Competitive Marketing Strategy based on Lanchester’s equations of combat

By John Schuler

SEMI Market Statistics Department Published in Channel Magazine

After a roller-coaster ride in the semiconductor industry this past few years and the expectation of more to come (DRAM price decline and the Asian Financial Crisis) it’s a good time to stop and take a look back at the historic perspective. A short ten years ago, with the prediction of the imminent demise of the US semiconductor industry, the majors went wimping off to Washington for a dose of industrial policy (read money) and SEMATECH was formed. The collective wisdom was that with lower interest rates and devotion to quality the Japanese industrial juggernaut would sweep all in its path.

The semiconductor industry is by no means a special case. How many other industries or sectors have joined the walking wounded after having their market share surgically removed? For a poignant view of the loss of market share and national pride, take a look at the article (Newsweek, April 13, 1998) by the Rt. Hon. Alan Clark, English parliamentarian for the London borough of Kensington and Chelsea and former minister for trade in the Thatcher administration. Clark bemoans the loss of indigenous automobile manufacturing in UK. He points to BMW and VW sparring over ownership of the last remnants of British automobile manufacturing, and “crown jewels” of the Rolls Royce Car Company. As Clark puts it, “forty years ago British Leyland was cranking out almost 500,000 cars a year, while today every major automobile plant is owned outside the United Kingdom.”

We have heard it all before, if only we had “lower amortization rates,” if only we had “better R&D tax credits,” the inevitable “lower interest rates” or we need to implement ISO 9000/TQM/Baldridge/QFD/ Quality Program du jour. For the answer to why these obvious answers don’t fit the bill, we need to turn the clock back a bit further to the mid 50s.

We know that at that time quality guru W. Edwards Demming was working closely with the Japan Union of Scientists and Engineers (JUSE) to improve the quality of a Japanese industry. Demming shipped a crate of technical books to JUSE. For the most part the books were on quality and statistics but also included a slim volume by Morse and Kimball titled “Foundations of Operations Research” published in 1951 and describing the use of Operations Research in WWII.

The Lanchester connection

For the key to the puzzle, we need to turn the clock back almost half a century to WWI and the publication in 1916 of the equations of combat for mechanized warfare in F. W. Lanchester’s book “Aircraft in Warfare.”

Chapter three of Morse and Kimball called “Strategical Kinematics,” describes the use that was made of Lanchester’s equations of combat in WWII, with examples from the battle in the Pacific and the anti-submarine campaign in the North Atlantic. In addition, the extension of Lanchester’s equations to the case of global warfare was given. For the Japanese in the 1950s, faced with rebuilding a shattered economy and striving to enter world trade markets, the possibility of applying Lanchester’s ideas to sales and marketing was, no doubt, an interesting concept.

Outline of the Lanchester Strategy of Sales and Marketing

The Japanese development of Lanchester’s laws for sales and marketing proceeded on two fronts. On the one hand, using Lanchester’s equations and the principle of concentration a set of strategies were developed, which provide insight into competition between companies and rules for selecting the appropriate tactic. For small companies or new product introduction, the choice is one-on-one combat to secure a market beachhead. Well-established companies with existing markets to protect need to do battle under the N-Square Law where the survival rate is greater.

The second thrust of the Japanese development involved the development of a theory of market structure with important break points and market share ratios. For example the conventional wisdom is that a 50% market share gives control, however the Lanchester Strategy shows that a 41.7% market share will give control of the market.

Why the Sun-Tzu / Samurai warrior model of marketing doesn’t work

There are many popular books available to the business community that purport to show how strategy based on a mixture of Sun-Tzu, Mishima, Attilla the Hun et al. seasoned with a dash of Von Clausewitz can be used as a basis of marketing strategy. However, all of these books were written before machanized warfare developed and deal only with the one-on-one combats that takes place under Lanchester’s Linear Law. In reality, the art and practice of military technology has progressed somewhat since the days of the samurai warrior. A few well-aimed bursts from a machine gun will dispatch a fair-sized army of samurai warriors.

Today, sales and marketing takes place under Lanchester’s N-Squared Law. Since there are always multiple participants in any given market sector. Of course there are a few special cases of one-on-one competition, such as Boeing and Airbus (the only two manufacturers of jumbo jets) and in wide screen cinema projectors (Imax and Iworks the only two manufacturers of wide screen systems). Consequently, Western marketers are going into battle with, at best, half a theory and ignorant of the power of Lanchester’s principle of concentration and the N-Squared Law.

A paradigm shift for the marketing community

The realization that a more comprehensive theory of marketing exists that is based on the mathematical equations first postulated by F. W. Lanchester in1916 is what the late Thomas S. Kuhn would call a paradigm shift. It you’re not convinced that this material is new, take a look back to your MBA marketing course content and textbooks, you won’t find Lanchester Strategy mentioned.

In summary, the Lanchester Strategy will give you a greater insight into the dynamics of the marketplace, and the tools and techniques that can be used to maintain and increase your market share.

Note on Lanchester Equations:

Lanchester’s Linear Law. This equation of combat relates to individual combat between soldiers where the outcome is dependent on the ratio of weapon efficiency (E) of the individual combatants, and the combat strength of the army = E(number of troops). The outcome of the battle is the difference between the original troop numbers.

Lanchester’s N-Squared Law. For the case of mechanized warfare, with modern weapons, each soldier can attack multiple targets and is also subject to incoming fire from many directions. In this case the attrition rate is proportional to the number of troops on the opposing side. Solution to the first order differential equation leads to Lanchester’s

Second law, combat strength of the army = E(number of troops squared) also called Lanchester’s N-Squared Law.

Lanchester’s Principle of Concentration. The basis of strategy is that of concentration; the concentration of the main strength of force at one point in the field of operations.

With modern long-range weapons, the concentration of firepower gives an immediate superiority that the inferior force is unable to respond in like terms.

What this means is that the superior force should always choose to fight under N-Squared Law conditions, because the end result will leave the victor with a greater number of survivors than when fighting under the Linear Law. Secondly, for an inferior force, there is often an opportunity for winning by using a tactical device to split the larger force and annihilating each section of the enemy in sequence. This is illustrated by Lanchester in his book “Aircraft in Warfare” using Admiral Lord Nelson’s battle plan for the Battle of Trafalgar back in 1805.

Note on F. W. Lanchester: the Leonardo of the machine age

F. W. Lanchester (1868-1946) was an early pioneer in engineering and aeronautics. He studied at the Royal College of Science London in engineering and mining technology. Lanchester is the co-discoverer of the circulation theory of flight with Prandtl, with two books on aerodynamics published in 1907, and was awarded the Guggenheim gold medal for aeronautics in 1931. He had 236 patents awarded out of almost 400 applications including ducted fan propellers (1897), disk brakes (1902), and invented many of the systems of today’s car such as power steering, four wheel drive, low voltage ignition, the box chassis and dynamically balanced engines. He designed and built the first car in England in 1895 and went on to found the Lanchester Car Company. He invented the method of dimensions for scaling experiments, go-no-go gauges and wrote on such diverse topics as music, poetry, relativity, optics, acoustics and relativity.

His book “Aircraft in Warfare” published in 1916 describes the construction, armament, tactics and strategy for the use of aircraft in support of ground and naval operations in WW1. In the book Lanchester develops his principle of concentration of attack and the equations of combat, that are still taught today in military colleges. Lanchester is recognized as the founding father of the science of Operations Research with the annual Lanchester Prize presented by the Operations Research Society.