Past Behaviour Predicting Future Performance

Often we've heard the phrase "Past behaviour is [not] a good predictor of future performance".

The above sentence includes the word [not] in finance, but excludes the word [not] when dealing with people (I think most psychologists would suggest). In short, history predicts people, but not companies or markets.

It kind of bothers me when I see maxims which are essentially identical in one case (individuals), but don't apply en mass (for groups). However, it reminds me of an interesting result I noticed relating to random motion.

If you have a dot in space, and you define it's movement as being "random", over time, the dot will essentially remain in the same spot (the expected value of random movement for one dot is zero change over time).

However, if you have multiple dots on a page, each who's movement is individually defined as "random", over time, you will actually experience diffusion. This is a bit counter intuitive as you would expect that since each individual's dot is random and because of the above result (where individual dots with random movement are expected not to stray to far from their original position) that individual dots won't move. If I'm not mistaken, the diffusion should actually take a normal distribution.