CTR Prediction Model

Overview

CTR prediction estimates the probability that a user clicks on an ad given context (user, query, ad, position). Forms the core of ad ranking: AdRank = Bid × pCTR. Typically uses logistic regression or gradient-boosted trees. Training on billions of impressions.

When to Use

Trigger conditions:

Building or improving an ad ranking system
Predicting click probability for bid optimization
Evaluating ad creative effectiveness from feature analysis

When NOT to use:

When predicting post-click conversions (use conversion rate model)
When setting bid amounts (use bidding strategy skill)

Algorithm

IRON LAW: A CTR Model Must Be CALIBRATED
Predicting relative ranking is insufficient. The predicted probability
must MATCH actual click frequency (e.g., predicted 5% → 5 clicks per
100 impressions). Without calibration, bid optimization breaks:
  Expected Value = Bid × pCTR × pConversion
  If pCTR is off by 2x, bids are wrong by 2x.

Phase 1: Input Validation

Collect impression logs with: user features, ad features, query features, position, click label (0/1). Handle class imbalance (CTR typically 1-5%). Gate: Sufficient volume (100K+ impressions), click labels verified, no data leakage from position.

Phase 2: Core Algorithm

Feature engineering: user demographics, ad category, query-ad match, historical CTR, time/device features
Train model: logistic regression (interpretable) or GBDT (higher accuracy)
Calibrate predictions: Platt scaling or isotonic regression on holdout set
Evaluate: log-loss (calibration) + AUC (ranking quality)

Phase 3: Verification

Check calibration: bucket predictions into deciles, compare predicted vs actual CTR per bucket. Plot reliability diagram. Gate: Calibration curve close to diagonal, AUC > 0.70.

Phase 4: Output

Return predicted CTR with confidence interval and top contributing features.

Output Format

{
  "prediction": {"ctr": 0.035, "confidence_interval": [0.028, 0.042]},
  "top_features": [{"feature": "query_ad_match", "importance": 0.32}],
  "metadata": {"model": "gbdt", "auc": 0.78, "log_loss": 0.21, "calibration_error": 0.008}
}

Examples

Sample I/O

Input: Trained logistic regression with 3 features and these coefficients:

intercept: -3.0
position_1:  0.8
query_ad_match: 1.5
user_is_mobile: 0.3

Features for current request: position_1=1, query_ad_match=1, user_is_mobile=1

Expected: logit = -3.0 + 0.8 + 1.5 + 0.3 = -0.4 pCTR = sigmoid(-0.4) = 1/(1 + e^0.4) ≈ 0.401 → 40.1%

Verify: for features all 0 (baseline), pCTR = sigmoid(-3.0) ≈ 0.047 (4.7%). Calibration is checked by bucketing predictions and comparing to actual CTR in each bucket.

Edge Cases

Input	Expected	Why
New ad, no history	Use ad category average	Cold start for features
Position 1 vs position 4	Different CTR, same relevance	Position bias inflates top-slot CTR
Very rare query	Low confidence	Insufficient training data for that query

Gotchas

Position bias: Ads in position 1 get more clicks regardless of relevance. Train on position-debiased data or include position as a feature and normalize at inference.
Data freshness: CTR patterns change rapidly (seasonality, trends). Retrain daily or use online learning.
Feature leakage: Including click-derived features (e.g., historical CTR of this exact ad-query pair) creates leakage if not handled carefully with time-based splits.
Class imbalance: 97% no-click, 3% click. Use proper evaluation metrics (log-loss, AUC), not accuracy. Consider downsampling negatives during training.
Multi-task learning: CTR and conversion rate are related but different. Joint models can improve both by sharing lower layers.

References

For feature engineering best practices, see references/feature-engineering.md
For position debiasing techniques, see references/position-debiasing.md

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