This chart compares the theoretical normal distribution (outlined circles) with actual weekly market returns (filled circles) over the past 10 years. Each circle represents one week, stacked vertically within 0.5% return bins. The normal distribution assumes returns follow a bell curve based on observed mean and standard deviation. Circles colored blue fall within the theoretical distribution; red circles represent weeks that exceed what a normal distribution would predict, revealing in particular the market's fat tails corresponding to extreme events. 

Data: Weekly S&P 500 returns from August 2015 to August 2025 (522 weeks). Returns binned at 0.5% intervals spanning -14.5% to +12.4%. Normal distribution fitted to observed parameters.