KS Calculation - step by step

 let's walk through a step-by-step example of the KS statistic using 10 observations with:

• Actuals (ground truth): 1 = defaulter, 0 = non-defaulter

• Predicted scores: from a classification model

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🧾 Sample Data: 10 Observations

Obs	Actual (Y)	Predicted Score
1	1	0.95
2	0	0.90
3	1	0.85
4	0	0.80
5	0	0.70
6	1	0.60
7	0	0.40
8	0	0.30
9	1	0.20
10	0	0.10

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📊 Step 1: Sort by predicted score descending

Rank	Actual (Y)	Score	Cumulative Positives	Cumulative Negatives	(+ve%) - (-ve%)
1	1	0.95	1 / 4 = 0.25	0 / 6 = 0.00	0.25
2	0	0.90	1 / 4 = 0.25	1 / 6 = 0.167	0.083
3	1	0.85	2 / 4 = 0.50	1 / 6 = 0.167	0.333
4	0	0.80	2 / 4 = 0.50	2 / 6 = 0.333	0.167
5	0	0.70	2 / 4 = 0.50	3 / 6 = 0.500	0.00
6	1	0.60	3 / 4 = 0.75	3 / 6 = 0.500	0.25
7	0	0.40	3 / 4 = 0.75	4 / 6 = 0.667	0.083
8	0	0.30	3 / 4 = 0.75	5 / 6 = 0.833	-0.083
9	1	0.20	4 / 4 = 1.00	5 / 6 = 0.833	0.167
10	0	0.10	4 / 4 = 1.00	6 / 6 = 1.000	0.00

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✅ Step 2: Identify KS

Look for the maximum difference between:

• (Cumulative positives) — % of defaulters seen so far

• (Cumulative negatives) — % of non-defaulters seen so far

The maximum value in the last column ((Cumulative positives%)  - (Cumulative negatives %)) is:

$$\boxed{0.333} \text{ at Rank 3 (score = 0.85)}$$

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🔍 Interpretation:

• KS = 0.333 → The maximum separation between defaulters and non-defaulters occurs when the score threshold is around 0.85

• At that point:

  • You've captured 50% of defaulters

  • Only 16.7% of non-defaulters

• This is the optimal score threshold for maximum model discrimination