Were First-Time Holiday Buyers as Likely to Buy in Month 3 and Month 12?

Three months after their first purchase, first-time buyers from the holiday months were less likely to have bought again: 11.1% were active in month 3, against 22.5% of first-time buyers from other months. A year later it flipped: 22.1% against 16.6%.

The data are one UK online shop's purchases. We put customers in groups by the month of their first purchase. Each group is called a cohort. Then we asked, one age at a time, how many of them bought again in that month. That share is called retention. Same shop, same two groups, two different answers, depending on which age you read.

Also on this topic: how to build and read a retention table and what counts as starting and what counts as coming back.

Our position: read retention at one age at a time, and say which age. A single "retention rate" hides a result that flips from lower to higher.

The answer first: a real shop's first-time buyers

We compared two groups of first-time customers at two ages. The holiday group first bought in October or November 2010. The regular group first bought from February to September 2010. We fixed the two ages, month 3 and month 12, before running this analysis.

"Month 3" means the customer bought in the third month after the month of their first purchase. "Month 12" means the twelfth. Each age is read on its own. A customer counts at month 3 only if they bought in that third month, not if they bought at some point in the first three. A gap is the holiday share minus the regular share, counted in points. One point is one percentage point, so 11.1% against 22.5% is a gap of 11.4 points. The 95% range is a band around each gap. Bands made this way hold the true gap about 95 times in 100. At month 3 the band is -14.3 to -8.4 points: the holiday group bought less often, by about 8 to 14 points. At month 12 the band is 2.0 to 9.0 points: the holiday group bought more often, by about 2 to 9 points. Neither band touches zero, so luck alone is a poor explanation. The bands cannot tell you why.

*Data: Daqing Chen (2012), Online Retail II, UCI Machine Learning Repository, CC BY 4.0. Changes: grouped by month of first purchase by MCP Analytics. Customers whose first purchase was in December 2009 or January 2010, or in December 2010 or later, are left out. December 2011 is a partial month and is not used.

What this means for your decisions

• Name the age every time you quote retention. "Holiday buyers retain worse" is true at month 3 and false at month 12 in this shop. A number with no age attached can point the wrong way.
• Treat the two ages as two questions. Month 3 asks whether a customer bought in the third month after their first purchase. Month 12 asks about the twelfth. Which one matters depends on what you plan to do with the list.
• Check the list before you act on it. These data show a pattern. They do not say what a message or an offer would change.

This is a pattern, not proof of a cause. It links when a customer first bought to when they were active. Customers who first buy in the holiday months can differ in other ways, for example gift buyers or trade buyers. So the table does not show that the season changed how they behave.

What cohort retention is

A cohort is a group of customers who started in the same period. Here the start is a customer's first purchase, and the period is a month. Retention is how many of the cohort were active at a later age.

Age is the number of months since the start month. A customer is active at age 3 if they bought in the third month after the month of their first purchase. The share of the cohort that was active is the retention at that age.

• Cohort = customers whose first purchase fell in the same month
• Age = months since that first month
• Retention at an age = customers who bought in that month, divided by the size of the cohort

One age at a time vs any return in the first months

There are two ways to count "came back". They give different numbers, so do not mix them.

• One age at a time asks whether a customer bought in month 3, or in month 12. This is the measure in this article, and the one the free tool reports.
• Any return asks whether a customer bought at any point in the first three months. It is a different question, and it gives a different table.

If one report uses the first and another uses the second, the two tables are not comparable, even when both are called retention.

How to run one on your own file

You need two columns: a customer ID and the date of each purchase.

1. Group customers by the month of their first purchase.
2. Pick one age, say month 3.
3. Count the customers in each group who bought in that month, and divide by the size of the group.
4. Repeat for a second age, and compare the groups at each age on its own.

What you need and what you get back

What your file needs:

• One row per purchase or visit.
• A customer ID, the same for the same customer every time.
• The date of each purchase.
• Optional: a segment column, such as a plan, channel or region, to compare groups.

What you get back (from the free cohort retention tool):

• How many customers were active one, three and twelve months after their first purchase.
• One age at a time, for each group of customers.

Try it: the free cohort retention tool runs this on your own purchases.

Questions readers ask

Why read one age at a time?

Because the answer can change with the age, as it does here. Counting "any purchase in the first three months" is a different measure from "bought in month 3". Mixing them makes two tables look alike when they are not.

Why did the holiday group flip between month 3 and month 12?

These data do not say. They show that the gap was below zero at month 3 and above zero at month 12. To explain why, you would need more facts about these customers than the file holds.

Does this show the holiday made those customers different?

No. The groups are set by the month of the first purchase. Customers who first buy in the holiday months can differ in other ways, such as buying gifts or buying for a business.

Why leave out December 2009?

It is the first month in the data, so a customer seen then may have bought before it. We cannot tell, which is why those customers are left out. January 2010 is left out as the month after the holidays. Customers whose first purchase was in December 2010 or later do not have 12 months of follow-up. December 2011 is a partial month, because the data end on 9 December.

How many customers do I need?

More customers give narrower ranges. Here the smaller group had 702 customers, and the ranges for the gaps are several points wide. Read the size of a gap as roughly its range, not as one number. A much smaller group would give a wider range.

What counts as buying again?

Whatever purchase you decide counts. Here it is any purchase in that one month (month 3 or month 12) by a customer with a recorded first purchase.