Weight of evidence and information value: formulas and an Excel example

What weight of evidence measures

A credit scorecard cuts every characteristic (credit card utilisation, debt-to-income, time at address) into a handful of coarse classes and counts, for each class, the goods (loans that performed) and the bads (for example 90+ days past due within 12 months). Weight of evidence compares two distributions:

• % of goods = goods in the class ÷ all goods
• % of bads = bads in the class ÷ all bads
• WoE = LN(% of goods ÷ % of bads)

WoE = 0 means the class has exactly the average risk. A positive WoE means the class holds relatively more goods than bads (better than average), a negative WoE the opposite. Because it is a log ratio, a WoE of +0.916 means the goods-to-bads ratio of the class is e^0.916 = 2.5 times the portfolio average. Some textbooks and tools use LN(% of bads ÷ % of goods) or multiply by 100, which flips the sign or the scale but not the ranking, so always check the convention before comparing numbers.

Information value and the usual IV bands

WoE describes single classes. The information value summarises the whole characteristic: for each class multiply the difference (% of goods − % of bads) by its WoE, then add up. Both factors always have the same sign, so every IV part is zero or positive and the IV grows with every class that separates goods from bads. Analysts use the IV to screen characteristics before building a model, with a widely quoted rule of thumb:

• below 0.02: not useful
• 0.02 to 0.1: weak
• 0.1 to 0.3: medium
• 0.3 to 0.5: strong
• above 0.5: suspiciously strong, check for a variable that leaks the outcome (such as an in-house collections flag)

These bands are conventions, not statistical tests. The IV also grows with the number of classes, so compare characteristics that were binned with similar care.

Step by step in Excel

With classes in A2:A6, goods in B2:B6 and bads in C2:C6:

• =B2/SUM($B$2:$B$6) in D2: % of goods. The lowest utilisation class has 2,350 of 9,400 goods, 25.0%.
• =C2/SUM($C$2:$C$6) in E2: % of bads, 60 of 600 = 10.0%.
• =LN(D2/E2) in F2: WoE = LN(2.5) = 0.916.
• =(D2-E2)*F2: the IV part, 0.15 × 0.916 = 0.1374.
• =SUM(…) of the IV parts: 0.410.

Copy the formulas down and keep the totals absolute with $. Both percentage columns must add up to 100%, which the total row checks. In the example the WoE falls steadily from +0.916 for the lowest utilisation to −0.999 for 75% and above, while the bad rate climbs from 2.5% to 14.8%.

Worked example: weight of evidence and information value for credit card utilisation

Rows 2 to 6 are the coarse classes of one characteristic with their good and bad counts (inputs in yellow). Columns D to F turn them into distributions and the weight of evidence. Rows 10 to 14 add the bad rate, the odds and each class's contribution to the Information Value.

Worked example: weight of evidence and information value for credit card utilisation

	A	B	C	D	E	F
1	Utilisation class	Goods	Bads	% of goods	% of bads	WoE
2	Below 10%	2,350	60	25.0%	10.0%	0.916
3	10% to 30%	3,050	120	32.4%	20.0%	0.484
4	30% to 50%	2,000	140	21.3%	23.3%	-0.092
5	50% to 75%	1,250	150	13.3%	25.0%	-0.631
6	75% and above	750	130	8.0%	21.7%	-0.999
7	Total	9,400	600	100.0%	100.0%
8
9	Utilisation class	Bad rate	Odds good:bad	IV part
10	Below 10%	2.5%	39.2	0.1374
11	10% to 30%	3.8%	25.4	0.0602
12	30% to 50%	6.5%	14.3	0.0019
13	50% to 75%	10.7%	8.3	0.0739
14	75% and above	14.8%	5.8	0.1367
15	Information Value (sum of the IV parts)			0.410
16	Predictive power (rule-of-thumb bands)			Strong
17	Overall bad rate			6.0%
18	Overall odds good:bad			15.7
19	Tiny class, 40 goods and 0 bads: WoE with 0.5 added			1.630

Synthetic counts for a fictional lender. Educational example, not credit or financial advice. Real scorecards are built on far larger samples, validated out of sample and must meet fair-lending and anti-discrimination rules.

Monotonic patterns and merging classes

Scorecard points should follow a pattern a credit committee can explain: for utilisation, more usage should never earn more points. Check that the WoE (and the bad rate) moves in one direction from class to class. A reversal, one class that breaks the trend, is usually noise from a small sample. The common fix is to merge it with a neighbour, add up the goods and bads and recalculate the WoE. Merging costs a little IV but makes the scorecard more stable on new applicants. A middle class whose WoE is close to zero, like 30% to 50% here (−0.092, an IV part of only 0.0019), is fine: it simply carries average risk.

Zero counts and tiny classes

If a class has no bads, % of bads is 0 and LN returns #DIV/0! or #NUM!. Do not wrap it in IFERROR and move on: a class without bads usually means the class is too small. Merge it with its neighbour first. If you must keep it, add a small constant such as 0.5 to the empty count: a class with 40 goods and 0 bads then gets a WoE of =LN((40/9400)/(0.5/600)) = 1.630, a large number driven entirely by the correction. A common rule is that every coarse class should hold at least 5% of the applications.

From WoE to scorecard points

In a classic scorecard the WoE values replace the raw characteristic as inputs to a logistic regression. The model predicts the log of the good:bad odds, and the credit team scales that to points with a base score, base odds and points to double the odds (PDO): Factor = PDO ÷ LN(2) and Offset = base score − Factor × LN(base odds). With 20 points to double the odds the factor is about 28.85 points per unit of log odds, so a class's WoE translates directly into how many points it earns. After launch, the population stability index, which uses a very similar formula, checks whether new applicants still look like the development sample.

Common mistakes

• Mixing sign conventions. LN(% goods ÷ % bads) and LN(% bads ÷ % goods) give opposite signs. State the convention in the header and stick to it.
• Using bad rates instead of distributions. WoE divides each class's share of all goods by its share of all bads, not the bad rate by the good rate.
• Hiding zero counts with IFERROR. A class with no goods or no bads is too small. Merge it before you calculate the WoE.
• Too many fine classes. Twenty narrow bins inflate the IV and produce zig-zag WoE patterns that will not hold on new data.
• Trusting an IV above 0.5. A suspiciously strong characteristic often contains information from after the decision. Check how it was collected.
• Relative totals. Without $B$2:$B$6 the denominator shifts when the formula is copied down and the percentages no longer add up to 100%.