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Points-to-Double-the-Odds Score Scaling

Source: R/obwoe_score.R
obwoe_scale.Rd

Computes the two constants that turn a model's log-odds into scorecard points: the factor that fixes how many points double the odds, and the offset that anchors a reference score to a reference odds.

Usage

obwoe_scale(
  pdo = 20,
  score_ref = 600,
  odds_ref = 50,
  direction = c("higher_is_safer", "higher_is_riskier")
)

Arguments

pdo

Numeric. Points to Double the Odds. Default 20.

score_ref

Numeric. The reference score. Default 600.

odds_ref

Numeric. The good-to-bad odds at score_ref, expressed as a ratio (50 means 50 non-events per event). Default 50.

direction

Character string fixing which end of the scale is safe: "higher_is_safer" (default, the scorecard convention) or "higher_is_riskier".

Value

An object of class "obwoe_scaling": a list with pdo, score_ref, odds_ref, direction, factor and offset.

Details

Scorecards are scaled on the good-to-bad odds:

$$\mathrm{Score} = \mathrm{Offset} + \mathrm{Factor}\cdot \ln(\mathrm{odds}_{good:bad}), \qquad \mathrm{Factor} = \frac{\mathrm{PDO}}{\ln 2}, \qquad \mathrm{Offset} = \mathrm{Score}_0 - \mathrm{Factor}\cdot\ln(\mathrm{Odds}_0)$$

Every model in this package predicts the log-odds of the event (the bad), which is the other direction, so the deployed form is

$$\mathrm{Score} = \mathrm{Offset} - \mathrm{Factor}\cdot \eta$$

The minus sign is the whole point: a bin with a high Weight of Evidence is a risky bin, and a risky bin must score fewer points.

Two identities pin the scaling completely, and obwoe_score is tested against both:

  • Anchor. A case whose odds are odds_ref scores exactly score_ref.

  • Scale. Doubling the good-to-bad odds adds exactly pdo points, at every point of the scale.

References

Siddiqi, N. (2006). Credit Risk Scorecards: Developing and Implementing Intelligent Credit Scoring. John Wiley & Sons. doi:10.1002/9781119201731

See also

obwoe_score to apply the scaling, obwoe_scorecard for the full pipeline.

Examples

scaling <- obwoe_scale(pdo = 20, score_ref = 600, odds_ref = 50)
scaling
#> Scorecard scaling
#>   20 points double the odds; 600 points at 50:1 good:bad
#>   factor = 28.853901, offset = 487.122876
#>   score = offset - factor * link   (higher_is_safer)

# a case at the reference odds scores the reference score
obwoe_score(-log(50), scaling)
#> [1] 600

# halving the odds of being good costs exactly one PDO
obwoe_score(-log(25), scaling)
#> [1] 580