Predicting the next six months of every customer

Two years of real transactions from a UK online wholesaler, 5,878 customers, the top 10% bringing 64% of revenue. Classic buy-till-you-die models, implemented from their likelihoods, predict each customer's next 26 weeks and are checked against what each customer actually did.

Code on GitHub Dataset on Kaggle

-2%error on total purchases, BG/NBD (naive: +68%)

64%of next-6-month revenue from the top 10% ranked

151% → 24%ML baseline error once features stopped growing with tenure

26%of one-time buyers return, though the model calls them alive

01Three numbers per customer are enough

Model	Total purchases error	MAE	Spearman	Revenue, top 10%
Naive past rate	+68%	1.67	0.56	60%
LightGBM, fixed-window RFM	+24%	1.26	0.53	62%
BG/NBD x Gamma-Gamma	-2%	1.04	0.62	64%

Mean purchases in the holdout by calibration frequency: BG/NBD tracks the actual line closely at every level, LightGBM overshoots for low-frequency customers, the naive rate overshoots everywhere. — Holdout June-December 2011. BG/NBD sees only frequency, recency and tenure, and follows actual behaviour at every frequency level.

The machine-learning baseline first overshot by 151%: trained when the data was six months old and applied when it was eighteen, its lifetime-total features were far outside anything it had seen. Fixed 13- and 26-week windows fixed that. Revenue is still underestimated by 13% because the holdout contains Christmas and the models are stationary.

02Ranking customers by value

Cumulative share of next-26-week revenue against share of customers ranked by predicted value; both models sit close below the perfect-foresight curve. — For targeting, the order matters more than the totals.

03Where the model is wrong

Bar chart of the share of customers buying again by P(alive) band; it rises from 19% to 56% and then drops to 53% in the top band. — In BG/NBD a customer can only drop out after a repeat purchase, so one-time buyers sit in the top band by construction. Only 26% of them returned, against 85% of repeat buyers in the same band.

Heatmap of monthly cohort retention; cohorts from September to December 2010 are visibly lighter than the rest. — Cohorts acquired September-December 2010 came back at half the rate of others in months 2-6 (10.7% vs 21.2%), but those months are the January-May low season, so one year of data cannot separate customer quality from the calendar.