Adding purchase day counts changed Brier score from 0.20340 to 0.20333 in a 2011 test at one retailer

We tested whether purchase day count improves a forecast of a later purchase beyond invoice count, spending, recency, and observed tenure. We used the public UCI Online Retail II record from one UK gift retailer. We fitted logistic models on January-to-March 2010 inputs and April-to-June 2010 outcomes. We tested the same months in 2011. Both years used the same 121-day tenure observation period. For 1,776 test customers, adding purchase day count changed Brier score from 0.203397 to 0.203326. The difference was -0.000071. A descriptive 95% range from paired customer resampling was -0.000722 to +0.000606, with fixed fits. This test did not establish a gain or equal performance. Replacing invoice count with day count gave a score of 0.203265. The two counts differed for only 134 test customers. Shorter outcomes, other penalties, UK customers, and a multi-invoice cohort gave small observed changes. A separate fixed check used all earlier source rows for tenure. It gave the test year more possible history and raised baseline Brier score to 0.306434. These results apply to the tested models and one firm. They do not measure customer departure or a causal effect. The package has a compact invoice dataset, provenance, code, plans, all forecasts, figures, and repeat instructions. An independent source reader checked all 36,969 invoices. Separate calculations checked every main input and outcome and all score rows. A second model run matched all seven core result files.

human behavior · repeat purchases · event aggregation · purchase days · probability forecast · temporal validation · open data · RFM