# Does the threshold value of a logistic regression hypothesis has an effect on the accuracy?

It is true that the threshold value of a logistic regression hypothesis has an effect on the Precision/Recall metrics.

Suppose you have trained a logistic regression classifier which is outputting $$h_\theta(x)$$

Currently, you predict $$1$$ if $$h_\theta(x) \geq \text{threshold}$$, and predict $$0$$ if $$h_θ(x).

Higher the threshold, the higher the precision. Lower the threshold, the higher the recall.

This happens due to the Precision/ Recall trade-off.

But, does the threshold affect the accuracy at all?

• Let's make 4 classifications. A and B are category 0, while C an D are category 1. Our model gives P(A=1) = 0.1, P(B=1) = 0.4, P(C=1) = 0.6, and P(D=1) = 0.9. Set the threshold to 0.5, and you get 100% accuracy. Set the threshold to 0.3, and you get 75% accuracy. – Dave May 24 at 11:30

Yes. If you set the threshold to $$1$$, then the classifier will always predict 0, which will make its accuracy $$p(y = 0)$$; if you set the threshold to $$0$$, the classifier will always predict 1, and have accuracy $$p(y = 1)$$; in between, it will go through various different values.