The Bass model1 is a widely accepted model for estimating sales data from sales of the same product in previous years, or for estimating sales of a new product using comparative historical data for a similar product.

Bass difussion model Fig. 6 Actual sales and sales predicted by regression for black & white tv

The Bass model is based on the assumption that there are two types of consumers. The innovators, who buy a product on their own initiative and judgement, and the imitators, who decide to buy a product only after social contact with previous buyers. Initially, only some of the innovators buy the product. From there, the sales growth rate increases in each sales period as more innovators buy the product and imitators start to follow their lead, until the sales growth rate reaches a maximum. After that, sales growth starts to decline as fewer and fewer buyers are left at each step. Finally, the market becomes saturated, i.e. no new buyers are interested in the product.

The Bass model prefers to use sales data over longer periods of time, such as a year, as this smoothes out erratic consumer behaviour. In the graph on the left, which shows actual sales data for black and white televisions between 1947 and 1961, we can see how volatile consumer behaviour can be and why it is so difficult to predict future sales figures. Predictions are again discrete data points, but often lines are drawn between data points because human eyes can more easily spot trends. 

The Bass model uses three parameters to fit the model to past sales data: the rate of innovation p, the rate of imitation q, and the size of the market M, either in terms of units sold or sales or market share m as a percentage of the total market. Market size M and market share m can be easily calculated from each other using the sales price per unit. In the following, we will use market share m because it makes it easy to compare products with different unit prices.

The Bassmodel for sales and accumulated sales with a variation of the q-parameter

As the data provided by Bass in his 1961 paper relate to a time when the rate of diffusion was low, I have used more recent data compiled by Rajeev Kohli et al5 and plotted these data on a graph. Kohli et al restricted their data to successful consumer durables introduced in the United States. They included sales data only after significant sales began to occur.

The Bass Diffusion Model above is populated with data from Kohli showing accumulated sales for household appliances, housewares and electronic devices.

Market Size as a function of ownership

The market size in the diagram above is the percentage of potential buyers who have purchased a product. In the case of mobile phones, this is the number of people over a certain age; in the case of household goods and appliances, it is the number of households in a country. Products that have been on the market for a long time in an affluent country may have reached, or be close to, saturation. For example, most households will have a cooker as a basic appliance, but a dishwasher is not considered a necessary appliance in every household.

In the graph below, the appliances are ranked by the average ownership rate in the countries presented, and the countries are ranked in ascending order of household disposable income. As we can see from this graph, there is no strict correlation between household disposable income and ownership rate. Therefore, since market shares will obviously vary from country to country, it is important to evaluate a patent individually for each country.

Ownership rate of major household appliances in selected countries for 2023

Accuracy of the Bass Difussion Model

In the absence of sufficient data for previous sales periods or historical data for similar products, the data generated by the Bass model is highly speculative and unreliable. As you may have learned at school, you need at least three data points for a mathematically correct fit of a curve defined by three parameters. With more data points, the accuracy of the prediction can be improved, but with less than three data points, any mapping of a curve to two or only one data point is ambiguous. Bass pointed this out in his original paper when proposing a forecast for sales of colour televisions:

“In principle, since there are three parameters to be estimated, some kind of estimate is possible with only three observations of the first of these observations occurs at T = 0. Any such estimate should be viewed with some skepticism, however, since the parameter estimates are very sensitive to small variations in the three observations. Before applying estimates obtained from a limited number of observations, the plausibility of the estimates should be closely scrutinized.”

In later comments2 on his model  Bass also notes that:

“Clearly, an estimate for a model with three parameters and three observations would not be reliable”

Looks-like analysis in absence of actual sales data for a new product

When the Bass model is used in cases where no data is available because no actual sales have been made, it is an accepted method to use instead <strong>comparison data sets</strong> with known parameters p and q. The critical component of looks-like analysis is that the product and its historical data should reflect a similar level of innovation and time to market of the new product in question.3 A detailed analysis4 for the introduction of a neurostimulator device uses the known diffusion parameters p and q of ultrasound imaging, mammography and CT scanners. These three historical devices are compared to the new device in a scorecard to determine the similarity of each of these 'old' products to the new product. The results of the <strong>scorecard</strong> are then used to construct a weighted average of the p and q parameters.


[1] Frank M. Bass, "A New Product Growth for Model Consumer Durables", Management Science, Vol. 15, No. 5, Theory Series (Jan., 1969), pp. 215-227,

[2] Frank M. Bass, "Comments on 'A New Product Growth for Model Consumer Durables'", Management Science, Vol. 50, No. 12 Supplement, December 2004, page 1834.

[3] G.L. Lilian and A.Rangaswamy "Diffusion Models: Managerial Applications and Software in New-Product Diffusion Models", Kluwer Academic Publishers, 2000.

[4]  Franaz Ganjeizadeh, Howard Lei, Preetpal Goroya, Erik Olivar, "Applying Looks-Like Analysis and Bass Diffusion Model Techniques to Forecast a Neurostimulator Device with No Historical Data", 27th International Conference on Flexible Automation and Intelligent Manufacturing, FAIM2017, 27-30 June 2017, Modena, Italy.

[5] Rajeev Kohli et al, "Extent and Impact of Incubation Time in New Production Diffusion", J PROD IINOV MANAG 1999; 16:133-144.