Quantile Scoring

Quantile scoring converts a measure into a small ordinal score by cutting the population into equal-sized groups — quintiles give 1 to 5, deciles 1 to 10. A customer scores 5 not because they crossed a fixed threshold but because they sit in the top fifth of everyone measured.

The advantage is comparability. Days, order counts, and currency amounts cannot be added together, but their percentile ranks can be placed side by side and combined into one code. Scale and currency drop out, and so does the need to justify an arbitrary cutoff.

The cost is that scores are relative. A score is a statement about position within this population at this moment, so it moves when the population moves. Recomputed monthly, a customer can fall a band without changing behavior, simply because others improved — which matters whenever someone reads a score drop as a warning sign.

Equal groups also depend on the measure being continuous enough to split. Small integers are not: with many customers sharing a value, quintile boundaries land on the same number and the cut fails outright — pandas raises a ValueError about non-unique bin edges rather than guessing.

Assigning distinct ranks before cutting avoids tied bin edges, but tied observations can then receive different scores. With pandas rank(method='first'), ties are ordered by their position in the input. A tied set crossing a score boundary can therefore be split between bands. Group sizes can still differ by a record when the population does not divide evenly into the requested number of groups. When identical behavior must receive identical scores, use explicit thresholds and accept unequal groups instead.