> For the complete documentation index, see [llms.txt](https://pyhub01.gitbook.io/python-complete-tutorial/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://pyhub01.gitbook.io/python-complete-tutorial/data-mining-and-machine-learning/f1-score.md).

# F1 score

If a factory produces a batch of products, if we improve the process level, the defective rate of the product will decrease, but the cost will also increase. If we reduce the process level, the defective rate will rise, but the cost will also decrease.

Then the technological level has entered the state of Nash equilibrium. We don’t want the level of craftsmanship to be too high, because it will make our prices unattractive, but we also don’t want too low a level of craftsmanship to cause our factories to produce mobile phones that will explode. So how should we decide?

In the previous chapter, we talked about precision and recall. If the precision is high, you need a low level of craftsmanship, and if the precision is high, you need a high level of craftsmanship. Then if we use an average (we said before that the harmonic average is suitable for dealing with such problems) to average the precision and recall, then we can find a suitable level of craftsmanship.

![F1 score](/files/A9H2T8RCK0YgPFCImA5P)

F1 score is the harmonic average of precision and recall.

In sklearn we can easily calculate the F1 score, the procedure is as follows:

```python
true_table = [1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1]
pred_table = [0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1]

from sklearn.metrics import f1_score

print( f1_score(true_table, pred_table, average='macro') )
print( f1_score(true_table, pred_table, average='micro') )
```

The calculation results are as follows:

```python
0.5714285714285714
0.5714285714285714
>>> 
```

## illustration

In real life, we will receive a lot of emails, but many emails are spam and contain advertisements and fraudulent content.

We can make a language model to detect which emails are spam and which are not spam.

![illustration](/files/9FD2IKJRohvsQmBjOXl2)

As shown in the figure, we have explained the precision recall rate and F1 score.

![Fβ](/files/xYRN6Amq97ZaVyCgNLhz)

In our real life, there are some events that require a high precision rate, and some events require a high rate of precision.

For example, if nuclear power plants always release high-risk news but actually there is no problem at all, it will cause public panic and not trusted.

If a high-intensity infectious disease breaks out, but the patients are not effectively isolated, it will cause the collapse of the social system.

So we need to add a coefficient to the Fβ score to ensure that we take into account both the precision and recall.

When beta is equal to 1, it is the f1 score we talked about earlier.

{% embed url="<https://scikit-learn.org/stable/modules/generated/sklearn.metrics.fbeta_score.html>" %}
read the document in sklearn
{% endembed %}

> The `beta` parameter determines the weight of recall in the combined score. `beta < 1` lends more weight to precision, while `beta > 1` favors recall (`beta -> 0` considers only precision, `beta -> +inf` only recall).

fbeta\_score has been implemented in sklearn, it is very simple to call:

```python
true_table = [1,0,0,0,1,1,1,0,0,0,1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0,1]
pred_table = [0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0,1]

from sklearn.metrics import fbeta_score

print( fbeta_score(true_table, pred_table, beta=0.5, average='macro') )
print( fbeta_score(true_table, pred_table, beta=1, average='micro') )
print( fbeta_score(true_table, pred_table, beta=2, average='micro') )
```

The results of the operation are as follows (this data is not very good, so the results of f0.5 and f1 and f2 are the same)

```python
0.5714285714285714
0.5714285714285714
0.5714285714285714
>>> 
```

In the next chapter, we will explain the ROC curve and the area under the curve.

## Statistics

Start time of this page: December 29, 2021

Completion time of this page: December 31, 2021


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://pyhub01.gitbook.io/python-complete-tutorial/data-mining-and-machine-learning/f1-score.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.