What is a good PSI value?

The industry-standard reading from Siddiqi's Credit Risk Scorecards is: below 0.10 the population is stable and no action is needed; 0.10 to 0.25 is a moderate shift worth investigating; 0.25 or above is a significant shift where a model or scorecard built on the baseline likely needs recalibration or retraining. These thresholds assume the natural-log form of the index.

How do you calculate the Population Stability Index?

Split both distributions into the same bins, normalise each column to fractions (Eᵢ = expectedᵢ / Σexpected, Aᵢ = actualᵢ / Σactual), then for every bin compute (Aᵢ − Eᵢ) × ln(Aᵢ / Eᵢ) and add them up. For expected fractions [0.5, 0.3, 0.2] against actual [0.2, 0.3, 0.5] the bin contributions are 0.2749, 0, 0.2749, giving PSI = 0.5498 — a significant shift.

What is the difference between PSI and CSI?

The formula is identical. PSI (Population Stability Index) is applied to the model's output — usually the score or predicted-probability distribution — to check whether the overall population has drifted. CSI (Characteristic Stability Index) applies the same calculation to a single input feature to see which variable is driving that drift. Run this tool on your score bands for PSI, or on one feature's bins for CSI.

What PSI value means the model needs retraining?

A PSI of 0.25 or higher is the conventional trigger for recalibration or retraining, because the population being scored no longer resembles the data the model was built on. Between 0.10 and 0.25 you should investigate which bins moved and monitor the trend rather than retrain immediately. Always confirm the drift is real and not a data-pipeline or binning change first.

How do you handle empty bins when calculating PSI?

A bin with a 0 fraction breaks the formula because ln(0) and division by 0 are undefined. The standard fix, used by Evidently AI and in Siddiqi's examples, is to clip any 0 fraction to a small epsilon (this tool defaults to 0.0001) before taking the log, so every term stays finite. The better long-term fix is to re-bin so no bin is empty, because one clipped empty bin can dominate the index.

Should I use counts or percentages as input?

Either works — the tool normalises each column to fractions internally, so [50, 30, 20] counts and [50%, 30%, 20%] give the same PSI. Use raw counts when you have them; they let the tool warn you about tiny or empty bins that percentages can hide. If you paste percentages, they do not need to sum to exactly 100; the tool normalises and flags a column that is noticeably off.

Does log base change the PSI verdict?

The published thresholds (0.10 and 0.25) are defined for the natural log, so the verdict always uses the ln-based value. Switching to log2 reports the same index in bits, where PSI(bits) = PSI(nat) / ln(2). It is offered for readers who prefer an information-theoretic unit, but do not compare a log2 value against the 0.10 / 0.25 cut-offs.

Is PSI the same as KL divergence?

They are related but not the same. PSI is symmetric — it adds a term for the actual-vs-expected gap and the expected-vs-actual gap — which is why every bin contribution is non-negative. KL divergence is directional and uses only Aᵢ × ln(Aᵢ / Eᵢ). PSI's symmetry and fixed thresholds are why it became the standard for scorecard monitoring; use the separate KL divergence tool if you need the directional measure.

Does this calculator send my data anywhere?

No. Parsing your bins, normalising the columns, clipping empty bins, and computing every contribution all run in your browser with plain JavaScript. Nothing is uploaded, logged, or stored, and the page keeps working offline once loaded, so you can paste production monitoring numbers with no privacy concern.

AI · Model monitoring

Population Stability Index (PSI) Calculator

Paste an expected (baseline) and an actual (current) distribution across the same bins to get the Population Stability Index — the standard measure of data and population drift for ML models and credit scorecards. You get the total PSI, a per-bin breakdown showing which segment moved, and a stable / moderate / significant verdict. It runs entirely in your browser and needs no signup.

By Induwara Ashinsana— Executive Director, Ryzera TechnologiesUpdated Jul 12, 2026

PSI drift calculator

Input mode

Zero-bin handling

Log base

Epsilon (ε)

0 < ε ≤ 0.01. Clips empty bins.

Distribution bins

Bin label	Expected (%)	Actual (%)

Presets

Total PSI

0.1014

Σ per-bin contributions

Verdict

Moderate shift (0.10–0.25)

Bins

No empty bins

Column sums

100 / 100

Expected / actual (raw)

PSI = 0.1014 — in the 0.10–0.25 band, a moderate population shift. Investigate the drifting bins and monitor closely; recalibration may become necessary if the trend continues. The largest single driver is "Bin 1", contributing 0.0405 (40% of the total).

Per-bin breakdown

Bin	Eᵢ	Aᵢ	Aᵢ − Eᵢ	ln(Aᵢ/Eᵢ)	Contribution
Bin 1	0.3000	0.2000	-0.1000	-0.4055	0.0405
Bin 2	0.3000	0.2500	-0.0500	-0.1823	0.0091
Bin 3	0.2000	0.2500	0.0500	0.2231	0.0112
Bin 4	0.2000	0.3000	0.1000	0.4055	0.0405
Total PSI					0.1014

Method: PSI = Σ (Aᵢ − Eᵢ)·ln(Aᵢ/Eᵢ)with Siddiqi's <0.10 / 0.10–0.25 / ≥0.25 thresholds. Empty bins are clipped to ε (Siddiqi / Evidently AI convention). Sources cited below the calculator. No data leaves this page.

How it works

The Population Stability Indexanswers a single question: has the distribution I am scoring today drifted away from the distribution my model was built on? It is the workhorse drift metric in credit-risk model validation and MLOps monitoring, defined in Naeem Siddiqi's Credit Risk Scorecards and implemented the same way in production tools such as Evidently AI.

You supply two distributions binned the same way — for a scorecard that is usually score deciles. Call the baseline the expected distribution and the current period the actual distribution. Each column is normalised to fractions:

Eᵢ = expectedᵢ / Σ expected Aᵢ = actualᵢ / Σ actual

Then each bin's contribution and the total are:

PSI = Σᵢ (Aᵢ − Eᵢ) · ln(Aᵢ / Eᵢ)

Normalise. Counts and percentages both become fractions, so the scale of your data does not matter — only the shape of the two distributions.
Clip empty bins. A 0 fraction makes ln(Aᵢ/Eᵢ) diverge, so any 0 is replaced by a small ε (default 0.0001) before the log — the Siddiqi / Evidently convention. Every term stays finite; no Infinity or NaN can appear.
Sum the contributions. Each (Aᵢ − Eᵢ)·ln(Aᵢ/Eᵢ) is always non-negative, because the difference and the log ratio share the same sign — so PSI is a distance-like number that grows as the two distributions separate.
Read the verdictagainst Siddiqi's action thresholds: below 0.10 is stable, 0.10 to 0.25 is a moderate shift to investigate, and 0.25 or above is a significant shift that usually calls for recalibration or retraining.

The same formula applied to a single input feature rather than the model output is called the Characteristic Stability Index (CSI), which is how analysts trace which variable caused a population to drift. The thresholds are defined for the natural log; the log2 option reports the identical index in bits (PSI / ln 2) for readers who prefer an information-theoretic unit.

Worked examples

Moderate shift — PSI 0.1014 (the default preset)

Expected % = [30, 30, 20, 20], Actual % = [20, 25, 25, 30]
Normalised: E = [.30, .30, .20, .20], A = [.20, .25, .25, .30]
Bin 1: (.20−.30)·ln(.20/.30) = (−.10)·(−0.405465) = 0.040547
Bin 2: (.25−.30)·ln(.25/.30) = (−.05)·(−0.182322) = 0.009116
Bin 3: (.25−.20)·ln(.25/.20) = ( .05)·( 0.223144) = 0.011157
Bin 4: (.30−.20)·ln(.30/.20) = ( .10)·( 0.405465) = 0.040547
PSI = 0.101366 → moderate shift (just over 0.10)

Significant shift — PSI 0.5498 (raw counts)

Expected counts = [500, 300, 200] (Σ=1000), Actual = [200, 300, 500] (Σ=1000)
Normalised: E = [.5, .3, .2], A = [.2, .3, .5]
Bin 1: (.2−.5)·ln(.2/.5) = (−.3)·(−0.916291) = 0.274887
Bin 2: (.3−.3)·ln(1) = 0
Bin 3: (.5−.2)·ln(.5/.2) = ( .3)·( 0.916291) = 0.274887
PSI = 0.549775 → significant shift (≥ 0.25); the low and high score bands swapped

Empty bin — clipping keeps it finite (edge case)

Expected counts = [50, 50, 0] (Σ=100), Actual = [40, 40, 20] (Σ=100)
Bin 3 expected fraction is 0 → clipped to ε = 0.0001 before the log
Bins 1,2: (.4−.5)·ln(.4/.5) = 0.022314 each
Bin 3: (.2−.0001)·ln(.2/.0001) = .1999·7.600902 = 1.519420
PSI ≈ 1.564049 → significant, and finite (never Infinity/NaN)
Lesson: one empty bin dominates — re-bin rather than trust a clipped result

Frequently asked questions

Sources & references

The formula and thresholds on this page were last cross-checked against these sources on 2026-07-12. PSI is a stable mathematical definition, so this tool needs no rate or schedule updates — only the worked examples are periodically re-reconciled.

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