Also known as: Platt's method, sigmoid calibration, logistic calibration
Platt scaling fits a logistic sigmoid on top of a model's raw scores to produce calibrated probabilities. Cheap, two parameters, the standard first-resort calibration method for SVMs, classifiers, and uncalibrated rerankers.
Platt scaling is the cheapest way to retrofit calibration onto an uncalibrated model. Take the model’s raw score
p_calibrated = σ(a · s + b)The two parameters
A reranker that’s rank-correct but uncalibrated emits a score on some arbitrary scale — maybe 0-1, maybe a logit, maybe a centered z-score. The ordering is right but a score of 0.7 doesn’t reliably mean “70% probability of relevance.” Platt scaling fits a sigmoid that maps the raw scale onto empirical relevance rates from a labeled validation set, so the post-Platt score satisfies the probability calibration property.
σ(a · s + b) before returning.Platt scaling is two parameters that turn a rank-correct score into a probability. That’s almost always enough to make a downstream threshold (“drop everything below 0.5”) work consistently across queries — which is the entire reason you wanted calibration.
Platt’s sigmoid form assumes the raw scores under each class follow a roughly Gaussian distribution with the same variance but different means. The sigmoid is the Bayes-optimal posterior under that assumption. In practice the assumption is rarely exact — embedder scores aren’t Gaussian, reranker logits have heavy tails — but the two-parameter family is forgiving enough that even violated assumptions produce a usable calibration most of the time.
The standard comparison:
If you have fewer than 1K labels, Platt. If you have more than 10K labels and a clearly non-sigmoid miscalibration shape, isotonic. In the 1K-10K range, fit both and pick by held-out cross-entropy.
A one-variable logistic regression is the entire fit:
from sklearn.linear_model import LogisticRegression
import numpy as np
# raw_scores: shape (N,) — the reranker's uncalibrated scores
# labels: shape (N,) — 0 / 1 ground-truth relevance
clf = LogisticRegression()
clf.fit(raw_scores.reshape(-1, 1), labels)
# At inference:
calibrated = clf.predict_proba(new_raw_scores.reshape(-1, 1))[:, 1]That’s the entire method. The coef_ is Platt’s intercept_ is
The thing to be careful about: never fit Platt on the same data you trained the reranker on. The reranker is overfit to its training set, so its training-set scores are over-separated and Platt will fit a too-aggressive sigmoid. Use a held-out validation set the reranker never saw.
Three failure modes worth knowing:
A few hundred labeled examples is usually enough. Platt only has two parameters (slope and intercept of the sigmoid), so it's data-efficient. Below ~100 labels the fit becomes noisy; above ~10K labels you're past the point where Platt's two-parameter family can capture additional structure — switch to isotonic regression.
The original Platt (1999) paper derived the sigmoid from a Gaussian-noise model over the raw scores, where positives and negatives have shifted but equal-variance score distributions. That assumption is almost never exactly true, but the sigmoid is robust enough to work decently even when the underlying distributions are skewed — which is why it's the default.
When the miscalibration is non-monotone (a score of 0.7 means more relevant than 0.6 and more relevant than 0.9 — physically rare but happens with overfit models), or when the empirical calibration curve has kinks that a sigmoid can't bend around. Isotonic regression handles both at the cost of more data and more overfitting risk.
