### How The Math Works - A 1st Time Buyer

Have you ever taken a look at what a first-time buyer is up against, as the customer (hopefully) makes the journey from a first purchase to a loyal buyer?

The math, unless you are Starbucks, is daunting.

Here's what I saw in a recent analysis.

Let's pretend the customer purchased for the first time in October 2014. In the remainder of October, we have the following metrics:
• 4.1% chance of buying the remainder of October. 23.2% chance of buying in the next year.
Oh oh.

I know, you're going to say "yabut, the customer just purchased, give the customer a chance to buy again."

Ok, let's do that.

In November 2014, here's the math for the customer who has yet to purchase for the second time:
• 4.7% chance of buying in November. 21.3% chance of buying in the next year.
In December 2014, here's the math for the customer who has yet to purchase for the second time:
• 2.8% chance of buying in December. 18.4% chance of buying in the next year.
In January 2015, here's the math for the customer who has yet to purchase for the second time:
• 2.4% chance of buying in January. 16.8% chance of buying in the next year.
From here on out, it gets ugly. Monthly conditional repurchase rates after January are 2.0%, 1.8%, 1.7%, 1.5%, 1.3%, 1.2%, 1.2%, 1.3%, and 1.7% (seasonality helps in months 11, 12, and 13).

In months 13-24 after a first purchase, if the customer has not purchased again, the probabilities are even lower ... 1.1%, 0.9%, 0.7%, 0.7%, 0.6%, 0.7%, 0.5%, 0.5%, 0.5%, 0.5%, 0.5%, and 0.8% (seasonality in month 24).

So if you want to push this customer to loyal status, when should you make the push?

(a) In months 0/1, right after a customer purchased for the first time.

(b) In month 23, as part of a "win-back" program.

The answer is self-evident, isn't it?

The math is fully against first-time buyers.

Take advantage of the first two months after a first purchase, and exhaust every possible opportunity you have to encourage a second purchase before the customer lapses.