The model is patented, and is known as the Personal Space Model. The patent is held by Klaus Brauer, Boeing's (as well as the industry's) leading expert on the perception of passenger comfort and the optimization of cabin interiors.
Some have called his Personal Space Model the e-mc2 of cabin layout, and it is almost as elegant in its simplicity.
The formula is
Personal Space = effective seat width x seat pitch
In this case, effective seat width is defined as seat width + armest + (percentage of passengers seated adjacent to empty seats x 4.25 inches) + (sidewall clearance at passenger eye level x percentage of passengers seated in window seats.)
Most businesses, including airlines, like to deliver a consistent product. Yet airplanes vary widely in length, width and layout, and most airlines have a mix of different airplane models in their fleets. Adding to the complexity, passengers use different criteria in deciding what airline (or airplane) to fly depending on the length of the flight. For a shorter flight, where there is usually an appointment or a connecting flight at the end, they make their choices based on schedule and fare, frequent-flier plans, airline image. On a long-range flight, comfort becomes a very high selection criterion. So an airline wanting to keep its customers happy will increase the personal space available to passengers on longer flights.
So if you're an airline that uses a number of different kinds of airplanes for a particular mission (such as short-range flights, medium-range flights or long-range flights), you can deliver the same level of comfort to your passengers, even if the seats on one model are narrower than on another, or the sidewall clearance or the armrest width varies or the cabin layout varies. You do so by multiplying the effective seat width times the seat pitch (the distance between rows) for the airplane and configuration that delivers the level of comfort you want. Doing so will give you a number. Let's say that number is 654, but on the other two models you fly, the number comes out to 612 and 585 -- which would be very substantial differences. To deliver a consistent level of comfort, the airline must increase the seat pitch on those two models until their numbers also reach 654. In practice, that may mean an airline has to remove a row or two of seats from the airplane, so it can improve the space on board. The tradeoff is the enhanced consistency of the product you offer your customers, which enhances the airline's image and will help retain those customers and attract new ones.