Curves that Matter: Normal and Rhythmic Curves

Normal Curve

Shape and characteristics of the curve. The normal curve, or bell curve, is one of the most recognizable distributions and describes many natural patterns and phenomena. The curve is symmetrical around a middle or median with 50% of the values to the left of the midpoint and 50% of the values to the right. The curve can lean or skew to the left or right or it may appear flatter or taller (kurtosis). When applied to probabilities the curve is a valuable predictor of natural distributions from human traits, to where flying balls land, to just about any kind of random variation in outcomes of a system, either simple or complex.

The central limit theorem further explains the normal curve by suggesting that the distribution of any combination of a large number of generally random activities or variables will produce a normal distribution with an expected value for the mean and predictable variation around the mean. For example, rolling a pair of dice 100 times or so will produce a lot of 7s and far fewer 2s and 12s.

The curve allows many kinds of behaviors to be explored with good estimates of expected results. The area under the curve between any two points is interpreted as the likelihood or probability of events occurring within that range. The curve is divided into segments called standard deviations, positive to the right and negative to the left. Approximately 68% of the distribution lies within one standard deviation of the mean; 95% of the distribution lies within two; and 99.7% within three standard deviations.

Some examples. There are many applications and examples where the normal curve is enlightening. Here are a few:

Natural and biological traits - Early in the formulation of the normal distribution were studies based on the growth patterns of pea plants. In 1809, Gauss used the then new normal curve to better understand astrological data. In the years that followed, it was discovered that when considering a large group of humans, nearly all basic traits like height, weight, strength, or intelligence are normally distributed. Today, the normal distribution is fundamental to learning about how natural and biological systems and traits are understood.

Test scores - Like human traits, the tests that measure them produce scores that are normally distributed. But testing gets a double whammy from the normal curve. The tests themselves are not perfect and have errors in their scores as estimates of the traits. Those errors themselves are also normally distributed and when planning to use scores, measurement professionals account for both the normal distribution of the traits and the normal distribution of the errors.

System errors - No machine or system is perfect and like tests, the errors that are made are normally distributed. When machines that cut nails, for example, are inspected for variation, the lengths of the nails that result form a normal distribution. The tails of the distributions, those extremes on either the higher or lower end can serve as cut points for when a nail is too long or too short. The normal distribution helps us understand and mitigate system and machine errors, both in simple machines like nail cutters and more complicated systems like medical testing where the stakes are higher.

Population and organizational behavior - We know that large groups are normally distributed along any number of group and individual characteristics. But these groups, whether in populations or in organizations, have a unique behavior known as regression to the mean. Upon repeated measurement of a single trait or behavior, individuals who exhibit extreme traits, slowly regress or move toward the mean.

Insights for strategy crafting. The normal curve yields trustworthy insights for crafting strategy. The consistent patterns of symmetry, distribution and variance around the mean, predictable deviation, and regression to the man apply in universal ways.

Standard scores, performance, and selection systems - The normal distribution can be standardized, or set to a mean of 0 and standard deviation of 1. This allows for distributions of many kinds of traits or characteristics to be compared and used in analytical ways. One such application that yields insight to strategy is performance measurement and selection systems. A critical part of strategy execution is establishing and managing the resources necessary to drive implementation. For large organizations, tracking the performance of human resources and selecting the right resources for the execution path is a critical matter. The normal distribution of performance outcomes gives key insight to managing the resource necessary for success.

Predictable outcomes in the environment - Like human performance internally, many kinds of environmental outcomes are normally distributed and wise strategy crafters can use these expected or predictable distributions to their advantage. As if making a bet, investing strategy with an expected outcome near the mean yields the best likelihood of success, and expecting results between -1 and 1 standard deviation will result on average with two-thirds of the results realized. The biomedical and agricultural industries build their core strategic models on these behaviors. On the other hand, less than 1 percent of outcomes fall outside the extremes of -3 and 3 standard deviations. Insurance companies use knowledge of the normal curve in their strategy crafting to both protect customers during extreme events and consistently generate profit margins.

Game theory and simulations - Modeling future scenarios is a key activity for strategy crafting and advances in computing have allowed gaming and simulations to become help tools in building strategies. By combining normal distributions of multiple forces, both current and future, likelihood scenarios can be developed to help uncover which strategic choices may have more advantage over others.

Diffusion of innovations or new ideas - One classic use of the normal distribution was developed by Rogers in the Diffusion of Innovation. The graphic below shows traits of adopting new ideas across the normal curve.

Adapted from Rogers Diffusion of Innovation, 1962

Rogers suggested that individuals adopt new ideas with the largest proportion being the majority, or 68% between -1 and 1 standard deviations, where the first group is the early majority and the second group the late majority. Interesting are the groups outside of one standard deviation. Only 2.5% of a normal distributed population could be considered innovators and 13.5% the early adopters. On the other side of the distribution, the tails beyond one standard deviation are the laggards, the last ones to adopt the news ideas - if they ever do.

Rhythmic Curves

Shape and characteristics of the curve. Rhythmic curves, periodic (or sine) waves are most often observed in the behaviors of stable systems where there is motion (things are not completely at rest) but the system has settled into a pattern. Rhythmic curves are centered around a midpoint and oscillate over time returning the midpoint at regular intervals. These curves exist because energy is moving through a system.

Rhythmic curves can be described by at least four different kinds of characteristics: frequency, period, wavelength, and amplitude. Frequency is the how often the rhythm cycles in any given time segment and a related characteristic, period is how long it takes for the pattern to repeat. Like the tempo of a song, these curves can have rapid frequencies vibrating extremely fast or very slow frequencies lasting thousands of years. Wavelength is the distance between peaks of the curves. For curves representing physical phenomena, this can be seen as an actual distance. Finally, amplitude is the maximum deviation of the curve from the midpoint and can be understood as the height of a wave.

Some examples. Almost all stable, dynamic systems are characterized by one or more rhythmic curves. Some notable examples include:

Natural and manmade rhythms - Simple mechanical systems display nearly perfect waveforms. From the swinging pendulum, to the rhythms of clockworks, these systems have clear and predictable cures. Biological systems are equally driven by rhythms like heartbeats and the well-recognized sinus rhythm and more complicated biorhythms that drive our waking and sleeping, hormonal, and hibernation cycles.

Flow of energy through matter - Like a ripple in still water, most forms of energy flow through states of matter (liquid, gas, and solids) in wavelike patterns. Whether it be the rise a fall of an earthquake, waves lapping on the shore, or the winds rising and falling on the mountainside, there are constant examples of energy in our environment.

Community and organizational rhythms - More complicated systems do display rhythms as well. Most of our organizations are driven by management induced rhythms and there is a long history of organizations being viewed as machines. We see annual and quarterly reports and cycles, monthly and weekly meetings, and daily and hourly metrics all as evidence of rhythmic curves. Communities as well display rhythms. They go through both cycles of birth, growth, and decline, as well as rhythmic cycles of productivity, energy levels, and convening and communicating.

Cultural, economic, and societal rhythms - At the broadest level, we see societies and economies cycling in rhythmic patterns. Many cultural rhythms have their source in current or historical seasonal variations. From agronomic economies and religions to more modern fashion trends and educational academic years, we observe a large number of cycle inducing causes and effects. But there are other long-term rhythms and cycles. For example, it can be observed through history that periods of creativity and romanticism have cycled with periods of science and technological advances. And on the grandest natural scale, we are aware of epochs and ages that last millions of years in length.

Insights for strategy crafting. Most strategy crafters, whether intentional or not, count on either stability, straight lines, or rhythms for success. Uncovering, understanding, and anticipating rhythms are key insights for those crafting strategy.

Capturing the energy contained in waves - Rhythmic patterns are in essence energy driven and many waves both contain energy in themselves or in the behaviors that they induce. Strategies can be crafted with the intention of capturing this energy in a sense and using it to the strategy’s advantage. From the simple approach of selling lemonade in summer to the more subtle insight to synchronizing communications with naturally occurring rhythms in a new markets cultural behavior, strategists should seek out the rhythms at play in their environments of concern as well as hope to capitalize on their permanence and characteristics as they move into the future.

Making waves - Often, we find that an organization or its environment is lacking the necessary rhythms to make change, create stability, or strength along the lines of our strategic intent. The insight here is that rhythms can be intentionally induced. Whether it be a slow quiet drumbeat or a high energy noisy pattern, new rhythms serve to enhance flow of energy through organizational systems and their environments.

Changing the scale of rhythms - There are two ways in which strategies can be crafted to acknowledge the major forces acting on an organization or its environment so as to benefit from the naturally occurring waves; one by amplifying and another by dampening. Amplifying a rhythm as a strategy adds energy to the wave by either increasing the primary characteristics frequency, period, wavelength, or amplitude. Acting on the same characteristics, dampening takes energy away from the rhythm and decreases its impacts and effects.

Laminar flow versus turbulence – A final insight about rhythms for the strategy crafter is about the stability in the system that allows the waves to remain intact and persist. Rhythms keep up and waves move along well when the environment is smooth. Those that study how energy transmits through substances call this smooth flow as laminar flow. Its opposite is turbulence. During turbulent flow, unsteady vortices appear on many scales and interact with each other, disrupting energy in the system and it’s existing rhythms. Strategies for intentional turbulence can be used to change cultures, break bad habits, or prepare for new ideas to have impact by breaking down rhythms of stability. This also gets us ready for more complicated curves and their inherent nonlinearity. More to come.