Comments on: Modeling market adoption in Excel with a simplified s-curve

By: Debbie

Debbie — Thu, 24 Jul 2008 13:57:13 +0000

Hi Juan,
Thanks for providing this example. It’s very useful! What I would like to do, however, is to find the gradients of the S-Curve at any desired point. How would I find that using excel, after my Curve has been created?
Thanks!

By: Tim Snijder

Tim Snijder — Thu, 26 Jun 2008 07:42:05 +0000

Thanks a lot for the great example. I want to create an s-curve that I can use to estimate the effects of marketing expenditures on sales. I know that normally this should be based on transaction data. In this case, I don’t have this data so I just want to create a curve where I manually enter saturation levels and base sales (number of sales generated without any marketing expenditures)
Does anybody have an idea how to apply this?

By: Billy

Billy — Wed, 25 Jun 2008 13:29:39 +0000

Hi Juan,
I like the way you have rephrased the parameters of the model to useful inputs that people can work with. I use the Bass curve in new product forecasting using an interactive dashboard to get everyone involved in the ‘what if’ sensitivity analysis process. There is a link to it on my blog page http://acasoanalytics.wordpress.com/2008/06/25/interactive-bass-diffusion-model/ . I’ll have a go at doing the same with your approach.

By: Mathias

Mathias — Mon, 09 Jun 2008 00:01:36 +0000

Hi Juan,
Thanks for your series on the S-Curve, which was most helpful. I needed to be able to specify a curve through any pair of values, and not just 10%/90%, and resolved that question here, in case you are interested. While more flexible, the formula I end up with is also way more complicated / painful, and I would therefore recommend that people stick with yours in general, as it is much more compact and readable!

By: S-shaped market adoption curve

S-shaped market adoption curve — Sun, 08 Jun 2008 20:20:41 +0000

[...] products entering the market would follow a S-curve. After some digging and googling, I came across this excellent post by Juan C. Mendez, where he proposes a clean and very practical way to use the logistic function, and calibrate it [...]

By: Ryan

Ryan — Fri, 16 May 2008 19:31:17 +0000

If you want a generalizable way to specify the penetration level before the hypergrowth starts, you can add a variable “Penetration Level Before Hypergrowth” and use this instead of 81:

((saturation/penetration_before_hypergrowth)-1)^2

In the example above, penetration reaches 3% (or 10% of the 30% saturation) before hypergrowth, so:

(( 30% / 3% ) - 1) ^ 2 = 9 ^ 2 = 81

Cheers,
Ryan

By: Ider

Ider — Mon, 28 Apr 2008 11:44:35 +0000

Hello Juan,
I also want to express my grattitute
Could you explain me about how (in what extent) is it reliable to consider that behaviour of the curve before and after hypergrowth period is same in real business. In other words, in real business can we believe that growth size before and after hypergrowth would be same?
Sorry for my poor English if I couldn’t express my question.
Thank you!

By: Juan C. Mendez

Juan C. Mendez — Fri, 07 Mar 2008 03:12:29 +0000

Phil

Thank you for your message. The modified formula, as you would like to use it would be

=initial_adoption + (saturation-initial_adoption)/(1+81^((hypergrowth+takeover/2-year)/takeover))

Hope it helps!

By: PhilT

PhilT — Thu, 06 Mar 2008 09:48:18 +0000

Hello Juan,

Many thanks for providing a great and comprehensible work around for lpeople (like me) wanting to utilize s curves in an excel model, without really understanding the maths behind it. Could you possibly spell out in idiot proof terms (the idiot being yours truly), the full formula with the ‘initial adoption’ parameter added as per Pushkars mail. It would be greatly appreciated. Thanks, Phil.

By: Juan C. Mendez’s pages » Blog Archive » System dynamics interpretation of the logistic and Bass models

Fri, 21 Dec 2007 19:42:30 +0000

[...] have received a number of comments regarding the Simplified Excel Model for market adoption that I published a few months ago. Reader Vince asked how to extend the math behind it to [...]

By: Juan C. Mendez

Juan C. Mendez — Thu, 01 Nov 2007 02:58:10 +0000

@Donald, @Kevin
I just posted a screencast that should help with your questions

By: Kevin

Kevin — Sat, 20 Oct 2007 07:51:21 +0000

Um…
Excuse me. I have a problem.
How to use the simplified formula in Excel?
Cause I have try various way, but I can’t draw S-Curve.
Could you send me an example?xls? to my e-mail ?
Thank you so much.

By: Donald

Donald — Wed, 19 Sep 2007 17:04:33 +0000

Juan,
I cannot see the formula you have pasted in cel B8.
Where can I find it, if I am may ask?

By: Juan C. Mendez’s pages » Blog Archive » Relationship between the Bass and the logistic market adoption models

Tue, 31 Jul 2007 03:09:27 +0000

[...] 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 [...]

By: Juan C. Mendez

Juan C. Mendez — Sat, 14 Jul 2007 17:22:23 +0000

The folks at provenmodels.com linked to this page as a resource. http://www.provenmodels.com/570 — They are an excellent source of managerial models and frameworks - highly recommended.

By: Juan C. Mendez

Juan C. Mendez — Sat, 07 Jul 2007 03:29:51 +0000

Molly
Thanks for your comment. I posted a note with the math at http://jcandkimmita.info/jc/2007/07/excel/math-on-the-simplified-market-adoption-s-curve-for-excel/
Usually I forget the math when I need to use the formula, and the trick I use is to enter the formula with the factor (81,16,360, etc) as a reference to a cell, instead of a fixed value, then use Excel’s Goal Seek to change that cell until I get the desired value for the period hypergrowth. Finally, I simply replace the formula in all the cells with the computed constant. Good luck with your modeling!

By: Juan C. Mendez’s pages » Blog Archive » Math on the simplified market adoption s-curve for Excel

Sat, 07 Jul 2007 03:22:17 +0000

[...] 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 [...]

By: Molly

Molly — Tue, 03 Jul 2007 14:22:22 +0000

Juan - I know that you have mentioned that the 81 in the formula can be changed to represent different growth percentages in the first part of the tail. Could you tell me how that number is calculated so that I may have the option of choosing any number between 0% and 100% instead of just 10%, 20%, and 5% with 81, 16, or 360.

By: Juan C. Mendez

Juan C. Mendez — Wed, 13 Jun 2007 12:03:09 +0000

Pushkar
Thanks for your comments. Yes, your approach is exactly what is needed. Let’s say you have a product that is already in the market and you’ll roll out new features you expect will drive a significant increase in adoption. This initial penetration may be 5% and you expect the new features will drive to 35% in 7 time periods (months, years,…). Then you would use saturation = 30% (35-5), and add to the formula an initial_adoption parameter as you did, which will be 5%.
By the way, I only used years as an example because I work in the auto industry where product lifecycles are long. The s-curve formula presented can be used with months (electronics lifecycles), days (disease spreading), or whatever time period desired

By: Pushkar

Pushkar — Tue, 12 Jun 2007 21:47:24 +0000

I tried the following approach for incorporating the initial adoption:

Lets say we have the following inputs:
saturation = 100%
hypergrowth = 2
takeover = 5
initial_adoption = 20%

then this can be modeled as:
saturation_new = saturation - initial_adoption
hypergrowth_new = hypergrowth
takeover_new = takeover

and the formula for each year’s penetration will be:
year_penetration_new = + initial_adoption

Essentially, I have scaled down the curve by reducing saturation level and then shifted the curve upwards to include the initial adoption rate.

Do you think this approach should work good?

By: Pushkar

Pushkar — Tue, 12 Jun 2007 21:33:39 +0000

Very nice formula to get the S-curve.
However these curves do not take initial adoption (adoption at t=0) as an input and probably assumes it to be 0. How should I modify the formula so that it takes the initial adoption rate as input as well.

Thanks in advance

By: Juan C. Mendez

Juan C. Mendez — Mon, 04 Jun 2007 05:15:49 +0000

Ken - Thanks for your comment, and sorry for the late response. I had comment notifications off because of a recent slew of spam.
If you want an s-curve that reaches 20% (of the saturation value) in the first part of the tail (i.e. by the period denoted by the parameter hypergrowth), you can use 16 instead of 81 in the formula. Such curve will only reach 80% at the period hypergrowth+takeover, and it will look much “softer”. A “sharper” curve, that reaches 5% in the first part, grows and reaches 95% at hypergrowth+takeover can be obtained using 360 instead of 81.
Best regards, Juan C.

By: Ken J

Ken J — Wed, 30 May 2007 14:31:17 +0000

Very nice. Simple and practical. I always get customers questioning the shape of the S curve and this is a great way to do it.

One question I have is 81. I assume you get to this based on your 10% in the first part of the tail. What do I use if I want 20% in the first part of the tail?