The simplified market adoption model I described on previous postings (1,2) is an Excel implementation of a kind of logistic function. The Bass model is one of the most popular models used in marketing, and management of technology to think about product introductions. (See Wikipedia article). From a mathematical perspective, when the parameter p is 0, the Bass model reduces to the logistic function.
What is most interesting, from a business perspective, is how you arrive to each of those functions by modeling real-world interactions. On both models, you can conceptualize the world as two different pools of people (or stocks, in the system dynamics terminology). One is the pool of potential adopters, and the other is the pool of adopters. The flow between these two pools is controlled by the adoption rate, a variable that models how probable is that a potential adopter becomes “infected” by a current adopter. On the logistic model, it depends solely on how much they interact, how big the total population is, and how “contagious” the product is. On the Bass model, an additional parameter accounts for external factors, the most common being advertising. The Bass model overcomes what is called the startup problem of the logistic model: how a initial base of zero adopters can spread “infection” of the product.
There are more refinements that can be done to the Bass model: accounting for changes in the total population over time, learning and experience curves, etc. For projects where the sensitivity of the model to these factors is high, I definitely recommend to spend more time calibrating your model, understanding which of the different available curves fits better any data you may have, and most critical of all, whether the chosen coefficients for any of the functions have strong impacts on the critical business issues you want to model — capacity planning, pricing, profitability, etc.
For many projects like business plans, revenue projections, etc. I’m willing to sacrifice the ability to fine tune parameters in a model like the BDM for the clarity provided by a model like the Excel logistic function I described. I can generate more tangible conversations with executives by discussing what they believe will be the takeover time, when they believe it will be the start of the fast growth, how much share they believe will be reached in steady state, etc.
Mekko charts are two dimensional graphs that analyze how data is partitioned against two variables, the X and Y axes. The width of the columns is proportional to data represented by the columns. Individual segment height is a percentage of the respective bar total value.
Two improvements over the technique described by Juice Analytics and posted in Lifehacker: better resolution and solid-looking bars that show better at different font sizes.
If your values are integers in a range 0-9 or so, you can use the REPT formula as presented there, and perhaps you like the dashed type bars, so the formula as shown would work perfectly for you. If not, keep reading.
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I’ve got a number of questions on the simplified Excel s-curve formula I published some time ago, so here are more details for those interested in the math behind it. The previous posting focused on how business analysts sometimes need to model market adoption, and provided a simple and easy to maintain formula to do so in Excel.
The formula =saturation/(1 + 81^((hypergrowth + takeover/2 - year)/takeover)) suggested for Excel is a simplification of the formula for a sigmoid function (See the Wikipedia article)
The graphic below shows the shape of both functions is identical. The saturation parameter just scales the function to a desired value, instead of going from 0 to 1. The factor 81 on the Excel formula determines how “sharp” the curve is, in this particular case, reaching 0.1 at the period hypergrowth and 0.9 at hypergrowth + takeover. Note that 81^x can be re-written as e^(ln(81)*x), so whatever factor is used there is simply going to affect the shape by compressing or expanding it horizontally.
This is how the scaling factor can be computed. Let’s say we want the penetration to be 5% at the period specified by hypergrowth. We can work out the solution off the second function. We need to solve for 1/(1+e^(-x) == 0.05, which gives x=-2.94444. Since the function is symmetrical, we also know for x=2.94444 P(x) == 0.95.
Since factor^((hypergrowth + takeover/2 - year)/takeover)) can be re-written as e^(ln(factor)*(hypergrowth + takeover/2 - year)/takeover)), we can solve ln(factor)*(hypergrowth + takeover/2 - (hypergrowth + takeover))/takeover == 2.94444. Reducing all the math, we arrive to
1/(1 + e^(-0.5*ln(factor))) == 0.95, and factor would be 361. If the desired penetration at hypergrowth is 20%, then we solve 1/(1 + e^(-0.5*ln(factor))) == 0.80, leading to factor == 16
This weekend I set up a backup wireless connection using my Bluetooth cell phone (Motorola RAZR v3xx). Pretty painless, thanks to Ross Barkman’s scripts, and Ed Thomson’s post.
More or less standard modem configuration. I had almost forgotten about such old good times when you had to deal with modem connection strings and those type of things.
Anyway, the process was:
- Downloaded the Motorola GPRS modem scripts from Ross Barkman’s page into /Library/Modem Scripts
- If you are trying to follow these instructions, but have not paired the phone already, you can do it now and the Bluetooth Setup Assistant will guide you through the steps. If you had already paired the phone, then from the Bluetooth menu item, you can choose “Open Bluetooth Preferences” to open the Bluetooth Setup Assistant. Here I was able to configure the phone.
- The specific settings I used:
- Account Name: ISP.CINGULAR, which should allow me to use the GPRS 128k/sec service, or ISPDA@CINGULARGPRS.COM
- Password: CINGULAR1
- Modem type: Motorola GPRS CID1 (will only appear with Ross’ scripts
My speed test was OK: 690-860 kbps downstream, and 220 kbps upstream with delays of up to 220 ms. Not a T3, but quite acceptable for occasions where I have no other net access
I’ve had a couple of issues using ISP.CINGULAR, where after 3 or 4 times of connecting fine, it stopped connecting. Last 2-3 times I’ve used ISPDA@CINGULARGPRS.COM it seems to work better, and with the speed described above
With both of the address, there is something causing the first connection attempt to fail. Perhaps I’ll look into it later - my current workaround is not that bad, just reconnecting after it fails once.
The guys at Strobist posted today a series of tips on how to get the most out of your webcam. Very interesting. One thing that still is puzzling me is why after I installed Windows XP on our 17 inch iMac with BootCamp 1.2, the quality of the webcam image on Windows is better than what I’m getting on MacOS!! Really strange.
The Windows drivers that come with BootCamp make a USB emulation of the built in iSight, and perhaps there is either some color correction done during the emulation, or what would be most ironic, that the color correction algorithms on MacOS are actually trying too hard to compensate and end up making the image worse.
That iMac’s setting is problematic for video conferencing because the iMac is in the opposite side to a window, and facing the wall. The back light coming through the window creates a dark webcam pic. If anyone has solved this problem, I’d love to know.
The sites I refer to when I talk about charting, data analysis and good (and bad) charting techniques are normally quite different from the ones where I satisfy my gearhead lust with the news from the latest car models in the market. This time the guys at motortrend did it for me in their article “Finding the best-handling car in the US”: both fixes in just one page 
Look at the following chart: well, it’s easy to tell the winner on their tests is the yellow line (if you are curious, the Porsche 911GT3). But can you tell from the green and red lines in the middle of the pack which one is better?
If you go to their gallery, you’ll see many other charts that fight fiercely for the top place in the Junk Chart museum. Just a couple of samples below
Spider charts may be useful, but only in very limited cases. Leave the webs to the guy in the custome, enjoy the movie, and stick to other chart types in your professional reports. You would be better off. Your audience will get it faster.
Read on to see a proposal on how this chart could be better.
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UPDATE 10/31/2007: Here is a screencast for this model
Often business analysts need to model the adoption of a new product or service for financial planning. There are several approaches, but a common one is the s-curve (see Wikipedia article). Here is a simple implementation in Excel that can be easily added to your spreadsheets. It reduces all the math to just three parameters:
- saturation - What is the maximum expected penetration after the product becomes mainstream? i.e. what is the value that the top of the s-curve will reach?
- start of fast growth - By this year, the penetration will be 10% of the saturation value, and it will start to grow rapidly. 10% was an arbitrary choice to simplify the model, and by doing some math you could change the formula to any value. It is a reasonable choice in most cases. We’ll call this parameter hypergrowth
- takeover time - How long it will take for the product to “catch on”? - The operational assumption in the formula is that this number of years after the start of fast growth, the product would have reached 90% of the saturation value and will start to slow down. Again, 90% is an arbitrary value I chose.
The s-curve model focuses in the early phases of the product lifecycle, until maturity is reached. Penetration decay is NOT covered by this model.
The formula for each year’s penetration would simply be:
=saturation/(1+81^((hypergrowth+takeover/2-year)/takeover))
See it in action:
In the sample spreadsheet above, look at cell B8 where you can see the formula in use. It is the same for all row 8.
saturation, hypergrowth and takeover are names defined for the parameters on rows 2 to 5 (you use names in your models instead of plain cell references, don’t you?)
Very simple, easy to maintain, light on calculation times… happy market adoption modeling!
PS: The chart shown is NeoOffice, an open source alternative to Excel for Macintosh users, based on OpenOffice
Martin Theus posts here an example of poor charting or “junk charts”. I’ve had the opportunity to work with many organizations as a management consultant, and it’s sad to report that is more the norm than the exception to see charts like that one in the workplace.
Feeding my bad habit of thinking anytime anytime I see a chart how would I restate it to make it cleaner, here is how I would do it. On top, the original chart, below a proposed improvement.
The key questions, whenever one draws a chart, are “Who is my audience?” and “What is the message I want to communicate to them?”. For such chart, I would imagine the audience are the users of a software system for which we are reporting the different sources of errors”, and the underlying message, most likely, is what are the most relevant sources, so we can fix them.
In the original chart, transparency, 3D and color are used, but they are not adding any new information. The pieces of the pie do not show any meaningful order, either. The audience will have to look at the callouts to see which category corresponds to which piece of the pie, and their work is going to be harder by having to follow the callout lines that in some cases converge.
What makes the second chart better?
- The improved chart uses sorting as a way to help the audience. The largest sources of errors appear first.
- Once the data is sorted, it uses the Pareto principle to focus on the main sources of errors, removing from the audience’s eyes a lot of unnecessary detail. Today’s interactive media allows to drill-down into details with a click. Printed presentations can always have backup charts. Simple is beautiful. The Pareto principle is one of those “business commonsense” things that almost everyone has heard about, to the point is almost a cliche, yet people fail to appreciate how powerful it is.
- The use of color is non-gratuitous. Color is very powerful. Most people can differentiate between colors without effort. But they can also get quickly overwhelmed if many colors are used in a chart. Think twice before adding a new color to your chart. Is it communicating something?
The improved chart has some visual effects, like drop shadows and some color gradient, to make it more appealing. However they don’t work against how easily the message will be understood by the audience, they don’t leave out people with difficulties to tell colors apart, and they will not break when you make a black and white printout of the chart.
One thing that can’t be denied is Kerkorian’s persistence to get part of the action in the US automotive industry.
First, his attempt to take Chrysler private in the early nineties followed by the 2003-2005 drama of a Kerkorian-initiated federal lawsuit in which he charged that he had been deceived by DaimlerChrysler management, winning his support for the $36 billion deal in 1998 by portraying it as a “merger of equals” when, in fact, it was a takeover of Chrysler by Daimler-Benz.
More recently, when he then tried to broker an alliance between General Motors, Renault of France and Nissan of Japan, and replace Rick Wagoner by Carlos Ghosn.
Now his investment arm, Tracinda Corporation, made a $4.5 billion cash offer yesterday for the Chrysler Group.
The offer looks to obtain winning the exclusive right to negotiate with DaimlerChrysler and a deal with the United Automobile Workers union that could mean worker concessions.
The U.A.W. did not comment on the Tracinda bid, but its president, Ron Gettelfinger, previously said that he preferred to see the company remain part of Chrysler rather than be sold to an investor. Gettelfinger sits on the DaimlerChrysler supervisory board, which will ultimately decide Chrysler’s fate.
