## Modeling Customers Switching Between Brands – The General Case

*This is the last installment of a four-part series. The first three parts can be accessed by clicking on the links below.
Methods for Using Arrays Effectively*

Modeling a Watershed with Arrays

Modeling Customers Switching Between Brands

Modeling a Watershed with Arrays

Modeling Customers Switching Between Brands

**Generalizing the Model**

When I showed Steve Peterson (at Lexidyne) my brand switching model, he told me there is a more general version that separates the customer loss fraction from the fraction won by another competitor. This has been presented in Pharmaceutical Product Strategy by Mark Paich, Corey Peck, and Jason Valant.

In my original formulation, the *switching probability* matrix was the product of these two variables. However, in many practical cases, the data available comes from two different places and reflects these two separate components. The revised model structure is shown below.

Instead of one composite *switching probability*, this model uses a *switching out probability* that is distinct from the *switching in probability*. The *switching out probability* is a one-dimensional array that, for each product, contains the fraction of customers lost to rivals every time unit (in our case, month). A sample for the five brands *A*, *B*, *C*, *D*, and *E* appears below.

Brand | Fraction Lost |

A | 0.091 |

B | 0.170 |

C | 0.046 |

D | 0.026 |

E | 0.071 |

**switching out probability**

We can see from this table that Brand *B* is losing 17% of its customers to rivals each and every month! Whoever is managing that product had better do something quickly.

The other side of the story has to do with which brand the customers are switching to. The *switching in probability* matrix contains, for each brand, the fraction of lost customers that migrate to a rival brand. Thus, each row of this matrix *must* add up to one (100% of lost customers). A sample appears below.

From\To | A | B | C | D | E |

A | 0.00 | 0.11 | 0.33 | 0.55 | 0.01 |

B | 0.18 | 0.00 | 0.29 | 0.41 | 0.12 |

C | 0.22 | 0.02 | 0.00 | 0.44 | 0.32 |

D | 0.04 | 0.00 | 0.77 | 0.00 | 0.19 |

E | 0.02 | 0.07 | 0.28 | 0.63 | 0.00 |

**switching in probability**

Note the diagonal will always be zero.

We can determine a lot of things from this table. For example, brand *B* offers no competition to brand *D*, brand *D* is the biggest rival of all the other brands, and brand *C* is brand *D’*s biggest rival.