You’re right, the brier score would be a good addition to this.

I used sklearn. metrics.brier_score_loss() to calculate the score on both logistic and random forest results:

from sklearn.metrics import brier_score_loss as bsl#logistic regression
bsl(y_test_1,y_1_prob)Out: 0.181#random forest
bsl(y_test,y_1_prob)Out: 0.215

Logistic regression wins here also.