Allen Downey - Extremes, outliers, and GOATS: on life in a lognormal world | PyData Global 2023

Log-normal distributions are more common in real-world data than typically assumed, often providing better models than Gaussian distributions

The distribution of human weight follows a log-normal pattern, while height can be modeled well by both Gaussian and log-normal distributions

Two key mechanisms contribute to log-normal distributions:

• Proportional gain: Changes occur as percentages of current value
• Weakest link process: Performance is limited by the worst performing factor

Greatest of All Time (GOAT) performers are statistical outliers even among elite performers due to the long tail of log-normal distributions

Elite performance requires multiple factors:

• Natural talent/aptitude
• Training opportunities
• Persistence/passion
• Resources
• All factors must be present; lacking any one prevents reaching elite levels

The Central Limit Theorem Corollary explains why multiplying random factors tends to produce log-normal distributions

Birth weights follow a Gaussian distribution, but adult weights become log-normal through proportional gain over time

Traditional statistical methods often default to assuming Gaussian distributions, but testing against log-normal models is important

Log-normal patterns appear in diverse fields including:

• Athletic performance
• Chess ratings
• Musical ability
• Professional achievements

Quantitative comparison between models can be done by:

• Comparing CDFs
• Calculating areas between curves
• Using maximum likelihood methods