# Credit Scoring model IV max value

I'm making a credit scoring model and I get that one variable has Information Value (IV) more than 1, is that possible?

Formulas are pretty simple for weight of evidence(WoE) and information value(IV)

$$WoE_i = \log \left( \dfrac{\dfrac{g_i}{g}}{\dfrac{b_i}{b}} \right)$$ where $$g_i$$ represents the number of goods (no default) in category $$i$$ of variable $$x_i$$, $$b_i$$ represents the number of bads (default) in category $$i$$ of variable $$x_i$$, $$g$$ represents the number of goods (no default) in the entire dataset, $$b$$ represents the number of bads (default) in the entire dataset, $$N(x)$$ is the number of levels in the variable $$x$$, that is number of categories $$IV = \sum_{i=1}^{N(x)}\left( \dfrac{g_i}{g} - \dfrac{b_i}{b} \right) \cdot WoE_i$$

Also, what is a perfect fit in the model?

By the perfect fit I understand that there is just two categories in x: the first includes all goods and the second includes all bads. In that case when computing $$WoE_1$$ I get 0 in $$log$$ denominator, because $$b_1 = 0$$. When computing $$WoE_2$$ I get 0 in $$log$$ numerator, because $$g_2 = 0$$. Does that make sense?

IV of greater than 1 is possible, and very common. Assume you are using the natural logarithm? You can deduce the limit by using two categories. Say the model/feature can separate the good and bad perfectly, and let $$G_1, B_1, G_2, B_2$$ be the proportion of goods and bads falling in the two categories. Then let $$G_1 \to 1, B_1 \to 0, G_2 \to 0, B_2 \to 1$$. So we are assuming a large pool and the Model is perfectly separating the goods/bads. Then easy to check that that the IV equals:
$$\ln \left( \frac{G_1}{B_1}\right) -\ln \left( \frac{G_2}{B_2}\right)$$