.
Is 15.05 the right cutoff?
No. It is where best F1 and Youden's J agree on this data, and nothing more. The key sets no costs, so no cutoff here is the right one.
Why do four ways give three cutoffs, not four?
Best F1 and Youden's J agree on this data, at 15.05, so they count as one cutoff. The precision target (14.25) and the recall target (14.60) each sit at a different point.
Why are these figures optimistic?
Because each cutoff was chosen and scored on the same samples. A new sample may behave differently.
Is this a screening tool?
No. It is a teaching example of choosing a cutoff.
References
- Wolberg, Mangasarian, Street and Street (1993). Breast Cancer Wisconsin (Diagnostic). UCI Machine Learning Repository. doi:10.24432/C5DW2B (CC BY 4.0)
Three checks on this reading
What we checked before we trusted the numbers.
The same sweep as the free tool
Every observed score is a candidate cutoff and a sample is flagged when its score is at or above it. The free tool, run on the same 569 rows, gives the same cutoffs (best F1 and Youden's J share one) and the same counts.
The score was chosen in advance
The mean radius is the first measurement listed in the data, fixed before looking at any cutoff, not picked for how well it separates the groups.
In-sample and optimistic
Each cutoff is chosen and scored on the same samples, so it flatters new data. No costs are set, so no cutoff here is the right one.