The Toolkit

300 positives and 700 negatives. The area under the ROC curve computed from ranks is 0.7531; the share of all positive–negative pairs in which the positive scores higher is also 0.7531. That is what AUC means: the probability that a random positive outranks a random negative — a ranking measure, blind to the threshold you will actually use.

• A good AUC can hide poor performance in the region you operate in; look at the curve near your threshold, or at partial AUC.
• AUC is insensitive to calibration: multiplying all scores by 0.1 leaves it unchanged.
• With rare positives, the ROC curve looks good while precision is poor; check the precision–recall curve too.

from scipy.stats import rankdata
rng = np.random.default_rng(1)
pos, neg = rng.normal(1.0, 1, 300), rng.normal(0, 1, 700)
ranks = rankdata(np.r_[pos, neg])
auc_rank = (ranks[:300].sum() - 300 * 301 / 2) / (300 * 700)      # Mann-Whitney U, scaled
auc_pairs = (pos[:, None] > neg[None, :]).mean()                   # P(random positive outranks random negative)

Assumes import numpy as np and import pandas as pd (and SciPy where imported). Each snippet simulates or makes up its own data, as the comments say.

# Python — ROC & AUC
from sklearn.metrics import roc_curve, roc_auc_score
import matplotlib.pyplot as plt

fpr, tpr, thresholds = roc_curve(y_true, y_prob)
auc = roc_auc_score(y_true, y_prob)

plt.plot(fpr, tpr, label=f'AUC = {auc:.3f}')
plt.plot([0,1],[0,1], '--', color='gray')
plt.xlabel('FPR'); plt.ylabel('TPR')
plt.legend(); plt.show()