Kolmogorov-Smirnov (KS) statistic
The Kolmogorov-Smirnov (KS) statistic is the largest gap between the cumulative distributions of goods and bads across a credit score. It is calculated by sorting score bands from riskiest to safest, adding up the shares of all bads and goods at each band, then finding the largest difference between those running totals.
Example
For an illustration, suppose 60% of bads and 20% of goods fall below a score. The cumulative shares differ by 40 percentage points at that point, so the gap there is 40 points.
How the KS statistic is calculated
Order the score bands from riskiest to safest. For each band, add its share of all bads to the previous bad total, then do the same for goods.
Compare the two running totals at each band and note their gap. The largest gap identifies the peak band, and its size can be reported in points or as a fraction.
What KS shows beside Gini
KS locates the greatest separation at a particular point in the ordered score bands. Gini describes rank ordering across the whole score range, so the two measures give different views.
The KS value is tied to its peak, rather than describing separation at every point. It is one view of a score, not a complete account of its performance.
Questions we get asked
Can the KS statistic have more than one peak?
Yes. If the cumulative shares have the same largest gap at more than one band, each band is a peak for that KS value.
Does KS set a cutoff for approving a credit application?
No. KS describes separation across score bands, not an approval decision for an individual application. The lender supplies the data and writes the credit policy.
Does a higher KS automatically mean a better score?
A higher KS means the cumulative shares have a larger maximum gap in the evaluated score bands. The value alone does not establish whether the score suits a lender’s decision policy.
Decisimo’s KS statistic calculator calculates the statistic from score bands of goods and bads and shows where the gap peaks.
