Most people are familiar with the normal (or bell-shaped) curve. It shows the relative frequency of outcomes when the inputs consist of random events.

If we flip a fair coin 100 times and count heads, then repeat this “experiment” many times and plot the results, we’ll get a normal curve. The most frequent outcome will be 50, the top of the curve. 55 heads will be less frequent (to the right of center), and 25 heads will be even less frequent (left of center).

If we do the experiment enough times, we’ll see cases with 100 heads (extremely rare, way off in the right tail of the curve) and cases with 0 heads (equally rare, way off in the left tail). We express the distance from center in terms of standard deviations (SD). So a 2 SD event would happen 1 time in 20 (this is the famous p < .05 rule in statistics, for those who care); a 3 SD event would happen 1 time in 100; and a 6 SD event (or six sigma, for those who care) is equivalent to 1 in 37,000,000.

What does the normal curve have to do with picking stocks or betting on sports? Success rates in both endeavors resemble the normal curve. The average annual return for stock portfolios is 0% (sad but true). Some people can bring in 10% annually over many years, while others will average -10% returns. A tiny, tiny handful of people can maintain 30% annual returns for decades (Warren Buffet, Peter Lynch, George Soros). At the other end of the curve we have Brian Hunter, formerly of Amaranth Advisors, who lost six billion dollars (that’s billion with a b) in two weeks. These are 5-6 standard deviation performances. They are, by definition, (1) inevitable and (2) rare. This is what the normal curve tells us.

How about sports betting? Sites like pickspal will offer to sell you the picks of people who have a perfect record over (say) the last 3 months. A perfect record sounds impressive, but consider the brief time period. What’s more likely, 10 heads in 10 coin tosses or 100 heads in 100 tosses? These hot pickers will inevitably revert to the mean, and you would be well advised to avoid spending money for their picks.