Points to double the odds (PDO)
Points to double the odds (PDO) is the number of scorecard points over which the good-to-bad odds double. It sets the scale that converts log odds into a score, using a base score and base odds.
Example
For illustration, if a score of 600 is set at good-to-bad odds of 50:1 and the PDO is 20, a score of 620 means odds of 100:1. A score of 580 means odds of 25:1.
How PDO sets the factor and offset
For an illustration, take a base score of 500, base odds of 20:1 and a PDO of 40. The factor is PDO ÷ ln(2), so 40 ÷ 0.6931 is about 57.71.
The offset is base score minus factor times ln(base odds): 500 − 57.71 × ln(20) is about 327.06. Using these rounded values, the score at odds of 20:1 is 327.06 + 57.71 × ln(20), or about 500.
Reading a score as odds and default probability
For illustration, at good-to-bad odds of 9:1, the bad outcome is 1 of 10, or 10%. At 18:1, it is 1 of 19, or about 5.26%. If the bad outcome is defined as default, these are the corresponding default probabilities.
Keeping the same scaling across scorecards preserves a cutoff’s meaning when one scorecard replaces another. Read a score alongside its base score, base odds and PDO, since those inputs define its scale.
Questions we get asked
Is PDO a measure of how accurate a scorecard is?
No. PDO specifies how the odds map to score, not the accuracy of the scorecard. It describes the score scale, not model performance.
Why does the score formula use the natural logarithm of odds?
The natural log turns multiplicative changes in odds into additive changes in the score formula. That lets a fixed PDO represent a fixed points interval for doubling the odds.
Can I change the base score and keep the same PDO?
Yes. The base score sets the score at the chosen base odds, so changing it shifts the score origin. With the same PDO, the points interval for doubling the odds stays the same.
Decisimo’s free scorecard scaling calculator calculates the factor and offset, then presents score tables with corresponding odds and probability from the selected base inputs.
