- Julian Talbot

# Business Cases: The Merits and Pitfalls of Numbers

Did you know that 69.2% of all statistics are made up on the spot?

If you are publishing online or crafting business cases, you might be wise to make sure that YOUR data comes from the other 42%. The 42% that are rigorously researched, relevant, defensible and calculated accurately. Actually, that would be 30.8% but you get the point; when crafting a business case, no matter how many great arguments you have, it's essential to have your numbers correct.

But just how do you make sure that your business case will stack up? In the words of the nineteenth-century British prime minister Benjamin Disraeli, “*There are three kinds of lies: lies, damned lies, and statistics*.” Accordingly, I've become rather cynical of numbers (except when I'm the one who has had the opportunity to make them up or at least to graph them). Most managers and business professionals are probably the same, so if numbers are available, make sure they pass the test of the following 4 R characteristics:

**Relevant**—They must directly address the problem.**Reliable**—You must use figures whose authority can be demonstrated.**Representative**—You would not use basketball teams as your sole data in a survey of the average height of the population. The sample would be biased.**Readable**—Put the figures in a form that is easy to read (e.g., graphs, tables; remember that S can look like a the numeral 5).

This is not an article on statistics, but it would be remiss not to raise a few key points concerning the use of numbers and statistics in your business case. Use your data to its best effect, but remember that numbers can lie. A number of people have been attributed with the quote (or variations thereof) that, in essence "*If you torture numbers long enough, they’ll confess to almost anything*". Avoid the temptation to abuse statistics in your business case—someone will inevitably notice, and it is only going to detract from your argument when they do so.

One of my favourite ways to torture a confession (or apparent confession) out of numbers is with graphs. It's an old trick and doesn't strictly speaking, involve any deception or manipulation of numbers but it works. It won't work quite as effectively on you once you've read the following but it will work just fine on your victims (ie. your bosses and clients). Have a look at the following 5 graphs as ask yourself, which one would be most likely to encourage you to invest in my stock market investment offering. The data is exactly the same in every chart. Just some minor changes.

The first chart is just the basic data presented using Excel's default baselines.

In the following chart, I've changed the Y-axis to start at 7,000 to make the growth steeper (ie. more positive).

In the following chart, the Y-axis starts at -3,000 which makes growth look much more moderate and not so wonderful to invest in.

Same data again. The only change is that the 'trend-line' is now exponential. Still a legitimate mathematical analysis but doesn't it look more inviting than the trend-lines of the previous charts?

Last but not least, I've just cut a couple of years off the X-axis to take that nasty global financial crisis of late 2018 off the chart. You could legitimately do this if you wanted to just talk about 'historical performance' because the 2018 crash was a one-off six-sigma (ie. rare) event and not representative of actual long term returns. But you won't fall for that one any more will you?

**Some additional thoughts on using numbers**

**1. The mean can be cruel.**People have drowned in streams that are “on average” only two feet deep. Are you referring to the average depth across the causeway today or the average depth during the year? Are you using mean, median, or mode? Too many unanswered questions have been the death (financial or otherwise) of many an adventurous entrepreneur.**2. Meetings always start late**. My friend and I have to meet at 3:30, and it takes us on average thirty minutes each to travel from our respective workplaces. We each have a fifty-fifty chance of making it in that amount of time. If we both leave at 3:00, is there a 50 percent likelihood that we’ll both arrive on time? Your intuition is probably already telling you that something is just not right. Think about this in terms of a coin toss. If I have a fifty-fifty chance of tossing heads, and my colleague has a fifty-fifty chance of tossing heads, there is only one scenario in four in which we both toss heads. Net result—a 25 percent likelihood that we will both arrive on time.**3. Lies, damn lies, and project timelines.**If three consecutive stages of a project each have an 80 percent chance of finishing in less than ten days, you would be unwise to tell the boss that you have an 80 percent chance of completing it in less than thirty days. As illustrated in point 2, above, you only have a 51.2 percent chance of completing the project in thirty days. The first stage has a 20 percent chance of taking longer than ten days. If the second stage also has an 80 percent chance of finishing in less than ten days, that only amounts to a 64 percent chance that both stage 1 and stage 2 will each take less than ten days.**4. Half the risk is not the equivalent of double the benefit.**If spending ten dollars per person on a drug or vaccination offers a 50 percent reduction in the chance of acquiring a disease, this sounds great. But did the marketing brochure for the drug mention that my risk of acquiring the disease in the first place is only two in a million? Is it worth ten dollars to reduce my risk from a negligible two in a million to one in a million? This is a question for each individual, but if I am the minister of health in a country with twenty million people, it is going to cost taxpayers two hundred million to save twenty people from the disease. It’s a noble cause, but is it the country’s best use of ten million tax dollars per person saved?**5. Beware the optimist.**On-average profit will be less than the profit associated with average demand. Why? Your projections indicate on average a ten-dollar profit per widget with demand from fifty thousand to ninety thousand widgets per year, and therefore your average profit is seven hundred thousand dollars per year. Or is it? Suppose your widget factory can only produce eighty thousand widgets per year. This would create a situation where your profit is capped at eight hundred thousand dollars in all the years when demand exceeds eighty thousand units, and this will bring your average profit down below the projected amount.

**To find out more, check out the amazing work of literary fiction: **__"Business Cases for Risk Management"__

**DISCLAIMER**

Numbers are slippery little critters. Don't trust them. Especially don't trust them if you don't have extraordinarily reliable research. You will find me for example, very likely to use phrases such as " ... *is likely to ...*" or " *... a bystander was heard to say ... *". OK, maybe not the last one but I used to love listening to the evening news for that one. Or at least I did when I watched the evening news. I stopped when I realized that 69.2% of the evening news was made up on the spot. You can download a cool business case template from the relevant page on this website (hint: it's under the "DOWNLOADS" menu). It won't make your research any better but it will make it easier for you to convince 69.2% of managers that 69.2% of your business case is credible, which 'is likely to' lead to you getting roughly 69.2% of the money you asked for. Bonus hint: Submit lots (and lots) of business cases. That way you'll get very good at them, and may even find that 69.2% of your business case applications for funding will receive 69.2% of what you ask for. Or you may find you've just spent 10 minutes reading this article and you'll never get that 10 minutes back :-)