How to Calculate WoE and IV: A Complete Guide for Logistic Regression

Weight of Evidence (WoE) and Information Value (IV) are metrics widely used in credit scoring, variable selection, and logistic regression modeling.

These techniques are especially popular in the financial industry because they allow us to measure the discriminatory power of a variable in relation to a target event.

Traditionally, records are split into:

good - paying customers (non-defaulters)
bad - defaulting customers

In this article, we will use the dataset from Kaggle’s Titanic competition to demonstrate, step by step, how to calculate WoE and IV in a visual and intuitive way.

Our goal is to turn concepts that are often seen as abstract into something intuitive, interpretable, and easily applicable in practice.

Dataset Used

To demonstrate the calculation of Weight of Evidence (WoE) and Information Value (IV), we will use the gender variable (female and male) from the Titanic dataset in relation to passenger survival.

The table below shows the distribution of the target variable:

Segment	Did Not Survive (`target₀`)	Survived (`target₁`)
female	81	233
male	468	109
Total	549	342

Where:

target₀ represents passengers who did not survive
target₁ represents passengers who survived

Percentage of Each Class per Segment

The percentage of a class within a segment corresponds to the proportion of that group relative to the total of that respective class. These proportions represent the distribution of non-events (target₀) and events (target₁) across each segment.

For the target₀ class:

\[\%target_{0,segment_i} = \frac{target_{0,segment_i}}{target₀}\]

Looking at the female segment:

\[\%survived_{0,female} = \frac{81}{81 + 468} = \frac{81}{549} \approx 0.1475\]

In other words, approximately 14.75% of the passengers who did not survive were female.

For the target₁ class:

\[\%target_{1,segment_i} = \frac{target_{1,segment_i}}{target₁}\]

In the female segment:

\[\%survived_{1,female} = \frac{233}{233 + 109} = \frac{233}{342} \approx 0.6813\]

Thus, approximately 68.13% of the surviving passengers were female.

Percentage Distribution per Segment

Segment	`target₀`	`target₁`	% `target₀`	% `target₁`
female	81	233	0.1475	0.6813
male	468	109	0.8525	0.3187
Total	549	342	1.0	1.0

Note that the sum of the proportions for each class equals 1:

\[\sum \%target₀ = 1 \quad\text{and}\quad \sum \%target₁ = 1\]

These distributions will be used later in the calculation of both Weight of Evidence (WoE) and Information Value (IV).

Population Percentage per Segment

The population percentage represents the share of each segment relative to the total sample. This metric will be used later when calculating the ratio between distributions, which is an essential component of WoE.

This metric is calculated as follows:

\[\%population_{segment_i} = \frac{population_{segment_i}}{population}\]

For the female segment:

\[\%population_{female} = \frac{81 + 233}{81 + 233 + 468 + 109} = \frac{314}{891} \approx 0.3524\]

Therefore, females represent approximately 35.24% of the analyzed population, meaning roughly 35 out of every 100 passengers.

Population Distribution per Segment

Segment	Population	% Population
female	314	0.3524
male	577	0.6476
Total	891	1.0

This distribution helps clarify the representativeness of each segment within the database, which is useful when interpreting both Weight of Evidence (WoE) and Information Value (IV).

It will be compared against the distributions of target₀ and target₁ to identify discrepancies between the overall population and the behavior of specific classes.

Distribution Ratio

The distribution ratio compares the share of a segment between the target₀ and target₁ classes.

It is defined as:

\[Distr_{segment_i} = \frac{ \%target_{0,segment_i} }{ \%target_{1,segment_i} }\]

Values less than 1 indicate that the segment is proportionally more associated with the event (target₁), while values greater than 1 indicate a stronger association with the non-event (target₀).

Distribution Ratio	Interpretation
Distr < 1	The segment is underrepresented among non-events (`target₀`)
Distr > 1	The segment is overrepresented among non-events (`target₀`)

For the female segment:

\[Distr_{female} = \frac{0.1475}{0.6813} \approx 0.2166\]

This indicates that the proportion of women among passengers who did not survive is much lower than among passengers who did survive. In other words, the female segment is more strongly associated with the event (target₁).

Distribution Ratio per Segment

Segment	% `target₀`	% `target₁`	`Distr`
female	0.1475	0.6813	0.2166
male	0.8525	0.3187	2.6745
Total	1.0	1.0	—

Values:

Less than 1 indicate a higher relative concentration in target₁;
Greater than 1 indicate a higher relative concentration in target₀.

Weight of Evidence (WoE)

Weight of Evidence (WoE) is obtained by applying the natural logarithm to the distribution ratio. It quantifies the evidence of whether a segment is more strongly associated with the event (target₁) or the non-event (target₀).

The use of the logarithm makes the scale symmetric around zero, which simplifies interpretation and improves stability in linear models such as logistic regression.

Its definition is given by:

\[WoE_{segment_i} = \ln\left( Distr_{segment_i} \right)\]

Substituting the definition of Distr:

\[WoE_{segment_i} = \ln\left( \frac{ \%target_{0,segment_i} }{ \%target_{1,segment_i} } \right)\]

For the female segment:

\[WoE_{female} = \ln(0.2166) \approx -1.5299\]

The negative value indicates that the female segment has a higher relative concentration in target₁ than in target₀, meaning there is evidence in favor of the event.

Weight of Evidence per Segment

Segment	`Distr`	`WoE`
female	0.2166	-1.5299
male	2.6745	0.9834
Total	—	—

Interpretation:

WoE < 0: Higher relative concentration in target₁;
WoE > 0: Higher relative concentration in target₀;
WoE ≈ 0: Similar distribution between both classes.

Information Value (IV)

Information Value (IV) measures the predictive power of a variable relative to the target variable. It combines the intensity of the evidence (WoE) with the magnitude of the difference between the distributions, capturing both the strength and the statistical relevance of the segment.

The contribution of each segment to the IV is calculated as follows:

\[IV_{segment_i} = WoE_{segment_i} \times \left( \%target_{0,segment_i} - \%target_{1,segment_i} \right)\]

Substituting the definition of WoE:

\[IV_{segment_i} = \ln\left( \frac{ \%target_{0,segment_i} }{ \%target_{1,segment_i} } \right) \times \left( \%target_{0,segment_i} - \%target_{1,segment_i} \right)\]

For the female segment:

\[IV_{female} = -1.5299 \times (0.1475 - 0.6813) \approx 0.8166\]

IV Contribution per Segment

Segment	`WoE`	IV
female	-1.5299	0.8166
male	0.9834	0.5244
Total IV	—	1.3410

The total Information Value of the variable is obtained by summing the contributions of all segments:

\[IV = \sum_i IV_{segment_i}\]

Because IV is additive, variables with many segments can artificially inflate the total value.

In general:

IV < 0.02: No predictive power;
0.02 ≤ IV < 0.1: Weak predictive power;
0.1 ≤ IV < 0.3: Medium predictive power;
0.3 ≤ IV < 0.5: Strong predictive power;
IV ≥ 0.5: Very strong predictive power.

In the example presented, the gender variable has an IV of 1.3410, indicating an extremely high discriminatory power. Values this high can even suggest potential data leakage in real-world scenarios.

Important Considerations

When utilizing Weight of Evidence (WoE) and Information Value (IV), several precautions should be kept in mind:

Low-frequency categories can generate unstable values;
Division-by-zero issues must be properly handled;
Variables with excessively high IV may indicate data leakage;
WoE is widely used in logistic regression because it promotes more linear relationships between variables and the logit;
Binning processes can significantly impact both WoE and IV values.

Although WoE was originally designed for logistic regression, it can also be useful in tree-based models by reducing cardinality and noise.

Additional Resources

If you would like to deepen your knowledge of WoE and IV:

References:

Anderson, Raymond. The Credit Scoring Toolkit: Theory and Practice for Retail Credit Risk Management and Decision Automation. Oxford University Press, 2007.
Siddiqi, Naeem. Credit Risk Scorecards: Developing and Implementing Intelligent Credit Scoring. Wiley, 2006.
Sudarson Mothilal Thoppay (2015). woe: Computes Weight of Evidence and Information Values. R package version 0.2. https://CRAN.R-project.org/package=woe
Thilo Eichenberg (2018). woeBinning: Supervised Weight of Evidence Binning of Numeric Variables and Factors. R package version 0.1.6. https://CRAN.R-project.org/package=woeBinning