### The Life Table

In any Lifetime Value Simulation (#LTVS), the secret to measuring how customers develop is outlined in a Life Table analysis.

The Life Table tells us the probability of a customer purchasing in the next month, given that the customer did not previously purchase in the past "x" months.

For instance, for a first-time buyer, the first three months of a life table might look something like this:
• Month 1 = 8%.
• Month 2 = 6%.
• Month 3 = 4%.
Let's pretend we have 1,000 new customers.

After one month, 1,000 * 0.08 = 80 customers purchase, meaning that 1000 - 80 = 920 customers do not purchase.
• 80 Customers Now Have Recency = 1 Month and Frequency = 2 Purchases.
• 920 Customers No Have Recency = 2 Months and Frequency = 1 Purchase.
Let's look at the 920 customers who have yet to purchase. In Month 2, they have a 6% chance of purchasing. 920 * 0.06 = 55 customers purchase, meaning that 920 - 55 = 865 customers do not purchase.
• Of the 1,000 first-time buyers, after two months, 865 have yet to purchase for a second time.
We move on to Month 3. The 865 customers who have yet to purchase have a 4% chance of purchasing. 865 * 0.04 = 35 customers purchase, meaning that 865 - 35 = 830 customers are still stuck on one order.
• Of the 1,000 first-time buyers, after three months, 830 have yet to purchase for a third time.
Similarly, for customers with 2 purchases, or 3 purchases, or 27 purchases, we can create life tables that allow us to measure how likely these customers are to purchase in any given month, given where the customer resides in the life cycle.

The life table makes a Lifetime Value Simulation (#LTVS) possible.