Introduced on day 11
Log loss (cross-entropy)
The average negative log of the probability the model gave to the outcome that occurred; the objective logistic regression minimizes and a proper scoring rule for probabilities.
In detail
Confident wrong predictions are punished heavily: assigning probability 0.01 to an event that happens costs about 4.6, while 0.5 costs 0.69. Minimizing log loss is maximum likelihood for a Bernoulli outcome. Because it is a proper scoring rule, it rewards calibrated probabilities, unlike accuracy, which only looks at the side of a threshold. Compare it with the log loss of always predicting the base rate to see what the model adds.