Weight of evidence (WoE)
Weight of evidence (WoE) for a bin is the natural logarithm of the bin’s share of all goods divided by its share of all bads. A positive WoE means the bin has lower risk than average. Missing values can be grouped into their own bin and given their own WoE.
Example
For illustration, suppose a bin contains 10% of all goods and 5% of all bads. Its WoE is ln(10% ÷ 5%) = ln(2), or about 0.69, a positive value that indicates lower risk than average.
Calculating WoE for a bin
For an illustration, take a characteristic with 400 goods and 200 bads in total. One bin contains 80 goods and 20 bads.
The bin holds 80 ÷ 400 = 20% of all goods and 20 ÷ 200 = 10% of all bads. Divide 20% by 10%, then take the natural log: ln(2), or about 0.69.
Why scorecards use WoE across bins
A scorecard can replace a characteristic’s raw values with the WoE for each bin. This makes the characteristic linear in the log odds, which suits logistic regression. For ordered bins, the WoE values can show a monotonic trend if they move in one direction across the bins.
Missing values can have a bin of their own and their own WoE. Information value is also calculated per bin from counts of goods and bads, alongside WoE.
Questions we get asked
What does a WoE of zero mean?
A WoE of zero means the bin has equal shares of all goods and all bads. The ratio is 1, and ln(1) is 0.
Can WoE be negative?
Yes. If a bin’s share of all goods is smaller than its share of all bads, the ratio is below 1 and its natural log is negative. That indicates higher risk than average.
Can WoE alone decide an applicant’s credit outcome?
No. WoE describes the relative shares of goods and bads in a bin, not an individual applicant’s outcome. The lender supplies the data and defines the policy for how a scorecard uses it.
Decisimo’s information value calculator calculates WoE and information value per bin from goods and bads counts, or bins an uploaded file itself.
