Retention
Retention falls for the first months after a customer's first order and then rises again at month twelve. That rise is the autumn trading season, not loyalty.
A transaction log answers a question no country-year can: do the customers won in March still buy in September? The usual tool is a retention triangle, which groups customers by the month of their first purchase and counts how many are still active in each month afterwards.
The curve decays as expected, and then stops:
Retention falls from 20.8% in month 1 to a low of 13.6% at month 10 and then rises to 17.9% at month 12. Customers are not becoming more loyal at the one-year mark.
The heatmap explains it, in a direction the line chart averages away. Reading down a column shows ageing, or what happens to a relationship as it gets older. Reading along a diagonal shows calendar time, because every cohort passes through November 2010 on the same day at a different age. The dark band in the heatmap runs diagonally, and it lands on autumn.
Pooled across every cohort age, a customer is active in 23.6% of September-to-November months against 15.3% for the rest of the year. The business sells Christmas stock to shops, so its customers come back in autumn whenever they were first won. The month-12 rise is the same effect read along the other axis, since a cohort's twelfth month falls in the calendar month it started in.
Few summaries keep those two readings apart. A retention curve averages the diagonal into the column and presents the result as ageing, which is how a seasonal business talks itself into a loyalty problem every January.
Two caveats, both handled in the table itself and not noted underneath it. The triangle is ragged: a cohort formed in November 2011 has no month-12 row because the extract ends in December, and those cells are missing, not zero, so rows exist only for months that could have been observed. The first cohort is also left-censored, since December 2009 is the extract's opening month and its "new" customers include anyone who had been buying for years already, and every chart on this page leaves that cohort out.