One of the biggest shortfalls of strategy and strategists today is the level of innumeracy and the lack of mathematical ability. There appears to be very little appreciation of the role and importance of numbers in developing strategy. There are so many occasions where you will hear business people talk about direction and success with little understanding of the importance of the numbers. One example was a company which had aspirations of growing three times in the next five years. The company was a relatively small company with a turnover of £3m and wanted to grow to £10m. This was certainly possible. However, the management did not understand what was actually involved in growing to this size. At £3m the company was making one new sale per year, as a result of 20 enquiries i.e. a one in 20 hit rate. To grow to the necessary size the company needed to have 8 new customers per annum, which meant there needed to be 160 new enquiries, which actually meant that 4 new salespeople were needed. The numbers demonstrated the importance of investment, which was not really understood by the management.
Another interesting perspective is the lack of appreciation of meaning of numbers. Paulos in his book “Innumeracy” talks about an exercise where he asks his audience to estimate how long it would take to dismantle Mount Fuji, given certain criteria. It is interesting to see how many people estimate this to be around 20-100 years. The actual answer would be somewhere between 5,000-15,000 years given that Mount Fuji is 12,000 feet high. This illustrates the importance of introducing a more calculating method rather than guessing as many people lack a real appreciation of numbers.
In business terms it is not important to be precise and calculate an exact answer as to how much growth there will be, but we are looking for ball park answers. As with Mount Fuji case, the ball park is just not there. This also suggests that we do not want guesses, but want some level of thinking. Key mathematical principles for a strategist would be the following:
Basic arithmetic and percentages
A vital skill is the ability to calculate and manage numbers demonstrating relationships between figures. It is surprising how difficult some of the younger managers find to calculate percentages,. This is probably due to the reliance on computers. One of the most effective tools for the strategist is the percentage calculation as it shows the most basic form of relationship between 2 variables.
Rate of change, trends and forecasting
Strategy is all about change. This is probably the most important mathematical skill. Maybe we do not need to understand calculus, but the strategist certainly needs to understand how variables change whether it is growth in sales, market share etc over a period of time. The strategist also needs to understand the relationship between the variables as none of these variables exist in isolation. This understanding helps in being able to predict the movement of the numbers in the future.
Probability and distribution
Much of business is about estimation and this is where probability and distribution helps us understand and predict future movement in variables by attaching some level of risk to the uncertainty. This also needs to explore chance encounters and average or expected values. For example, in business there is a tendency for people to work with extreme numbers i.e. they will assume that the biggest success or failure is representative of the sample rather than looking at the movement of averages. These also tend to be more valuable than working with coincidences as they are more representative.
Strategic problems might be solved as follows using lessons from mathematics:
Understand the problem
What are the unknowns? What data is available? What conditions or assumptions are there in relation to the situation?
Find a connection between the data and the unknown
Have you seen the situation before? Have you seen the same problem in a slightly different form? Do you know a related problem? Look at a case which has solved a similar problem. What lessons can be learned from these? Can you restate the problem in a different way to provide the required answer? Have you used all of the data?
Check your solution
Can you justify your assumptions and solution? Can you check the result? Can you check the argument?
One of the most common arguments heard in business is that all you need is experience, but we still see major mistakes being made frequently! A simple process and simple understanding of working with numbers can make a huge difference.
Numerically strategists need to be able to explore what the size of numbers really mean. A test would be something like the Rubik’s cube, where people would try to guess how many different possible states there are. Not many people would guess there are 4X10 to the power 19 i.e. 4 with 19 zeros after it. For many people this size of number is not really understood. A more quantitative approach to strategy is vital to overcome some of the weaknesses we see in strategic management. Numbers and quantification creates a more tangible understanding of the issues facing an organisation. Always talk in terms of numbers. Quantify as much as possible and be sure to articulate the assumptions.
By Professor Rakesh Sondhi- Prof. Rakesh Sondhi is the managing director of BMC Global Services