SIX: THE LOTKA CURVE
The “This Can’t Be Right” Distribution of Eminence
Human talents typically follow a normal distribution, known as the bell curve, where most people are in the middle, with fewer individuals possessing very high or very low talents. This pattern applies to traits impacting life success, such as intelligence and work ethic. In the case of the 479 artists analyzed, they represent only a tiny fraction of the population and are all considered highly talented, existing on the far right side of the bell curve. However, being highly talented doesn’t guarantee eminence or excellence, as many other factors influence an artist's success. The anticipated distribution of eminence shows a narrow range among these artists, suggesting that most differences in their success come from factors beyond just talent.
The “This Can’t Be Right” Distribution of Index Scores in the Western Art Inventory
The index scores of Western artists active from 1200 to 1950 show a highly unequal distribution, with 71 percent of significant figures scoring in the lowest range and very few scoring above 60. Attempts to adjust measurements by focusing on more prominent artists or counting unique works still resulted in a skewed distribution. Over half of the artists represented had only one work listed. This pattern isn't unique to this study; similar skewed distributions have been observed in other inventories over the years, indicating a consistent issue with how Western artists are evaluated.
Alfred Lotka’s Discovery
Alfred Lotka was a Hungarian-American researcher who studied how many articles scientists published in the mid-1920s. He found that about 60 percent of the authors had only published one article. He also noticed that the number of scientists who published more articles dropped sharply, following a special curve called a hyperbolic curve. His work helped to understand the way scientists contribute to scientific literature and showed patterns in how they publish their research.
Substituting a Supposedly More Egalitarian Measure Makes the Distribution Even More Skewed
Substituting one measure for another can worsen the uneven distribution of achievements among individuals. An equation suggests that about 60 percent of people will produce only one article, but this is not a predictable law as the actual distributions vary. Instead, it represents a hyperbolic curve called the Lotka curve. Other mathematicians have proposed different models, but there is agreement that the general pattern of how achievements are spread among individuals resembles the Lotka curve, supporting its recognition in historiometry.
Lotka’s Curve Describing the Relationship Between the Scientific Literature and the Contributors to It
Lotka’s curve shows how many people contribute to scientific literature over time. It highlights that a small number of researchers publish most of the papers, while a larger group publishes fewer articles. This relationship indicates that as the amount of scientific work increases, the number of contributors stays relatively constant, with many making only a few contributions. This pattern helps to understand the distribution of research efforts in the scientific community.
Why Not a Bell Curve?
Human talents and accomplishments do not follow a simple bell curve; instead, they create a skewed distribution known as the Lotka curve. This indicates that extraordinary achievements are influenced by multiple factors rather than just high intelligence or creativity alone. Early thinkers like Francis Galton suggested that a mix of abilities, enthusiasm, and hard work leads to exceptional success. This idea was later expanded by William Shockley, who showed how normal traits combine to produce this skewed distribution.
Another explanation is the "Matthew effect," which suggests that success leads to further success due to accumulative advantages. For example, if a scientist gets a paper published, they gain confidence and better opportunities, while less successful peers may struggle. This cycle can create a pattern where successful individuals continue to succeed, illustrating how social dynamics can shape productivity.
Dean Simonton's chance-configuration theory adds depth by describing how creative individuals generate numerous ideas but can only develop a few into successful products. This randomness can also lead to a distribution that mirrors the Lotka curve. Overall, achievement is influenced by a combination of traits and external opportunities.
Fame or Excellence?
The discussion focuses on the concept of fame versus excellence, particularly illustrated by the Lotka curve, which indicates that a small number of individuals receive a disproportionate amount of recognition in their fields. One possible explanation for this phenomenon is that some individuals, like Shakespeare, may produce work of higher quality, leading to their greater fame. However, this explanation is questioned because of the extreme imbalance in fame distribution. For example, Shakespeare has significantly more books written about him compared to other writers.
To assess whether the Lotka curve represents true excellence or just fame, one can apply "face validity." This involves examining whether the most recognized individuals actually deserve their fame for their contributions. While many top figures do have stellar reputations, this method raises concerns about circular reasoning, making it challenging to differentiate between genuine talent and mere celebrity status.
Additionally, only a limited number of fields have objective measures of excellence. Sports offer clearer cases where achievements can be quantitatively assessed. For instance, in professional golf, individual statistics can accurately reflect a golfer's skill, and overall excellence can be measured through tournament victories. This highlights the complex relationship between fame and true excellence in various domains.
The Component Skills of Golf Form Bell Curves Even Among Professionals
In professional golf, a significant finding shows that 53 percent of elite players never won a tournament in their careers, highlighting the difficulty of winning. Among the 47 percent who did win, the distribution of victories shows a hyperbolic curve rather than a bell curve. Only 26 percent achieved a single win, which is much lower than expected. The data also shows that the maximum number of wins can reach as high as 71, indicating varying levels of success among golfers.
When the Measure Is Tournament Victories, the Bell Curve Is Replaced by a Lotka Curve, but One of Comparatively Modest Skew
When looking at tournament victories among golfers, the results show a Lotka curve with significant skewness. Most players who win tournaments usually only secure one, two, or three wins, with only a few winning more, such as Arnold Palmer and Jack Nicklaus, who achieved 61 and 71 wins, respectively. This trend continues when considering major championships like the U.S. Open and Masters. Here, nearly 60% of players have only won one major. Despite this being a select group of elite golfers, the distribution mirrors various sports like baseball and tennis, where success also follows a similar pattern. The key takeaway is that achieving high-level success in sports often deviates from a normal distribution, indicating that while many compete, only a few reach outstanding accomplishments through demonstrated skill and success.
As the Measure of Excellence Becomes More Demanding, the Lotka Curve Becomes More Extreme
The Lotka curve shows that as the standards for excellence in golf increase, the distribution of player success becomes more pronounced. This means that fewer players achieve high success levels, while a small number dominate the winners’ circle. The "eligible players" are those golfers who won at least one Major championship and were either retired or over 45 years old by the end of the 2001 season. This highlights the competitive nature of golf among top players.
Four Other Examples of Measures of Competitive Excellence That Produce Lotka Curves
Examples of measures of competitive excellence include statistics from Major League Baseball and the four tennis Grand Slam tournaments. Additionally, data is gathered from marathon events and world chess championships. These examples all show patterns that can be analyzed using Lotka curves, which illustrate the distribution of achievements among competitors in various sports and competitions. This helps in understanding how successes are spread out among players and how competitive environments function.
An Explanation: Difficulty
Lotka curves show how success is spread out in various fields, revealing that few people achieve a lot while many achieve very little. This pattern relates to how difficult a task is: the harder the task, the fewer the people who succeed at it. In sports like golf, professional players can easily perform basic skills, but winning a tournament under pressure is much more difficult. When the stakes are high, only a small number of athletes can succeed repeatedly.
In easier tasks, many people can achieve small successes, resulting in a bell curve where most get similar results. As tasks become more difficult, the achievement pattern shifts from many successes to fewer successes, resembling a Lotka curve.
This idea applies to the arts and sciences too. For example, while many researchers publish one article, getting published in top journals like Nature is very hard and requires unique skills, not just effort. Even if there were financial rewards for writing more articles, the level of difficulty in higher-end tasks would still matter.
Moreover, many famous figures today may not be remembered in the future, which highlights how tough it is to create lasting work. The discussion about Lotka curves across different areas shows that genuine excellence plays a big role in why some people achieve so much more than others. The differences in their accomplishments indicate that some individuals truly excel at what they do, emphasizing that being talented and skilled is important.
The “This Can’t Be Right” Distribution of Eminence
Human talents typically follow a normal distribution, known as the bell curve, where most people are in the middle, with fewer individuals possessing very high or very low talents. This pattern applies to traits impacting life success, such as intelligence and work ethic. In the case of the 479 artists analyzed, they represent only a tiny fraction of the population and are all considered highly talented, existing on the far right side of the bell curve. However, being highly talented doesn’t guarantee eminence or excellence, as many other factors influence an artist's success. The anticipated distribution of eminence shows a narrow range among these artists, suggesting that most differences in their success come from factors beyond just talent.
The “This Can’t Be Right” Distribution of Index Scores in the Western Art Inventory
The index scores of Western artists active from 1200 to 1950 show a highly unequal distribution, with 71 percent of significant figures scoring in the lowest range and very few scoring above 60. Attempts to adjust measurements by focusing on more prominent artists or counting unique works still resulted in a skewed distribution. Over half of the artists represented had only one work listed. This pattern isn't unique to this study; similar skewed distributions have been observed in other inventories over the years, indicating a consistent issue with how Western artists are evaluated.
Alfred Lotka’s Discovery
Alfred Lotka was a Hungarian-American researcher who studied how many articles scientists published in the mid-1920s. He found that about 60 percent of the authors had only published one article. He also noticed that the number of scientists who published more articles dropped sharply, following a special curve called a hyperbolic curve. His work helped to understand the way scientists contribute to scientific literature and showed patterns in how they publish their research.
Substituting a Supposedly More Egalitarian Measure Makes the Distribution Even More Skewed
Substituting one measure for another can worsen the uneven distribution of achievements among individuals. An equation suggests that about 60 percent of people will produce only one article, but this is not a predictable law as the actual distributions vary. Instead, it represents a hyperbolic curve called the Lotka curve. Other mathematicians have proposed different models, but there is agreement that the general pattern of how achievements are spread among individuals resembles the Lotka curve, supporting its recognition in historiometry.
Lotka’s Curve Describing the Relationship Between the Scientific Literature and the Contributors to It
Lotka’s curve shows how many people contribute to scientific literature over time. It highlights that a small number of researchers publish most of the papers, while a larger group publishes fewer articles. This relationship indicates that as the amount of scientific work increases, the number of contributors stays relatively constant, with many making only a few contributions. This pattern helps to understand the distribution of research efforts in the scientific community.
Why Not a Bell Curve?
Human talents and accomplishments do not follow a simple bell curve; instead, they create a skewed distribution known as the Lotka curve. This indicates that extraordinary achievements are influenced by multiple factors rather than just high intelligence or creativity alone. Early thinkers like Francis Galton suggested that a mix of abilities, enthusiasm, and hard work leads to exceptional success. This idea was later expanded by William Shockley, who showed how normal traits combine to produce this skewed distribution.
Another explanation is the "Matthew effect," which suggests that success leads to further success due to accumulative advantages. For example, if a scientist gets a paper published, they gain confidence and better opportunities, while less successful peers may struggle. This cycle can create a pattern where successful individuals continue to succeed, illustrating how social dynamics can shape productivity.
Dean Simonton's chance-configuration theory adds depth by describing how creative individuals generate numerous ideas but can only develop a few into successful products. This randomness can also lead to a distribution that mirrors the Lotka curve. Overall, achievement is influenced by a combination of traits and external opportunities.
Fame or Excellence?
The discussion focuses on the concept of fame versus excellence, particularly illustrated by the Lotka curve, which indicates that a small number of individuals receive a disproportionate amount of recognition in their fields. One possible explanation for this phenomenon is that some individuals, like Shakespeare, may produce work of higher quality, leading to their greater fame. However, this explanation is questioned because of the extreme imbalance in fame distribution. For example, Shakespeare has significantly more books written about him compared to other writers.
To assess whether the Lotka curve represents true excellence or just fame, one can apply "face validity." This involves examining whether the most recognized individuals actually deserve their fame for their contributions. While many top figures do have stellar reputations, this method raises concerns about circular reasoning, making it challenging to differentiate between genuine talent and mere celebrity status.
Additionally, only a limited number of fields have objective measures of excellence. Sports offer clearer cases where achievements can be quantitatively assessed. For instance, in professional golf, individual statistics can accurately reflect a golfer's skill, and overall excellence can be measured through tournament victories. This highlights the complex relationship between fame and true excellence in various domains.
The Component Skills of Golf Form Bell Curves Even Among Professionals
In professional golf, a significant finding shows that 53 percent of elite players never won a tournament in their careers, highlighting the difficulty of winning. Among the 47 percent who did win, the distribution of victories shows a hyperbolic curve rather than a bell curve. Only 26 percent achieved a single win, which is much lower than expected. The data also shows that the maximum number of wins can reach as high as 71, indicating varying levels of success among golfers.
When the Measure Is Tournament Victories, the Bell Curve Is Replaced by a Lotka Curve, but One of Comparatively Modest Skew
When looking at tournament victories among golfers, the results show a Lotka curve with significant skewness. Most players who win tournaments usually only secure one, two, or three wins, with only a few winning more, such as Arnold Palmer and Jack Nicklaus, who achieved 61 and 71 wins, respectively. This trend continues when considering major championships like the U.S. Open and Masters. Here, nearly 60% of players have only won one major. Despite this being a select group of elite golfers, the distribution mirrors various sports like baseball and tennis, where success also follows a similar pattern. The key takeaway is that achieving high-level success in sports often deviates from a normal distribution, indicating that while many compete, only a few reach outstanding accomplishments through demonstrated skill and success.
As the Measure of Excellence Becomes More Demanding, the Lotka Curve Becomes More Extreme
The Lotka curve shows that as the standards for excellence in golf increase, the distribution of player success becomes more pronounced. This means that fewer players achieve high success levels, while a small number dominate the winners’ circle. The "eligible players" are those golfers who won at least one Major championship and were either retired or over 45 years old by the end of the 2001 season. This highlights the competitive nature of golf among top players.
Four Other Examples of Measures of Competitive Excellence That Produce Lotka Curves
Examples of measures of competitive excellence include statistics from Major League Baseball and the four tennis Grand Slam tournaments. Additionally, data is gathered from marathon events and world chess championships. These examples all show patterns that can be analyzed using Lotka curves, which illustrate the distribution of achievements among competitors in various sports and competitions. This helps in understanding how successes are spread out among players and how competitive environments function.
An Explanation: Difficulty
Lotka curves show how success is spread out in various fields, revealing that few people achieve a lot while many achieve very little. This pattern relates to how difficult a task is: the harder the task, the fewer the people who succeed at it. In sports like golf, professional players can easily perform basic skills, but winning a tournament under pressure is much more difficult. When the stakes are high, only a small number of athletes can succeed repeatedly.
In easier tasks, many people can achieve small successes, resulting in a bell curve where most get similar results. As tasks become more difficult, the achievement pattern shifts from many successes to fewer successes, resembling a Lotka curve.
This idea applies to the arts and sciences too. For example, while many researchers publish one article, getting published in top journals like Nature is very hard and requires unique skills, not just effort. Even if there were financial rewards for writing more articles, the level of difficulty in higher-end tasks would still matter.
Moreover, many famous figures today may not be remembered in the future, which highlights how tough it is to create lasting work. The discussion about Lotka curves across different areas shows that genuine excellence plays a big role in why some people achieve so much more than others. The differences in their accomplishments indicate that some individuals truly excel at what they do, emphasizing that being talented and skilled is important.