Population Stability Index (PSI): how to calculate it, with an Excel example

The PSI formula

PSI = Σ (Aᵢ − Eᵢ) × ln(Aᵢ ÷ Eᵢ)

Eᵢ is the expected share of bin i, from the baseline (often the model's development or training sample), and Aᵢ the actual share in the current sample. Both are shares of their own sample, so each column adds up to 100%.

Every term is zero or positive: if the current share is higher, both the difference and the log are positive, if it is lower, both are negative. So PSI is 0 for identical distributions and grows with every shift, whichever way it goes. Mathematically it is a symmetric version of the Kullback–Leibler divergence: the KL divergence of A from E plus that of E from A.

Step 1: bins and shares

Cut the baseline into bins, usually ten deciles of the baseline scores, so that every baseline bin holds about 10%. Then count the current sample in the same bins, with the same cut-off values. In Excel, COUNTIFS(scores,">"&lower,scores,"<="&upper) counts one bin, and FREQUENCY counts all bins at once.

The two samples differ in size, 10,000 against 2,500, so compare shares, not counts: =B2/B$12 for the baseline and =C2/C$12 for the current sample.

Step 2: the PSI term per bin and the total

Each bin's term is =(E2-D2)*LN(E2/D2), copied down. The PSI is the sum of the terms, =SUM(F2:F11) = 0.153. You can also do it in one cell from the counts: =SUMPRODUCT((C2:C11/C12-B2:B11/B12)*LN((C2:C11/C12)/(B2:B11/B12))).

The terms show where the shift is. Decile 1 fell from 10.0% of applications to 4.4% and contributes 0.0465, 30% of the whole PSI. Decile 10 rose from 10.0% to 17.0% and adds 0.0371. Applications have moved from the bottom deciles to the top ones, while the middle hardly changed.

Worked example: PSI of a credit model's score deciles

The counts per score decile are inputs (yellow), the deciles are cut on the baseline scores. Columns D and E turn the counts into shares, column F holds the PSI term of each decile and F12 the PSI. Rows 15 to 20 classify the result and find the decile that drives it.

Worked example: PSI of a credit model's score deciles

	A	B	C	D	E	F
1	Score decile	Baseline n	Current n	Baseline %	Current %	PSI term
2	1	1,004	110	10.0%	4.4%	0.0465
3	2	998	140	10.0%	5.6%	0.0253
4	3	1,001	170	10.0%	6.8%	0.0124
5	4	1,003	200	10.0%	8.0%	0.0046
6	5	996	230	10.0%	9.2%	0.0006
7	6	1,000	255	10.0%	10.2%	0.0000
8	7	1,002	285	10.0%	11.4%	0.0018
9	8	997	320	10.0%	12.8%	0.0071
10	9	999	365	10.0%	14.6%	0.0175
11	10	1,000	425	10.0%	17.0%	0.0371
12	Total / PSI	10,000	2,500	100%	100%	0.153
13
14	Reading the PSI	Value
15	Watch from (PSI ≥)	0.10
16	Act from (PSI ≥)	0.25
17	Status	Moderate shift
18	PSI in one formula	0.153
19	Decile with the largest term	1
20	Share of PSI from that decile	30%

Synthetic data for a fictional lender. The 0.1 and 0.25 limits are industry conventions, not a statistical test. Educational only, not financial or model-risk advice.

Reading the PSI: 0.1 and 0.25

The common rule of thumb from credit scoring is: below 0.1 no significant change, 0.1 to 0.25 a moderate shift worth investigating, 0.25 or more a major shift that needs action. With thresholds in cells, one formula labels the result: =IF(F12>=B16,"Major shift",IF(F12>=B15,"Moderate shift","Stable")).

These limits are conventions, not a statistical test. The PSI also depends on the number of bins and on sample size: small samples produce noisy shares and a higher PSI by chance alone. Keep the thresholds in cells where the team can change them, and watch the trend over several periods rather than one value.

Empty bins and other practical details

• A bin with 0% in either sample makes LN fail (the ratio is 0 or a division by zero). Replace the zero share with a tiny value such as 0.0001, or merge the bin with its neighbour.
• Fix the bin edges on the baseline and keep them. Recomputing deciles on the current data puts 10% in every bin and hides the shift.
• Categorical features such as an application channel use their categories as bins.
• Missing values deserve their own bin. A sudden jump in missing values is often a broken data feed, not a changing population.

PSI on features, on scores and next to other tests

Run the PSI on the model's score and on every input feature, where it is sometimes called the characteristic stability index. A shift in the score tells you that something moved, the feature PSIs tell you where. For categorical data, a chi-square test adds a p-value, and for continuous data the Kolmogorov–Smirnov statistic measures the largest gap between the two cumulative distributions.

A drift alarm does not prove that the model got worse. Once outcomes arrive, check performance directly, for example with a confusion matrix, precision and recall.

Common mistakes

• Flipping the log ratio. LN(baseline ÷ current) makes every term negative. Use current ÷ baseline, matching the order of the difference.
• Using counts instead of shares. With samples of different size, counts always differ. Divide each count by its own sample total.
• Recomputing bins on the current data. New deciles put 10% in every bin and the PSI drops to about zero. Keep the baseline edges.
• Ignoring empty bins. A 0% share breaks LN. Smooth it with a tiny value or merge bins.
• Averaging the terms. The PSI is the sum over all bins, not the mean.
• Treating 0.1 and 0.25 as a significance test. They are rules of thumb. Small samples can cross them by chance.