The Prodigy of Statistics

Once upon a time, there was an esteemed statistician, whom we shall refer to as Mr. X. He was a well-regarded professor and had authored a widely used statistics textbook for students and professionals alike.

As part of an ambitious research endeavor, Mr. X dedicated years to gathering statistical data from various companies across different industries. This process of data collection and organization was an extensive task.

His data encompassed detailed information on expenditures, sales, salaries, rents, and more. Mr. X aimed to uncover patterns that might explain the reasons behind the success or failure of businesses.

The Groundbreaking Publication

After years of diligent work, Mr. X was prepared to share his findings. He published a comprehensive 468-page book titled "The Triumph of Mediocrity in Business," which astonished the business community.

The book included structured analyses with intricate tables and graphs. It was clear to discerning readers that this was not just another academic publication. Prior to this work, many believed that effective business practices guaranteed long-lasting success. However, Mr. X's findings significantly challenged this notion.

Success Diminishes Over Time

Mr. X’s research indicated that successful companies tend to decline over time. Interestingly, he also found that underperforming companies often improve as time progresses. He succinctly stated that both high and low performers gravitate towards mediocrity.

To emphasize his point, he wrote:

"…neither excellence nor deficiency tends to endure. Instead, mediocrity becomes the norm. The average intelligence of those engaged in business prevails, and the common practices of such a trade mentality dominate."

So, how did Mr. X arrive at this conclusion? Let’s find out.

The Methodology Behind the Findings

Mr. X categorized all companies by sector and ranked them based on various performance metrics. He divided these ranked firms into groups of equal size.

For example, after ranking 120 textile retailers based on their sales-to-expense ratios, he created six groups (sextiles) of 20 stores each. He anticipated that the top sextile would maintain its superiority over time. However, to his astonishment, within just six years, these top stores lost nearly all their competitive edge compared to average performers.

He replicated this analysis across various industries and for different performance indicators, such as wage-to-sales and rent-to-sales ratios. The results consistently pointed towards a trend of both high and low performers moving towards mediocrity over time.

The Insight — Regression to the Mean

From his extensive analysis, Mr. X concluded that in a competitive market characterized by free trade, this "mediocrity" effect is prevalent. High-performing organizations lose their advantages, while underperforming ones improve over time. He attributed this phenomenon to human behavior, suggesting that negative traits such as greed and corruption limit success.

Mr. X likened this to a classroom dynamic where capable and diligent students may be adversely influenced by disruptive peers. This perspective was quite radical for an academic.

While many focus on how successful organizations impact their less successful counterparts, Mr. X argued that the mediocrity effect stems from the influence of lower-performing organizations on the higher-performing ones. Consequently, he proposed that governments should intervene to protect high achievers from the detrimental effects of low performers. How did his peers respond to this?

The Notable Mathematician

Now, we shift our focus to another brilliant mind of the time, Mr. Y, a mathematician and statistician who respected Mr. X’s work. He also taught mathematics and had made significant contributions to statistics.

Upon reviewing Mr. X's book, the academic community responded positively, acknowledging its groundbreaking nature. Mr. Y expressed admiration for the effort Mr. X put into collecting and analyzing his data. However, he pointed out that the observed effects were predictable.

Mr. Y explained that when studying variables influenced by stable factors and random chance, regression to the mean is a natural outcome. He suggested that Mr. X did not need to struggle with extensive data to arrive at this "obvious" conclusion.

This critique did not sit well with Mr. X.

The Academic Debate

In a follow-up publication, Mr. X addressed Mr. Y’s comments, clarifying some misunderstandings. He asserted that the mediocrity effect was not merely a statistical anomaly but a significant finding supported by his data.

In a subsequent response, Mr. Y opted for a more clinical approach, effectively dismantling Mr. X's arguments with clear logic. He contended that the entirety of Mr. X’s thesis was trivial, likening it to proving multiplication through an elaborate arrangement of animals.

According to Mr. Y, while Mr. X’s analysis was visually impressive, it merely stated the obvious. As a result, Mr. X’s reputation suffered irreparably.

Understanding the Discrepancy

The key distinction between Mr. X and Mr. Y lies in their respective expertise. Mr. X was a statistician, while Mr. Y was both a statistician and a mathematician. What was apparent to Mr. Y was overlooked by Mr. X.

When analyzing one of Mr. X's top firms, Mr. Y argued that while the firm may have demonstrated superior management and wisdom, it likely benefited from an element of luck. Consequently, as time progressed, the firm’s luck would tend to revert to the average market luck, regardless of its superior skills.

Mr. X posited that successful firms diminished due to competitive pressures over time. However, Mr. Y challenged him to examine a recent top performer rather than one from the beginning of his data timeline. He suggested Mr. X look at past performance data for this newer top performer, hypothesizing that if competition truly caused a decline in success, this effect should be evident both retrospectively and prospectively.

It turned out that no such detrimental effect was present—only regression to the mean.

The Implications for Us

The narrative we’ve explored is not just an intriguing tale; it illustrates a common misunderstanding that frequently occurs. In various clinical studies and social science research, misinterpretations of regression to the mean abound.

For example, if a study involved very ill patients receiving a particular medication, and they showed improvement, the researchers might claim the medication was effective. However, these patients are also likely to revert towards average health over time.

This misinterpretation is so prevalent that it extends beyond academia. Consider a father who, upon discovering his daughter’s poor grades, has a serious conversation with her. Later, he observes an improvement in her grades and attributes this change to his talk. In reality, while his discussion may have had some impact, it’s likely that his daughter would have improved on her own, especially after an unusually poor performance.

Navigating the Challenges of Regression to the Mean

As humans, we often think linearly and seek to narrate the phenomena we observe. However, we sometimes misinterpret the narrative or the nature of the phenomenon. This inclination to explain is not inherently flawed; it has historically aided our survival.

Nonetheless, it’s essential to assume that regression to the mean might be at play before attributing narratives to phenomena we do not fully grasp. For instance, instead of only selecting very sick individuals for a medication trial, researchers could choose two randomly selected groups of sick individuals, administering the medication to one and a placebo to the other. This approach allows for a more balanced comparison, as regression to the mean is likely to affect both groups equally.

In our daily lives, it’s beneficial to approach situations with skepticism. Whether it’s trendy diets or quick fixes, regression to the mean can mislead us into thinking we understand something when we do not. Combined with placebo effects, discerning the truth becomes even more challenging.

If this feels daunting, remember that even experts take years to grasp the nuances of regression to the mean. It may seem simple, yet it is profoundly deceptive.

Epilogue

The story recounted is not fictional; it reflects historical events involving real individuals. Mr. X represents Horace Secrist, while Mr. Y embodies Harold Hotelling. I hold great respect for Secrist for his extensive efforts, only to have his conclusions deemed trivial.

Secrist’s top performers were not randomly selected, which significantly influenced the results. Unfortunately, he is not the first expert to fall into the regression trap, nor will he be the last. Many have mistakenly assigned narratives to phenomena that are merely regressing. You might think you are immune to such misunderstandings, but we are all vulnerable to the subtleties of regression to the mean.