Forecast Joy’s Database Includes Products with Monthly and Quarterly Data as Well as the Usual Annual

How to Find a Product with Data of a Specific Intervals

IntervalDropDownUsing Bass Model Calculator Online, under the Product Database tab, use the lower right filter to select the interval (e.g., Monthly).  For some intervals, additional filters must be set to specify just one product. Once a single product is selected, the graphs and parameter sliders will update to reflect the parameters for the selected product.



Forecast Joy Database of 104 Product Categories Now Available for Use as Analogies in New Product Forecasts

How to Use the Product Database

Using Bass Model Calculator, Select the Product Database tab above to explore the database. The dropdown lists are filters to access products with various characteristics.  When all the dropdown lists show values, the product parameters and variables will have been entered into the model and graphs.  Look at the Parameters tab to see the selected product parameter values, which can be adjusted to refine the curves.  Use the Export tab to save the graphs and data to an Excel spreadsheet.  To select a different product, click the Clear button to reset the filters.

All Help Appreciated …

I am still debugging and refining the product database and expect to be adding additional features and data soon.  If you notice any oddities in using the database, please note in a comment.  All help appreciated.

Market Forecast from Potential Market, First Year Sales and Years to Market Saturation with Example Internet of Pugs Forecast

Steps to an Example Forecast

LapotpPugThe following steps will build a forecast for the (inevitable) Internet of Pugs Cloud Service:

1.  Specify the product category — In the App above, click the Product tab and enter “Internet of Pugs Cloud Service.”  Notice that the title of each sheet reflects the change such that, for example, the first sheet title is Potential Market Penetration — Internet of Pugs Cloud Service.

2.  Click the App Parameters tab to enter the remainder of the required information.

PugM3.  Specify M, the potential market, which is the number of pugs that will ultimately be connected to the Internet and subscribe to the Pug Cloud Service.  I will assume (1) the number of pugs worldwide is 4 million (I have no clue except for the one under my desk) and will remain constant for the period of the forecast.  I will further assume that ultimately 50% of all pugs will be connected to the Internet.  Of course, all owners will want their pug connected; however, not everyone will be able to afford the connecting device and service.  In conclusion, I will use the potential market M as 2 million; therefore, slide the M slider to the far right as shown.

PugY14.  Specify the beginning year of the forecast as the first full year of product sales, which I will assume is 2017, which should be entered in the box to the right of the M slider, which is labeled Year 1.

Pugp5.  Specify p as the percentage of the potential market M that will be sold in the first full year of sales.  I’ll say 0.5%, which means p = 0.005.  Do this by either moving the p slider to select 0.001 or (as a shortcut) specify the maximum value of p in the box to the right of the slider and move the slider to the far right.

6.  Now for the fun.  Set the saturation slider (to the left of “saturation”) to some percentage of market penetration that you can get your head around.  I’ll use 60% here, but I often use 95% (which I think of as market saturation) so that I can compare to how long it took other products to reach market saturation.  Then select how many years you think it will take for the market to reach 60% saturation by using the slider to the left of “years to.”  I’ll use 15 years.

Notice as these two sliders are moved, the q slider moves automatically.  This is because years to saturation T and saturation level sat can be used to determine q.  This is done in the App using a solver-type search for q given p, T and sat.  The Bass Model curves are then calculated using the q so determined.  There is no simple formula for calculating directly from p, T and sat.

Years ago when I first started building this app, doing the search for q was too time-consuming for the app to be responsive. But technology has marched on until today the T and sat sliders are almost as responsive as p and q in spite of the nonlinear solver required.

The result is a market forecast with 3 graphs as well as the data that can be downloaded.  Now all we need is a press release …

“Forecast Joy Expects 1.4 Million Internet of Pugs Cloud Service Subscribers by 2031”

If I were a forecast publisher, I would wrap a few more pages about the pug connection market around this, profile a few expected competitors and charge $2,000 for the result — then on to the next hot product forecast.

More Intuitive Bass Model Parametes Designed for Managers and Forecast Publishers

 More Intuitive Parameter Options

The usual Bass Model parameters are the potential market M, the innovation parameter p and the imitation parameter q.

The potential market M is easy to understand as the ultimate number of adopters that will adopt the product. The number chosen for M may require much discussion, but at least management can understand and participate with modelers in its guesstimation.

But parameters p and q in isolation are not intuitive to anyone. The classical way of determining them is to fit the Bass Model to sales data series of past products that are similar to the new product being forecasted. The p and q parameters for analogous products are refined for use in a new product forecast. Management could participate in the selection of analogous products. In some cases analogies are easy to come by (e.g., a new generation of DRAM chips is analogous to the prior generation). In other cases, analogies are not so obvious so opinion dominates guesstimation.

We can replace p and q with more intuitive parameters. The parameter p is approximately the percentage of the potential market M adopters that will adopt during the first full year (or other interval) of sales, a quantity within management domain. The parameter q can be replaced by two quantities: the number of years (or other interval) from the first full year of product sales to market saturation at a selected level. The quantities to be guesstimated by management are then as follows:

  • sat — the saturation level that management feels is within their understanding and
  • T — the number of years that it will take for the product to reach that level of saturation.

For most products, the saturation level is set to 60% to 95% while the number of years to saturation varies from 5 to 30. The guesstimation of sat and T still benefits from analogous, but candidate analogies can be more intuitively compared.

A future post will suggest experiments in setting parameters using the Forecast Joy App.



What Is the Bass Model that Is Used by the Forecast Joy App?

In a Nutshell

The Bass Model is the most widely cited and applied new-product diffusion model.  It has been used to forecast the diffusion and sales of many types of new products (including services) and technologies.  The Bass Model was developed and published by Professor Frank M. Bass.

What Do I Have to Do with the Bass Model?

I had used the Bass Model long before I met its creator.  I had used it to forecast a variety of products (e.g., PCs, microprocessors, cellphones, DRAM chips, video titles, software).  I have even worked on litigation matters where an important issue was the appropriate and correct use of the Bass Model to make the forecast that served as the basis for damages calculations.  My quest to build a tool to ease the complexities of new product sales forecasting for us forecasters in the trenches, led me to my first meeting with Frank Bass.  That meeting resulted in collaboration on scholarly research and eventually marriage ended by his death in 2006.  Frank and I funded Frank M. Bass Institute (DBA Bass’s Basement), a 501c3 corporation that provides educational information concerning the Bass Model.

Origins of the Bass Model

The Bass Model was first published in 1963 by Professor Frank M. Bass as a section of the scholarly paper A dynamic Model of Market Share and Sales Behavior. The section entitled “An Imitation Model” provided a brief, but complete, mathematical derivation of the model from basic assumptions about market size and the behavior of innovators and imitators.   The paper did not provide empirical evidence in support of the model, which was provided later in the 1969 Bass Model paper.

When Professor Bass first published the Bass Model, a mathematical theory of product and innovation diffusion was just being born. Three years before in 1960, Fourt and Woodlock had published their pioneering paper about the diffusion of frequently purchased products.  In 1961 Mansfield’s now classic paper appeared.

In 1962 the first edition of Professor Everett M. Rogers’ pioneering book Diffusion of Innovations was published.  As was the norm in sociology at the time, Rogers’ thoroughly descriptive work was largely literary and did not include a mathematical theory.  Professor Bass, then a professor at the Krannert School at Purdue University, had been reading Rogers’ book thinking about how word-of-mouth applied to sales of new products when Peter Frevert (then an economics student, now retired from University of Kansas) came to Professor Bass’ office to ask how one would express mathematically the idea of imitators and innovators espoused by Rogers in the speech he had recently given at Purdue.

In response to Frevert’s question, Professor Bass thought

“The probability of adopting by those who have not yet adopted is a linear function of those who had previously adopted.”

He scratched out on a notepad the mathematical expression of this idea


Later, as Professor Bass manipulated the equation with the goal of finding the solution to this nonlinear differential equation, he discovered that if instead of the constant q he made the constant be q divided by the constant potential market M (in the well-established tradition of cleverly chosen constants), the equation would work out very nicely; thus, the Bass Model principle became


Professor Bass called p the “coefficient of innovation” because it did not interact
with the cumulative adopter function A(t). The coefficient that was multiplied
times the cumulative function was called “the coefficient of imitation” because it reflected the influence of previous adopters.  We will later define these symbols and their relationships.

Bass saw that Rogers’ work on the spread of innovations in social systems  due to word of mouth could be the basis of a new mathematical theory of how new products diffuse among potential customers.  The Bass Model assumes that sales of a new product are primarily driven by word-of-mouth from satisfied customers.  At the launch of a new product, mostly innovators purchase it.  Early owners who like the new product influence others to adopt it.  Those who purchase primarily because of the influence of owners are called imitators.

In 1967 Professor Bass wrote a Purdue working paper that provided empirical support for the model.   It has his handwritten notes and additional empirical cases over the 1969 paper.  The working paper became the classic Bass Model paper, which was published in 1969.  It expanded the theory and provided empirical support. The paper became one of the most widely cited paper in marketing science.  It was named by INFORMS as one of the Ten Most Influential Papers published in the 50-year history of its flagship journal Management Science.  On this occasion Professor Bass wrote a retrospective.

The Bass Model Principle

The Bass Model principle is


This is read

“The portion of the potential market that adopts at t given that they have not yet adopted is equal to a linear function of  previous adopters.”

In the above equation, t represents time from product launch and is assumed
to be non-negative.

An adoption is a first-time purchase of a product (including services) or the first-time uses of an innovation.

The three Bass Model parameters (coefficients) that define the Bass Model
for a specific product are:

  • M — the potential market (the ultimate number of adopters),
  • p — coefficient of innovation and
  • q — coefficient of imitation.

The potential Market M is

the number of members of the social system within which word-of-mouth from past adopters is the driver of new adoptions.  The Bass Model assumes that M is constant, but in practice M is often slowly changing.

Because in the Bass Model each adopter is assumed to make one and only one adoption, the terms mathematical term A(t) and a(t) can be thought of as either adoptions or adopters.

The coefficient of innovation p is so called because

its contribution to new adoptions does not depend on the number of prior adoptions.  Since these adoptions were due to some influence outside the social system, the parameter is also called the “parameter of external influence.’

The coefficient of imitation q received its moniker because

its effect is proportional to cumulative adoptions A(t) implying that the number  of adoptions at time t is proportional to the number of prior adopters.  In other words, the more people talking about a product, the more other  people in the social system will adopt. This parameter is also referred to as the “parameter of internal influence.”

Bass Model parameters for products with a sales history long enough to include the peak in adoptions are determined by curve fitting the model to time series data for sales.  A database of parameter estimates for such historical products are then used as a basis for guessing the parameters for a new product, the “forecasting by analogy” method.  For a new product, the potential market M is also often determined using marketing research (e.g., surveys).  The Bass Model parameters can be refined as actual sales data becomes available.

The other variables in the Bass Model principle above, which are calculated from M, p, q and t, are:

  • f(t) — the portion of M that adopts at time t.
  • F(t) — the portion of M that have adopted by time t,
  • a(t) — adopters (or adoptions) at t and
  • A(t) — cumulative adopters (or adoptions) at t.

There are other representations of the Bass Model using different symbols and what may seem to be a different equation, but they are all equivalent and can be obtained from the Bass Model principle through algebraic manipulation.  One equivalent equation is shown below.

The preferred Bass Model equations for use in curve fitting and forecasting
is the solution to the differential equation, mathematically it is


Want the Details on the Bass Model Derivation?

For additional information on these formulae, see the Bass Math page at

The Forecast Joy App implements the Bass Model.

New Diffusion Curves Are Amazingly Responsive to Parameter Changes


I am wowed by the responsiveness of this update to the Forecast Joy App.  Try it yourself: as a slider pointer is dragged along, the curves change instantly and smoothly.  The tabs at the bottom of the spreadsheet workbook can be selected to observe the various curves as the parameter change.

More About this Update

In this update the Telerik spreadsheet and charting components were replaced by SpreadsheetGear’s component.  All Bass Model calculations are done in the spreadsheet, which is apparently much faster than doing the calculations in code.  The Forecast Joy App continues to use other Telerik controls (e.g., RibbonView).

The spreadsheet resulting from changes to the Bass Model parameters can be downloaded using the App’s Export function.  The downloaded spreadsheet includes all formulae as well as charts.


Forecast Joy’s Interactive Bass Model App Updated to Save Model Data to Excel

App Can Now Export to Excel

After calculating and refining a Bass Model curve to obtain a forecast that you judge to be reasonable, select the Export tab, then click the Export to Excel button to save an Excel spreadsheet of the Bass Model series data.

Latest App on Forecast Joy App Page

These blogs will each use the latest version of the Forecast Joy App and may use a variant especially designed for the subject of the blog.  In any case, the latest and most complete version will be on the Forecast Joy App page.

Features Coming Soon…

  • Higher resolution sliders for choosing and refining p, q and M parameters.
  • Export to Csv and Txt formats.
  • Choice to export formulae with series data.
  • Choice to export charts.
  • Choices to set series labels according to the  meaning of quantities, for example, Cumulative Adoptions can be installed Base, Systems/Devices-in-Use or Subscribers depending on the type of product/service being modeled.
  • Database of example Bass Model parameters for historical products and services.
  • Option to add calculations for replacement purchases.
  • Option to add calculations for churn.
  • Option to model sub-category mix.

Please make suggestions for features in comments.

How I Built this Gadget

In general, I used Microsoft Visual Studio 2013 to create a Silverlight gadget, which is hosted in this blog page. The Silverlight gadget is based on three Telerik Silverlight controls: ChartView, Spreadsheet and RibbonView as well as sliders, buttons and textboxes.

The Export to Excel features implemented here was particularly simple to do because the Telerik Silverlight Spreadsheet control supports exporting the grid contents to Excel.  It also supports exporting to Csv and Txt formats, which I will implement soon.

Because it has some particularly desirable features, I am considering using the  SpreadsheetGear for Silverlight instead of the Telerik Spreadsheet control; however, I am concerned about responsiveness on updating the grid and charts when using the Bass Model parameter sliders.  That will require some testing, which I will share in a future blog post.

Microsoft Will Give the Finger OS to Its Competitors

But Is It Just a Rumor?

The rumor is building at Build 2014 that Microsoft will announce the Finger operating system for smart gloves, which it will give to Apple, Google, Samsung and pretty much anyone else who wants it.  Microsoft has been practicing giving  the Finger to these and other companies for years, so this is no surprise.

This rumor was first broken on this site yesterday April 1st in the article Wearable Smart Glove Annual Shipments Will Pass 300 Million Units in 2100.

I’ll be watching Build 2014, Microsoft’s annual developer conference today  on Microsoft’s Channel 9 and will report back to you if there is further news on the Finger.

Wearable Smart Glove Annual Shipments Will Pass 300 Million Units in 2100

Samsung Launches the Wearable Smart-Glove Category

Today, Samsung and HTC showed the first wearable smart gloves. is forecasting that wearable smart-glove annual shipments will pass 300 million units in 2100 and will be commonplace in homes and business around the world.

Smart Glove Shipments

However, because new software apps will be required to make use of these products, the smart-glove market will develop slowly with only negligible sales until 2020 when 100,000 smart gloves will be sold.  After 2020, the smart-glove market will gain momentum until, after 80 years of steady growth, sales will top 300 million units in 2100.  PCs required only 35 years to top 300 million units per year; however, the smart glove market will develop more slowly than did PCs because of the complexities involved in fitting users diverse requirements in smart glove sizes, styles and colors not to mention applications and capabilities.

By 2100 the smart-glove market will have reached 76% penetration of the 1 billion hands potential market with 759 million smart gloves in use.Smart Gloves in Use

Assumptions for Forecast Model of Wearable Smart Gloves Using the Bass Diffusion Model

This forecast makes the following assumptions:

  • The potential market for smart gloves is 1 billion hands.  This seems reasonable since there about 7 billion people in the world and the vast majority have two hands making an earthly universe of 14 billion hands.  Since there are now more than 1 billion PCs in use worldwide, it does not seem a stretch to predict that eventually there will be 1 billion smart gloves in use — after all there are twice as many hands as there are people.
  • The replacement rate for smart gloves will be about like that of smartphones — an average of every two years with the distribution: 25% after one year, 50% after two years and 25% after three years.
  • The penetration of smart gloves will develop at about half the speed of PCs and cellphones because smart gloves are not one-size-fits all devices.

Rumor: Microsoft Will Give the Finger OS to All Its Competitors for Use in Smart Gloves

At Build 2014, Microsoft will announce the Finger operating system for smart gloves, which it will give to Apple, Google, Samsung and pretty much anyone else who wants it.  Microsoft has actually been practicing giving the Finger to these companies for years, so this is no surprise.

Download Bass Model of this Forecast

Download Excel Model of Wearable Smart Gloves Forecast Using the Bass Diffusion Model

Wishing You Forecast Joy on this April 1st



Wearable Computing Unit Sales Will Decline 20% in 2015. Really?

This Wearable Computing Forecast Makes a Common Mistake

Why do professional forecasters do it?  Are they lazy or just ignorant?  I don’t know, but here is how it goes.

Consider the forecast published recently by Business Insider in the article

The ‘Internet Of Things’ Will Be Bigger Than The Smartphone, Tablet, And PC Markets Combined.  The BI  graph (below) shows the installed base of devices in several categories.  “Installed base” is simply the count of devices in use by year.

Internet of Things Installed BaseBI supplies an Excel file from which I extracted the data for wearable devices in use, which is graphed (below) as a line graph.

Wearables Devices in UseThe Wearables Devices in Use graph, as expected, looks like the beginning of a classic s-curve: starts low and rises steeply.  Although not shown on the graph, eventually this curve will flatten as the market approaches saturation or as the product is replaced by another type of product, in which case, devices in use may even decline.  The wearables market is at a very early stage and, if PCs and cellphones are good analogies, will have a run of at least 15 years before any sustained flattening takes place.

Let’s explore this wearables forecast a little further.  This Wearables Devices in Use series contains implicit information about Unit Sales of wearable devices  by year.  To dig it out we need a few definitions:

  • Wearable — a wearable computing device.
  • User — an owner of one or more Wearables.
  • Use — a function (or related functions) for a Wearable.  A Use is often defined by the location on the User’s  body (e.g., eyeglasses. watch).  A User may have one or more Uses.  A Device in Use is counted as one Use.
  • Potential Use — a Use that is not yet served by a Wearable device.
  • Devices in Use — the count of Wearable devices that are owned by Users and have not been retired (taken out of use).
  • Installed Base — same as Devices in Use.
  • New Use Unit Sales  — the number of Wearables sold in a given year for a Use that had previously been unserved.  New Use Unit Sales in a year is Devices in Use for the year minus the prior year’s Devices in Use. This is “Adoptions” in diffusion forecasting models.  The cumulative sum by year of New Use Unit Sales is Devices in Use (Installed Base) by year.  If needed, these quantities can be adjusted for forecasted Attrition by year.
  • Replacement Unit Sales — the number of Wearables sold to replace previously purchased Wearables.  A Replacement Unit Sale does not increase the number of Devices in Use.
  • Unit Sales — The Total of New Use Unit Sales plus Replacement Unit Sales.
  • Attrition – Uses that had been counted in Devices in Use in a prior year but are no longer in use; for example, a computer watch that was thrown away and not replaced.
  • Net New Use Unit Sales — If Attrition is included in the model, Net New Use Unit Sales is New Use Unit Sales adjusted by Attrition.

In the early years of a market, such has that being consider here, Replacement Purchases and Attrition are typically low; therefore, New Devices in Use is essentially Unit Sales.  In the graph below, notice that Wearables Unit Sales increases, then declines and continues flat.  Really?

Wearables Unit SalesTo better illustrate this unfortunate surprise calculate Unit Sales year-over-year growth rate (below).  Notice the negative growth in 2016. The jaggies in these charts are also unexpected. Historical data can be expected to have its ups and downs due to the unpredictable nature of complex systems. But, the forecaster has not yet been born who can justify forecasting jaggies like these. “Something is rotten in the state of Denmark.”

Wearables Unit Sales Growth Rate

Why Did BI Forecast that Wearable Computing Unit Sales Will Decline 20% in 2015.

The answer is: they surely didn’t mean to.  But, by estimating an Installed Base curve without attention to the implicit Unit Sales curve, they made a rather ridiculous forecast.  They are not alone in making this blunder.  It is all too common in the forecasting business.  I, too, have been there and done that — and, have been sufficiently embarrassed that I gave up such shortcuts many years ago.  When I see this mistake in a forecast, for me, the entire forecast has no credibility and should be considered only as an opinion that a new market will grow.  The Installed Base data points are not worth the bits they are printed on.

Why, Why, Why?  It Is So Much Easier to Do It Right!

The correct way to do a forecast, such as a forecast for Wearable devices, is to first forecast Unit Sales.  In the early years of a hot new market, forecasted Unit Sales should increase annually while the growth rate should gradually decline but is never forecasted to be negative.  Only in a mature market, when a product is being replaced by another (e.g., desktop PCs being replaced by laptops) should negative growth rates be forecasted.  Second, the forecasted Unit Sales by year are then summed cumulatively to yield the Devices in Use (Installed Base) curve.  If important, Devices in Use and Unit Sales can be adjusted by forecasted Replacements and Attrition.  By forecasting a nice smooth curve for Unit Sales first, the cumulative, which is Devices in Use, will be a nice smooth s-curve.  If, as BI did, the Devices in Use curve is estimated first, the Unit Sales curve will likely be weird.

An even better way to build a forecast for a new product  is to use a diffusion model (e.g., the Bass Model).  The diffusion model parameters can be varied until reasonable forecast curves are obtained.  A diffusion model for Wearables will simultaneously forecast Devices in Use and Unit Sales, as well as the penetration curve, years to saturation and the potential market size.  Soon I will  do this for wearables in another blog post using a downloadable Excel spreadsheet tool as well as an interactive Bass Model tool.

You May Quote Me:

“In forecast curves, only the past is jagged — the future is smooth.”