Work out sigmoid output instantly with clear inputs, formula shown and shareable results.
The logistic sigmoid maps any real number to (0, 1) via 1 / (1 + e^-z), which is why logistic regression outputs a probability. Its inverse is the logit, so z is literally the log-odds: z = 0 gives 50 percent, z = 2.2 gives about 90 percent. Shifting the decision threshold away from 0.5 trades precision against recall without retraining.
Logistic sigmoid
p = 1 / (1 + e^-z) where z = logit + bias; odds = p / (1 - p); log-odds = z
Each unit of z multiplies the odds by e, about 2.718. That is why coefficients in logistic regression are interpreted as odds ratios.
Only if false positives and false negatives cost the same and the classes are balanced. Otherwise pick the threshold from a precision-recall curve on validation data.