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

The Devil’s guide to spreadsheet creation

1. Just do it. Jump in and do it. The users will have to accept whatever you produce anyway.
2. Fire, then aim. You know what is really needed without having to ask.
3. Never simplify (that just makes it easier for other people to get your job); just keep adding bits without removing old stuff.
4. Deadlines live on.
5. Documentation is for wimps; specifications are for the timid.
6. Don’t obtain test data; whatever the spreadsheet result is, is right.
7. Don’t protect the sheet; that restricts the users’ right to improve your formulas by typing in what they want.
8. Don’t fill in the properties sheet, they’ll find out you were the author.
9. VBA (Very Buggy Application) debugging is easy; just keep making changes until something appears to work, then your responsibility is finished.
10. Never use in-cell comments or help text on the page; users should just know what to do.
11. If you know what units of measure are used, you can safely assume everybody else does too.
12. Mix input data with calculation cells to keep the users on their toes.
13. Never mix absolute and relative references, it can shorten billable time.
14. Hide some data in cells so that when users trip over it, their respect for your cleverness increases.
15. If asked to do a test run, ask “Don’t you trust me?”
16. Format with as many decorative colours and styles as possible, to relieve boredom.
17. Don’t keep backup copies of different versions of a spreadsheet, the latest is always the best.
18. Hardcode constants in formulas; after all, they don’t change.
19. Cross-tot checking is merely redundant calculation.
20. To test a spreadsheet, you only need to check whether the answers look reasonable.

Great list! I can’t recall a day when I’ve not seen a spreadsheet that evidences 3 or more of these

Recently reader Mina asked how to use the Excel model in the context of project management. The particular question is: if the project duration changes from 18 to 48 months, what is the new spending curve? Fast and quick answer would be – it’s not applicable. This post will take the question for a spin, though.

First off, the PMBOK, or Project Management Body of Knowledge, tries to standardize and unify the terminology that PMPs use when managing projects. The term used to refer to the spending curve, along the life of a project is called “s-curve” in the PMBOK, just because in real life, projects tend to have low budgetary requirements in the early stages (you are framing the project, defining what will be done, etc), then a bulk of spending in the middle, and finally, low requirements again at the end. With that general pattern, the cumulative spending plan roughly looks as an s-curve.

In most cases, the easiest way to answer the question would be to look at your Gantt chart, estimate which are the tasks that will be delayed/extended, and regenerate an spending curve.

If you are not actually managing the project, but instead you are doing analysis on “what ifs” regarding projects where you don’t have the actual list of tasks, or you are doing portfolio management and you are forecasting across a portfolio of projects with different life spans and budgetary needs, you may be fine using a logistic model. Your needs may be different.

With that preamble, here we go. I’m going to use the estimate percentages of spending in Mina’s question

The process will be quite simple:

1. Fit the data to a logistic model
2. Apply the derived model to the new project duration
3. Infer the spending by month under #2

An Excel file to do this can be downloaded here. By downloading it, you are agreeing that any damages, consequential or incidental arising from using this file or the information in this post are your sole responsibility, and you explicitly releases me from any liability.

If you look at the table below, the first two columns are the data provided by Mina, the third column just adds up previous spending, then column D uses my simplified Excel logistic model =saturation/(1+sharpness^((hypergrowth+takeover/2-year)/takeover)) to forecast the cumulative spending, and column E is simply the square of the difference between C and D. The formula for E2 is =(C2-D2)^2. We’ll use the sum of minimum square of errors to fit the curve, to keep things easy. Other fitting techniques are OK too.

Excel Table showing the process

Then we use Excel Solver, to minimize E21, subject to the condition that $D$19=1, by changing saturation, hypergrowth, takeover, and sharpness (C21 to C24). Fill in the most realistic guesses you can find for these parameters before running Solver. Given the technique Solver uses, your guess of sharpness will be barely modified (if at all), so spend some time looking at your data and tweaking manually.

As you can see in the image below, this step fitted the cumulative spending curve to the logistic function.

Fitted s-curve logistic function to data

Column F in the table just infers the spending by month by subtracting the cumulative on each period to the cumulative on the previous one. As you can see below, even if the cumulative curve fitted more or less nicely, the inferred monthly spending may look surprisingly different to the original.

Monthly spending curves side by side

You’ve got to remember, all models are a simplification of reality, to extract the things that are important for the particular use of the model. As mentioned above, if you are doing “what if” analysis or portfolio management, this simplification may be acceptable and the differences are not a surprise to you.

Finally, we define two new constants newhypergrowth=hypergrowth*newlength/oldlength, and newtakeover=takeover*newlength/oldlength which simply allows us to use the s-curve over a longer time span. The new cumulative spending (across months 1-48 in the example) would be =saturation/(1+sharpness^((newhypergrowth+newtakeover/2-newyear)/newtakeover))

I have attended his seminars, and definitely recommend his method. For anyone interested in improving their presentation skills, and generating action out of their presentations, it is must-read.

It allows students to experience first-hand how structure of business organizations impact their behavior, to some extent irrespectively of how skilled their managers may be. In the game, a 3 tier distribution system delivers beer from a factory to consumers. Only the retailer knows the consumer demand. As information and goods propagates through the chain with delays, oscillation occurs.

Students play competitively, as a pool of money collected from them at the start of the game will be awarded to the winners. A very entertaining and active dynamic develops during the 4 hour exercise.

The Systems Dynamics Society offers kits for playing the beer game, that I recommend. They include everything you need to run the game, as well as videos of Professor Sterman running a session.

I have attended many of his sessions, both as student and observer – my employer sponsors the Beer Game during incoming MBA orientation at MIT. Professor Craig Kirkwood at Arizona State University also has very good materials and hints.

I decided to run with a low-budget version that uses beans, pieces of paper and boards printed on common plotter paper. Everything is in Spanish language. I believe publishing the materials here may be useful to colleagues in Latin America and other Spanish-speaking countries.

Here is the board for the game, and here are the slides

For editable versions of these files, please contact me directly.

Avg_Profit = (1000*1200 + 200*300 + 500*2500 + 10*600 + 100*300) / (1000 + 200 + 500 + 10 + 100)

or

Avg_Profit = SUMPRODUCT(UnitsSold,ProfitPerUnit)/SUM(UnitsSold)

I’m using Excel notation, and assuming it is clear from the context that UnitsSold is a range that covers the second column, for all models, etc.

A less known way of averaging are Harmonic Averages. It is relevant when the data to aggregate is actually a ratio whose denominator is proportional to the weighting factor. A typical case is miles per gallon (MPG) for a bunch of vehicles. Gas consumption is directly proportional to the number of units.

Let’s add some MPG data to the table above.

Using Weighted Averages for an inverse ratio like MPG is plain wrong (24.3 MPG is NOT the average fuel economy)

The right thing is to use Harmonic Average:

Harm_Avg_MPG = (1000 + 200 + 500 + 10 + 100) / (1000/22.5 + 200/15.0 + 500/32.0 + 10/12.0 + 100/24.0)

As Excel doesn’t have a similar function to SUMPRODUCT for adding 1000/22.5, 200/15.0, etc. I will not use Excel notation, but plain math notation:

UPDATED formula

If you have to deal with Harmonic Averages, you may find interesting this note on how to do PivotTable Multidimensional Analysis with Harmonic Averages. There’s a similar one for Weighted Averages as well.

Let me know what you think.

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.

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.

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.

For larger values, when you reduce them to a 0-9 range by dividing by a factor, you can use the decimal part to show a half character, having effectively 20 steps on your bars, instead of just 10 you would get with the simple “|” character. The trick is to use unicode character 0×2588 (dec 9608) that will show a full block, and character 0x258c (dec 9612)that will show a half vertical block.

To get those unicodes you can hold and press the Alt key (Windows PCs), then type 09608 or 09612on the numeric keypad, then release the Alt key. For most, this should work with the default input methos. Unfortunately this method is not universal and depends on selected settings and input methods. You can just go to a Excel cell, choose the menu “Insert->Symbol” and type 2588 or 258c on the box at the bottom reading “Character code”

Finally the formula to use is
.

I’m showing above a picture so the formula shows well in your browser regardless of pagecodes. To copy and paste, here it is as text:

=REPT("?",TRUNC(D6/scale))&IF(MOD(D6/scale,1)>0,"?","")

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

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

In their sample chart, there’s only one bar and one line, so many people may ask “why bother?” — it’s not that confusing to have the overlay in the default way Excel will leave the combination chart.

The chart below is a good example of why the technique is powerful. Click to see full size. Disclaimer: as this is an excerpt from a slide, the sample is missing a lot of must-have elements of a good chart, like units, meaningful title, etc.

When showing a market and how it is partitioned across players, there are some useful elements you’d like to show:

• Is it a growing, stable or shrinking overall market?
• What is our share? Is it growing?
• How are competitors doing? Are there changes that merit closer understanding?

Most common charts I’ve seen people use for the problem are:

• One pie chart with the last year figures. Ok, but you miss the interesting historical perspective
• Two pie charts side by side. That one hurts my eyes! There are many reasons it’s a bad representation. People are not intuitively good at comparing areas. Requires a lot of effort to follow where in each chart is each player, and how is it doing relatively to competition… enough said!
• Stacked column charts. This is a reasonable approach. Shows the trends nicely. It is hard for people to judge the relative percentage of the bar segments, so sometimes people end up with the percentages annotated in each segment, and in that case the chart is very busy
• Lines showing the share. Basically, the bottom part of the chart shown. It is a nice approach, you can follow what happened to the market players along time. In stable markets, may be all what is needed. The chart may be misleading though in growing markets because it loses the overall market size.

The combination of a bar chart to show the overall picture, plus lines to show the individual player trends has the best mix of good features I’ve found. I’d love to hear suggestions on other ways to approach the problem. It is not easy to spot growth in absolute volume for a given player, but in this is not usually a major drawback. If you are happy with your 3% growth and the market has been growing at 45% you’ll be soon out of business. Talk about charting failure

That answers the question “What is the source of your data?”. More often than not, when you have to support your analysis, its also handy to know “Where is the source of my data?”. My recommendation decks are usually in Powerpoint, and I only sparringly use Office’s embedded file feature, so what is on the slide is just a picture of the spreadsheet, chart or table.

My source notes usually look as shown below:

The way I recommend analysts in training to do it is through the CELL function in Excel.

=CELL("filename")

The formula above will print the whole path and filename of the file. If you want only the filename, you can use

MID(LEFT(CELL("filename",A1), FIND("]", CELL("filename", A1))- 1), FIND("[",CELL("filename", A1))+1, 255)

Users of OLAP systems are very aware of multidimensional data. However, many spreadsheet users are not, so they manage to flatten the data the best they can, using pages or subtotals for dimensions beyond the second one.

Modern spreadsheets have “PivotTable” capabilities, which makes easier to deal with multidimensional data. To feed these pivot tables, the information has to be normalized. This post explains how to normalize data from non-normal representation, using a Visual Basic macro

If you are familiar with OLAP and normalized data, skip to the code. I’ll show samples of non-normalized data, how the same data would look normalized, and why this recipe is useful.

Very often people provide me with data on Excel sheets that I need to analyze across different “breakdown dimensions”. The specific workbooks I receive usually have several worksheets with similar structures (for instance, one per country). Within the worksheet there are usually several tables with similar structure, too, which add together. Easier to show with an example:

The numbers show a quantity (let’s say production) for products in a given platform, for different years. When a new year is needed, the tables are extended to the right, and new products are added in new lines as needed. Each table shows products belonging to a platform (or produced in a plant, or whatever). Now, let’s assume there are several countries. Typically, the Excel user just replicates the structure in another sheet and has one sheet per country. Quick and easy.

When analysis is required, things become harder. Usually formulas are added at the end of rows and columns to sum up. Sometimes, a “dimension” is worked out having subtotal rows. SUM ranges now become of different lengths depending on the number of rows in the subrange. Spreadsheets become error prone and hard to maintain because the data and the formulas are not separated. If 10 new products are added across several categories, the spreadsheet user will have to go inserting rows, expended formulas, etc. Some clever users add formulas in the corners of the table that compare the sum of rows with the sum of columns to make sure no formula was left improperly expended. Sounds familiar?

All the grief in maintaining those sheets can be avoided using PivotTables. There are many tutorials on PivotTables out there, so I won’t go into repeating it. Believe me… if the scenario depicted above is familiar to you and you are not using pivottables, make yourself a favor and read the tutorials. The two images below give an idea of the reports that the PivotTable tool will make for you. Need a report looking somhow different or with a different “cut” of the data? You can have hundreds of them linked to the same data and they will update automagically when you add data. New years? No problem… as soon as some data element refers say, to 2009 in the example, each PivotTable you had will extend in the appropriate dimension to include this year.

The only problem, is that to use PivotTables, the information

Sub normalize()
' Takes a matrix with names in rows and columns and turns it into a
' normalized version.
' Names for rows and columns are expected to be outside the selection
' Cell {-1,-1} is an attribute to be repeated in all entries
' Spreadsheet name is an attribute to be repeated in all entries
' Will modify the row and column structure of the spreadsheet
' Will overwrite anyting in the destination area
' Will not check if there is enough space on the spreadsheet

    Dim ss As Range
    Dim rr As Integer, cc As Integer
    Dim startRow As Integer, startCol As Integer
    Set ss = Selection

    rr = ss.Rows.Count
    cc = ss.Columns.Count

    If rr < 2 Then GoTo normalize_done
    If cc < 2 Then GoTo normalize_done

    startRow = ss.Row
    startCol = ss.Column

    If startRow < 2 Then GoTo normalize_done
    If startCol < 2 Then GoTo normalize_done

    ' Copy all the data transposed into rows
    For ci = 2 To cc
        Application.Intersect(ss, Columns(startCol + ci - 1)).Copy
        Cells(startRow + rr * (ci - 1), startCol).PasteSpecial xlPasteValues
    Next ci

    ' Copy the row names in all the transposed rows
    Range(Cells(startRow, startCol - 1), Cells(startRow + rr - 1, startCol - 1)).Copy
    Range(Cells(startRow + rr, startCol - 1), Cells(startRow + rr * cc - 1, startCol - 1)).PasteSpecial xlPasteValues

    Dim v As String
    v = ActiveSheet.Name
    ' Copy the column names, matrix name and sheet name in each of the rows
    For ci = 1 To cc
        Cells(startRow - 1, startCol + ci - 1).Copy
        Range(Cells(startRow + rr * (ci - 1), startCol + cc), _
            Cells(startRow + rr * ci - 1, startCol + cc)).PasteSpecial xlPasteValues
        Cells(startRow - 1, startCol - 1).Copy
        Range(Cells(startRow + rr * (ci - 1), startCol + cc + 1), _
            Cells(startRow + rr * ci - 1, startCol + cc + 1)).PasteSpecial xlPasteValues
        Range(Cells(startRow + rr * (ci - 1), startCol + cc + 2), _
            Cells(startRow + rr * ci - 1, startCol + cc + 2)).Value = v
    Next ci

    ' Move the last columns back to be closer to the data and clean up
    Range(Cells(startRow, startCol + cc), _
            Cells(startRow + rr * cc - 1, startCol + cc + 2)).Cut _
            Destination:=Range(Cells(startRow, startCol + 1), _
            Cells(startRow + rr * cc - 1, startCol + 3))
    Range(Cells(startRow - 1, startCol + 4), _
            Cells(startRow + rr * cc - 1, startCol + cc + 2)).ClearContents
    Range(Cells(startRow, startCol - 1), _
            Cells(startRow + rr * cc - 1, startCol + 3)).Select
    Selection.Style = "Normal"
    Application.CutCopyMode = False
normalize_done:

End Sub

Last time I used it to show budgeted project expenditures versus actuals, month by month. The right column, actuals, was broken down to show capital investment. The chart can also be created so the “entire” column is to the right and the “broken” one is to the left.

Here is the cookbok to make the chart:

• Create 4 series, horizontally as shown below: broken (bottom part) and broken (top part), entire and dummy. I’ll refer to these series as BB,BT,E and D respectively.
  
• Fill your data as needed. On the D series, put some value on the first cell – this is just to allow you to select the series and later on you will delete this value. Make this value close to the average of the rest of the data, so you can handle the segment comfortably.
• Select all five lines of the data: titles, the three series for the columns and your D series. Create a chart, choose column type, and stacked column on the subtype. Make sure series in columns is the selected option. Finish the chart wizard.
• Right click on the segment for the D series on the first column and move it to the secondary axis: Choose “Format data series” and on the “Axis” tab choose “Secondary Axis”.
• Do the same with the data corresponding to the E series. Before closing the “Format data series” dialog, go to “Options” and choose overlap -100, gap width 80. This setting will apply to both the D series and the E series.
• In the “Series order” tab you can choose if your E series will go to the left or to the right by moving it up or down
• Go to “Format series”, now for the BT series. overlap should be 100 and gap 320.
• Double-click the right axis to bring the “Format Axis” dialog. Choose the maximum to be equal to that of the left axis. Even if Excel chose by default the same value for both, make sure the checkbox close to maximum is unchecked. You want to make sure manually your axis are synchronized to avoid showing misleading information. By default, Excel charts start at 0, but if you change this, you must do it in both axis. While you are at this dialog, go to the “Patterns” tab and choose “None” in “Thick mark labels”.
• Delete the dummy value, the dummy label on the chart and format the chart to your liking

Enjoy!