In the realm of business and leadership, one statistical phenomenon often goes unrecognized yet significantly influences our understanding of performance and success. This is the concept of reversion to the mean. This seemingly simple statistical occurrence can profoundly impact how we perceive management strategies, leadership effectiveness, and even the fate of those gracing the covers of prominent magazines. To understand what is going on, read on!

You can also watch the following analysis as a video (in German):

Reversion to the mean refers to the statistical tendency for extreme or unusual results to be followed by more typical or average outcomes. In a business context, this might mean that an exceptionally high or low performance period is likely to be followed by results closer to the average. Understanding this concept is crucial for fair and accurate performance assessment.

One of the most telling historical examples of misinterpreting reversion to the mean comes from the U.S. military’s pilot training during World War II. Instructors observed that harsh criticism of a pilot’s poor performance often led to better results in subsequent sessions, while praise for good performance frequently preceded a decline. This led to the mistaken belief that punishment was more effective than praise.

In reality, what the instructors witnessed was a classic case of reversion to the mean. A pilot performing poorly on one day (below their average) was statistically likely to perform closer to their average (better) the next day, regardless of the criticism. Similarly, a pilot performing exceptionally well (above their average) was likely to return to more typical performance levels subsequently.

Let us put this in some broader context: Douglas McGregor’s Theory X and Theory Y present two contrasting views of workforce motivation. Theory X posits that employees are inherently lazy and require strict supervision and control, while Theory Y suggests that employees are self-motivated and seek responsibility:

The misinterpretation of reversion to the mean can erroneously bolster Theory X. When a manager sees performance improvement following punitive measures, they might attribute this to their authoritarian approach, not realizing that this improvement is part of a natural statistical trend:

# Defining the performance scores based on a sawtooth pattern
performance_scores <- c(70, 80, 70, 60, 70, 80, 70, 60, 70, 80)

# Setting up the plot
plot(performance_scores, type = 'o', col = 'blue', pch = 19, ylim = c(55, 85), xlab = 'Performance Assessment', ylab = 'Performance Score', main = 'Praise and Punishment: Reversion to the Mean')

# Adding a line for the true average performance
abline(h = 70, col = 'blue', lty = 2)

# Adding labels for praise (above 70) and punishment (below 70)
for (i in 1:length(performance_scores)) {
  if (performance_scores[i] > 70) {
    text(i, performance_scores[i], 'Praise', pos = 3, col = 'green')
  } else if (performance_scores[i] < 70) {
    text(i, performance_scores[i], 'Punish', pos = 1, col = 'red')
  }
}

The above plot demonstrates how performance fluctuates around a mean, leading to potential misinterpretations. Managers observing this pattern might mistakenly attribute the improvements to their strict measures (punishment) and the declines to leniency (praise), reinforcing a Theory X approach.

This misinterpretation is a form of the common logical fallacy known as “post hoc ergo propter hoc,” which is Latin for “after this, therefore because of this.” This fallacy occurs when someone assumes that because one event followed another, the first event must have caused the second.

Another intriguing manifestation of reversion to the mean is the so-called “Time Magazine Cover Curse”. This phenomenon suggests that individuals, companies, or stocks featured on the cover of Time (or similar publications) often experience a subsequent decline. The curse is actually a classic example of reversion to the mean.

Entities that make the cover usually do so because of extraordinary success or notoriety, levels which are inherently difficult to sustain. As performance reverts to the average, it appears as though the cover feature heralded a downfall. Nobel laureate Paul Krugman once joked, “Whom the Gods would destroy, they first put on the cover of Business Week.” Some technical analysts even use what they call a “magazine cover indicator” as a contrarian trading signal.

Speaking of investing: of course, reversion to the mean is here at play too! Just look at the best performing funds of one year just to find them in the average (or worse) section the next… that is reversion to the mean in action!

Understanding reversion to the mean is crucial for leaders, managers, and even investors. It teaches us to look beyond immediate outcomes and consider longer-term trends. It also warns against the hasty attribution of success or failure to specific actions or strategies. Recognizing the influence of this statistical principle can lead to better assessment of performance and success and fairer, more effective management practices.