Probability Scoring Tool Calculator

Example data table

Formula used

First, compute the linear score (logit): z = b0 + Σ(bi × xi).

Convert the logit to a probability using the logistic function: p = 1 / (1 + e^(−z)).

Odds are derived from the probability: odds = p / (1 − p).

Optional score scaling uses points-to-double-odds: Factor = PDO / ln(2), Score = BaseScore ± Factor × ln(odds / BaseOdds).

How to use this calculator

1. Enter your model intercept in the intercept field.
2. Add each variable with a coefficient and its observed value.
3. Set a classification threshold for Positive vs Negative output.
4. Optional: adjust base score, base odds, and PDO for scaling.
5. Press Submit to view results above the form.
6. Use CSV or PDF buttons to export the run summary.

Score inputs and linear aggregation

Probability scoring starts with a linear predictor built from an intercept plus weighted feature values. Each coefficient expresses the expected change in log-odds for a one unit change in the feature, holding others constant. Summing contributions makes model behavior auditable because every variable’s effect is visible and traceable. Use standardized units to avoid score drift.

Good inputs require consistent feature engineering: scaling, encoding, and unit alignment should match training. When features are missing, define a default value or add an explicit indicator so the logit remains meaningful across records.

From logit to probability

The calculator transforms the linear score using the logistic function, producing a probability between zero and one. This mapping is smooth and monotonic, so higher logit values yield higher probabilities. Showing odds alongside probability helps stakeholders interpret risk in ratio form, which is useful for ranking and decision policies.

Thresholds and decision outcomes

A threshold converts probability into a discrete label. Selecting it should reflect business costs, capacity constraints, and class imbalance rather than accuracy alone. For example, lowering the threshold increases sensitivity but may raise false positives. Tracking the chosen threshold with each run supports reproducibility when results are reviewed later.

Score scaling for operational use

Many teams prefer a points-based scorecard for communication and monitoring. Using points-to-double-odds, the tool converts odds into a scaled score anchored at a base score and base odds. You can choose whether higher scores indicate higher or lower probability, matching conventions used in different domains and portfolios.

The scaling factor is PDO divided by ln(2), so each PDO points multiplies odds by two. Anchoring makes scores comparable across runs, provided coefficients and base settings remain consistent.

Governance, monitoring, and exports

Transparent scoring is only the beginning. Calibration checks, drift monitoring, and periodic coefficient review keep probabilities aligned with reality. Exporting CSV and PDF summaries creates a lightweight audit trail of inputs, contributions, and outputs. These artifacts help with peer review, model cards, and incident response when performance changes.

Store exports alongside dataset snapshots and evaluation reports to explain decisions end to end. This practice reduces rework during audits and accelerates root-cause analysis when outcomes deviate.

FAQs

1) What does the logit represent in this tool?
The logit is the linear score before the sigmoid. It equals the intercept plus each coefficient multiplied by its value, and it can be interpreted as log-odds for the positive outcome.

2) Why show odds as well as probability?
Odds express risk as a ratio, which is convenient for ranking and for score scaling. They also change linearly with the logit, making it easier to see relative movement.

3) How should I choose the probability threshold?
Pick a threshold using expected costs and capacity, not accuracy alone. Compare false positive and false negative impacts, then validate the choice on a holdout set or recent production data.

4) What is PDO and why is it useful?
PDO means points to double odds. With score scaling enabled, increasing the score by PDO multiplies the odds by two, giving a stable, interpretable scorecard scale.

5) Can I use non-logistic models here?
Yes, if you can express your model as a linear score that maps to probability via a link function. For non-logistic links, you would need to modify the probability conversion step.

6) What should I export for audits or reviews?
Export the inputs, contributions, probability, threshold, and classification. Pair the export with the model version, feature definitions, and evaluation notes so reviewers can reproduce the result.