Purchase Probability Types

A Loyalty Builders White Paper

Loyalty Builders LLC provides its clients with information on their customers’ future purchase intentions in four distinct forms:

1. Loyalty Rank, an excellent predictor of future purchases
2. Probabilities of next purchase independent of product purchased (PurchaseProbs)
3. Probabilities of next purchase of a given product (ItemPurchProbs)
4. Probabilities of a first purchase of a given product (NextLogicalPurchaseProbs)

These probabilities are based on mathematical and statistical analysis of information contained in our clients’ invoice data and are calculated for specified time periods in the future (next month, next quarter, next year, etc).

Loyalty Rank. While different from purchase probability, Loyalty Rank correlates highly with the likelihood of a purchase in the next analysis period. Loyalty Rank is included in the basic Loyalty Segmentation Analysis.

PurchaseProbs. The likelihood of the future purchase of any additional product within a specified time period, purchase probability is based on the statistical analysis of the time between purchases. This analysis ignores the specific products already purchased or to be purchased in the future.

Example: The probability of an 11th purchase by a customer who has already made 10 purchases is based on combining his or her purchase behavior with a) the time between purchase 10 and 11 of other customers who have previously made 11 purchases, and b) the time since the 10th purchase of customers who have made only 10 purchases.

A customer with x purchases will have a low probability of a next purchase if a) very few customers with x purchases make additional purchases or b) a much longer time interval has elapsed since the x purchases than is normal for those customers who do make additional purchases.

The analysis underlying PurchaseProbs is most successful when customer purchase behavior is not influenced by the type of product. If some products typically have a long “lifetime” between purchases and others a short “lifetime," then the time between the x and x+1 purchase may not be very informative since it would be influenced more by the product than by pure timing.

ItemPurchProbs. This metric identifies customers who are likely to make additional purchases of specific items in the next month, quarter or some other specified time period. They avoid the pure time-interval focus of PurchaseProbs noted above. Item Purchase Probabilities are based on transaction history, by item, of the entire customer base. Item Purchase Probabilities are calculated by comparing the time between the analysis and the customer’s most recent purchase of item x with the time interval between a) the 10th and 11th (for example) purchase of product x by all customers who have purchased 11 or more and b) the elapsed time since their 10th purchase of all customers who have purchased only 10 of product x – a complex and time intensive calculation.

A customer with k purchases of item x will have a low probability of a next purchase if a) few other customers with k purchases of x make additional purchases or b) a much longer time interval has elapsed between the last purchase and the time of the analysis than is normal for customers who do make additional purchases of product x.

Both our validation procedures and our customers’ experience have shown the ability of ItemPurchProbs to identify customers who are likely to make additional purchases of specific products or services. Normally, our clients request that we supply them with the the 4 to 6 products having the highest probabilities of purchase and “Action Days” at which those probabilities decrease to specific values. “Action Day” information can be used to initiate marketing activities directed at ‘delinquent’ customers. Loyalty Builders can deliver a list of likely next purchases. This enables our clients to develop specific marketing packages that include items with high likelihood of purchase so they can promote additional purchases of other products.

ItemPurchProbs are less effective in predicting the first purchase of a specific product. They are also not effective when repeat purchases of a product is infrequent or when the item is typically purchased only once.

NextLogicalPurchProbs. This measure is designed to provide information on which customers are likely to make their first purchase of a new item type. These calculations involve the most complicated and time-consuming analysis of the four types.

Next Logical Purchase Probabilities are based on a “package” or “market basket” analysis of the various products customers purchase, ignoring the number of purchases of those products. If, at the time of analysis, a customer has purchased only products x and y, then, in many situations, an investigation of the additional items purchased by customers who have also purchased x and y will provide an estimate of the likelihood and ranking of the purchase of additional products by the customer. Time information concerning the next purchase, i.e., PurchaseProbs, is used to supplement the “package” analysis. Loyalty Builders normally delivers the 4 to 6 products most likely to be purchased with the estimated probability of purchase within the given future time interval. “Action Days” may accompany the delivery when clients order this information.

The analysis of NextLogicalPurchProbs is complicated when there are large numbers of products normally purchased by a large number of customers. In that situation, there can be a great many “packages” to be analyzed. Since package probabilities do not use the information gained from multiple purchases of specific products by a customer, they do not, typically, have the predictive power of PurchProbs. They have, nevertheless, proven very successful in identifying groups of customers likely to make their first (or only) purchase of specific products.

Combined Analysis. Normally our clients have a range of products that includes both “single purchase” and “multiple purchases” items. If one or the other of these product types dominates, then the appropriate type of analysis is clear. If, on the other hand, both product types are of equal or near equal importance then Loyalty Builders can analyze multiple purchases and single purchase products separately, and deliver estimates of future purchase probabilities separately, by product type, or combined.