In this particular case, we are assuming that the tornado shows the NPV of a project. We expect the project can be valued at $7 billion (the point where the vertical axis crosses), subject to uncertainties.

The tornado helps visualize these uncertainties. In the example, Conversion (i.e. how many of the people that shop for our product become a customer) is the largest uncertainty. We believe 35% of the shoppers would convert. If only 25% convert, the project’s NPV would drop to $4 billion, from the base case, $7 billion. On the other hand, if 45% convert, we have a large upside and the NPV would be $12 billion.

Next in relevance would be pricing, $25,500 in the base case. If it goes down to $20,500 the NPV would reduce to $5 billion. If we can raise price up to $29,500 due to a favorable competitive environment, then the upside is $4 billion from the base case.

By now, you can follow the logic of the chart, with the other variables.  Do you still have questions?  Go ahead and drop us a line.  We are happy to help.

Tornado diagrams are not used as frequently as one would expect, given how clearly they help showing the impact of different variables on a geven outcome. As suggested by Ted Eschenbach on a recent article of Engineering Economist, (issue of 06/22/2006), perhaps this is due to difficulties in constructing them.

Sensitivity analysis is needed to address the inherent uncertainty in engineering economy applications because (1) time horizons are measured in years or decades and (2) much economic analysis is done at the feasibility and preliminary design stages. This is often shown using relative sensitivity analysis charts or spiderplots, which have a long and rich history in practice and texts (they are described in 10 of 18 texts reviewed, including Blank and Tarquin (2002), Canada et al. (1996), Eschenbach (2003), Lang and Merino (1993), Park (2002, 2004), Sullivan et al. (2003), Thuesen and Fabrycky (2001), White et al. (1998), Young (1993). Tornado diagrams are not new, but they have not been used nearly as frequently. Only one of the 18 texts included a tornado diagram (Eschenbach, 2003)–

 

Searching Google on how to make tornado charts, you’ll get many results, most of them requiring you to download an add-in. Keep reading to see how you can create tornado charts with plain Excel in just 5 steps… very easy and straightforward!!

There is no need for any external add-ins for making good-looking tornado charts. And it takes only 5 steps. Let’s start with data in a table like this:

The data in rows 3 to 7 show the key levers or sources of uncertainty for the model, as explained before.

In columns B and C we put the lowest and highest values for the model output, changing only the given variable.  As discussed above, for conversion, if it is 25% (down from 35% base case), the NPV is $4b, not $7b. This is why $B$4 contains a 4.  If conversion is 45%, the NPV is $12b

So, once you set up the data in a table like the one shown, here are the promised 5 steps:

1. Select the data, excluding the Delta column
2. On the Insert ribbon, choose Bar. Pick Clustered Bar (first one in the 2-D section)
3. Right-click on the horizontal axis, choose Format Axis. On the bottom of the Axis Options pane look for Vertical Axis crosses:, choose the Axis value radio button, and type your base case value (7 in the example)
4. Without closing the window, choose the vertical axis of the chart. Again on Axis Options, check the box Categories in reverse order, and set the Axis Labels menu to Low
5. Without closing the window, click on any of the bars, which should bring the Series Options pane. Move the slider Series Overlap completely to the right (Overlapped).

That’s it! Now you can format the chart as you like. The final result should look like the chart shown above.

Now, watch a screencast, or download the Excel file

I hope this entry helps you use tornado charts in your decision support models.  Watch the screencast

There is no simple answer, and this post is an attempt to point readers to ways to think about what they want to model, as well as giving helpful resources for further study

In my opinion, one of the best approaches to understand market adoption is through system dynamics. One of the advantages of the methodology is that it allows you to conceptually link business effects and relationships to the equations. I touched on this issue on on a previous entry, and here I will try to explain further.

The logistic equation (shown below) is a commonly used way to model market adoption.

From a System Dynamics perspective, the logistic model can be explained looking at the following model (click for full size): The boxes, called “stocks” in SD terminology, represent an accumulated quantity over time. One way to think of stocks is a bathtub. The amount of water in the tub is the accumulation over time of how much water you added through the faucets, less how much water you let out through the drain.

On the model, there are two stocks: how many potential adopters are out there (left side) and how many adopters are (right side). The pipe that connects the boxes is called a “flow”, and it shows a valve, whose value represents how fast potential adopters turn into actual adopters (thus we call it Adoption Rate). Again, in the bath tub analogy, we can think of the value of the flow as how open or closed the faucet is.

Adoption rate depends on how big the population is (the larger the population, the larger the adoption rate), how much the adopters interact with potential adopters (creating the “word of mouth” benefits), etc.

As stocks are accumulations of whatever flows in minus what flows out, from a mathematical perspective, the value of a stock is calculated integrating over time the values of the net flow. On the logistic model, the arrow that links the stock and the adoption rate flow means that the flow changes proportionally to the stock – i.e. if I have more potential adopters, there are more possibilities for contagion, when a user talks favorably to a potential user about the product. The net result is an exponential behavior, which, after some mathematical reduction, is represented by the formula above.

If I want to explain a business audience some market adoption dynamic, it possible to do it talking in terms of stocks and flows (once the audience is comfortable with these terms). It’s almost a guaranteed failure if I try to explain it by using a mathematical formula with exponentials and integrals

The Bass model addresses one limitation of the simple logistic model, regarding how the system “gets started”: with no adopters, there is no chance for interactions, so there is no inflow to the adopters stock. It does it through the use of an external force, like advertising.

Below is a Systems Dynamics interpretation of the Bass model. As you can see, the only difference is that now the Adoption Rate is the addition of two elements, adoption rate from advertising and adoption rate from word of mouth. The latter is exactly the same as the AR in the logistic model.

Returning to Reader Vince’s specific question on how to extend the logistic or Bass models to comprehend effects like cross-segment interactions, I would frame it like this:

• Identify the most important cross-segment interactions – How much “cross-shopping” exists between the segments? (using data like second choice selection); are there characteristics of the upper segment that consumers will translate into the lower segment favorably/unfavorably? consumers replace their vehicles within segment or they try to go up segment? etc.
• Incorporate the key cross-segment interactions on the model – They will most likely affect the Adoption Rate. It also may be necessary to model another stock or stocks (Upper Segment Adopters and Lower Segment Adopters, for instance)
• Check sensitivity of cross-segment assumptions – Understand how different the results are when the cross-segment assumptions are considered versus when they are not. What are the assumptions that most impact the results? A tornado diagram, as discussed in a previous entry, may provide a good way to show the sensitivity to the assumptions

As more dynamic effects are considered for inclusion in a model, it is better to move from a tool like Excel to something like Vensim, or iThink. Chapter 9 of John Sterman’s excellent book “Business Dynamics” talks about both the logistic and Bass models as shown here, and expands on ideas on how to extend them.

Here are some other very good references on the topic

• Forrester, J. W. 1980. Information Sources for Modeling the National
  Economy. Journal of the American Statistical Association 75 (371):
  555-574.
  Argues that modeling the dynamics of firms, industries, or the economy requires use of multiple data sources, not just numerical data and statistical techniques. Stresses the role of the mental and descriptive data base; emphasizes the need for first-hand field study of decision making.
• Legasto, A. A., Jr., J. W. Forrester & J. M. Lyneis, eds. 1980. System Dynamics. TIMS Studies in the Management Sciences. Vol. 14. Amsterdam:
  North-Holland.
  Collection of papers focused on methodology. Includes Forrester and Senge on Tests for Building Confidence in System Dynamics Models and Gardiner & Ford’s discussion on Which Policy Run is Best, and Who Says So?
• Randers, J., ed. 1980. Elements of the System Dynamics Method.
  Cambridge MA: Productivity Press. Includes Mass on Stock and Flow Variables and the Dynamics of Supply and Demand; Mass & Senge on Alternative Tests for Selecting Model Variables; and Randers’ very useful Guidelines for Model Conceptualization.
• Richardson, G. P., and A. L. Pugh, III. 1981. Introduction to System Dynamics Modeling with DYNAMO. Cambridge MA: Productivity Press.
  Introductory text with excellent treatment of conceptualization,
  stocks and flows, formulation, and analysis. A good way to learn the
  DYNAMO simulation language as well.
• Morecroft, J. D. W. 1982. A Critical Review of Diagramming Tools for
  Conceptualizing Feedback System Models. Dynamica 8 (part 1): 20-29.
• Critiques causal-loop diagrams and proposes subsystem and policy
  structure diagrams as superior tools for representing the structure of
  decisions in feedback models.
• Roberts, N., D. F. Andersen, R. M. Deal, M. S. Grant, & W. A. Shaffer.
  1983. Introduction to Computer Simulation: A System Dynamics Modeling
  Approach. Reading MA: Addison-Wesley.
• Easy-to-understand introductory text, complete with exercises.
• Homer, J. B. 1983. Partial-Model Testing As A Validation Tool for
  System Dynamics. In International System Dynamics Conference: 920-932
• How model validity can be improved through partial model testing when
  data for the full model are lacking.
• Sterman, J. D. 1984. Appropriate Summary Statistics for Evaluating the
  Historical Fit of System Dynamics Models. Dynamica 10 (2): 51-66.
• Describes the use of rigorous statistical tools for establishing model
  validity. Shows how Theil statistics can be used to assess
  goodness-of-fit in dynamic models.
• Forrester, J. W. 1985. ‘The’ Model Versus a Modeling ‘Process’. System
  Dynamics Review 1 (1): 133-134.
• The value of a model lies not in its predictive ability alone but
  primarily in the learning generated during the modeling process.
• Richardson, G. P. 1986. Problems with Causal-Loop Diagrams. System
  Dynamics Review 2 (2 ): 158-170.
• Causal-loop diagrams cannot show stock-and-flow structure explicitly
  and can obscure important dynamics. Offers guidelines for proper use
  and interpretation of CLDs.
• Forrester, J. W. 1987. Fourteen ‘Obvious Truths’. System Dynamics
  Review 3 (2): 156-159.
• The core of the system dynamics paradigm, as seen by the founder of the field.
• Forrester, J. W. 1987. Nonlinearity in High-Order Models of Social
  Systems. European Journal of Operational Research 30 (2): 104-109.
• Nonlinearity is pervasive, unavoidable, and essential to the
  functioning of natural and human systems. Modeling methods must
  embrace nonlinearity to yield realistic and useful models. Linear and
  nearly-linear methods are likely to obscure understanding or lead to
  erroneous conclusions.
• Barlas, Y. 1989. Multiple Tests for Validation of System Dynamics Type
  of Simulation Models. European Journal of Operational Research 42 (1):
  59-87.
• Discusses a variety of tests to validate SD models, including
  structural and statistical tests.
• Barlas, Y., & S. Carpenter. 1990. Philosophical Roots of Model
  Validation: Two Paradigms. System Dynamics Review 6 (2): 148-166.
• Contrasts the system dynamics approach to validity with the
  traditional, logical empiricist view of science. Finds that the
  relativist philosophy is consistent with SD and discusses the
  practical implications for modelers and their critics.
• Wolstenholme, E. F. 1990. System Enquiry – A System Dynamics Approach.
  Chichester: John Wiley.
• Describes a research methodology for building a system dynamics
  analysis. Emphasizes causal-loop diagramming, mapping of mental
  models, and other tools for qualitative system dynamics.
• Mass, N. 1991. Diagnosing Surprise Model Behavior: A Tool For Evolving
  Behavioral And Policy Insights (written in 1981). System Dynamics
  Review 7 (1): 68-86.