To be fair, I must note that a few theorists have offered a plausible case against reversion based on chaos theory, arguing that “off-the-chart” results occur in real life that normal statistics claim are impossible. (For instance, based on the calculated daily volatility of stocks, there is simply no way the U.S. stock market could have dropped more than 20% in a single day. It still did so on October 19, 1987.) Thus, it is possible that the real-life equivalent of a coin-flipping test doesn’t produce four consecutive heads as often as expected, but under a unique condition will get locked in and produce heads 100 times in a row. Although this doesn’t really offer an argument for the mean, since chaos makes the average impossible to compute, it does at least allow that it might not be upwardly biased, as I suggested in the previous lesson. (Chaos theory also makes diversification even more important, as chaotic events are far more likely to be disasters than jackpots.)

But even if equity prices didn’t revert toward long-run averages, the mean return wouldn’t be very useful in the real world. Since the average return, once again, depends heavily on the occasional jackpot result, a single human being cannot consider the mean return to mean much. In a stadium containing Bill Gates and 49,999 paupers, the weighted average person is a millionaire, but if you were to ask anyone the wealth of the average person in that stadium, they’d say the average person was broke. When a game has a variety of possible outcomes, but can only be played once, the result that falls in the middle of all the others (the median) and the result that occurs most often (the mode) are far more useful guesses than the weighted average of all the possibilities (the mean). This result was $100 in the one-coin game I cited in Lesson 9. (In the 16 rounds, the eighth best and eighth worst results were grouped among the six that ended up at $100, so it was the median, and no other outcome occurred as often as six times, so it was the mode.)

Of course, there can be safety reasons not to choose the investment with the higher median (or mode) when the weaker possibilities of that investment are substantially worse than the weaker possible results of the investment with the lower median return. Going back to the Modern Portfolio Theory piece, however, you will be reminded that the more-diversified games always had BOTH a higher average return AND lower risk. In a single human life, playing a game with critical life consequences, the possibility of winning the lottery just can’t be taken seriously in estimating returns.