Wig-
The relationship between mathematical models and the reality they describe has always fascinated me. The patterns that result from randomness are often indististinguishable from the ones that result from choice and ability.
For example, baseball batting averages are distributed normally. If you graph them, you will see the classic bell-shaped curve we have all seen at one time or another. In other words, if baseball batting averages were completely random with no player better than another - it would look very similar to what we see in real-life where some players are better than another. What about a Tony Gwynn who batted .338 in his career? Doesn't he prove that some baseball players are better at hitting the ball? Well, you can't prove it by looking at the statistics. With enough players in the league and enough seasons - guys like Tony Gwynn will always appear even if everyone were of the same skill.
Why does a graph of something involving skill look random? I think it's because a skill involves an ability that influences the results in your favor but does not absolutely control it. The greatest hitters in the game go 0 for 4 all the time. The greatest quarterbacks have days where they complete less than 50% of their passes and throw more INT's than TD's. But over a whole season, the better players are more or less obvious. This bit of randomness whether it is 50% random factors, 25%, or even 75% leads to a bell-shaped curve. Batting average reflects a players ability to hit the ball, his competition, some random factors like twist on the ball, relative humidity, barometric pressure, winding of the core or whatever. A graph of all players batting averages has enough randomness to give us the bell curve. (Colin's guess anyway).
Heights are the same way. All our heights are influenced by our parent's heights but many random factors including genetic recombination, diet, and other things add a random element that shows up in the graph.
If this is truly the reason, then the bell curve shape should shrink in width as played become more skilled and there is less randomness to the game. Stephen Jay Gould pointed out that exactly this has happened. Players used to bat .400 and some used to bat under .200 but not anymore.
Many white papers have been written saying that all market returns are completely random. I think those academics are completely mistaking something that looks completely random from something that is completely random. I truly believe Mr. Buffett has understood the markets better than nearly everyone else and probably better than everyone else. He has imperfect skills though and can be taught a lesson or two by the markets just as Michael Jordan had days when he was 4 for 15 shooting and there didn't appear to be any good reason for it.
Last edited by Colin at Nov 14 2002, 11:53 AM
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