Data and lawlessness - think in frequency and when in doubt, think random

In his well-written book, Chancing It - The laws of chance and how they can work for you, Robert Matthews explains well the basics laws of chance and probability, but he also spends time describing what he calls the principles of lawlessness. It is a nice device to remember some important statistical concepts. 

The first law of lawlessness - do not look at events look at the frequency of events. Every number should be looked at in context, the context of likelihood. Ask the simple question - what is normal and what is abnormal. Risk management is all about getting the frequency right. 

The second law of lawlessness - When trying to understand random events don't assume they are independent and don't assume that correlated events will stay that way. Live would be so simple if the events were independent. The probability of A and B occurring is just the product of the individual probabilities. However, if you know the correlation of two variables, do not assume that this correlation will stay the same. Correlations change and may be related to a third variable.

The third law of lawlessness - randomness does not ultimately have patterns; but in the short-run there can be regularity. When in doubt, go with random. You may think you see a pattern in the short run, but that does not mean the pattern will continue, nor does it say that a time series is non-random. A random series does not mean-revert. A series of heads does not mean the next flip is more likely a tail, yet in the long run the frequency of a tail is .5.

Be cautious of any number and any count. A small sample will tell a different story from a large sample and the actual likelihood may be different from any data collected. When in doubt, trust randomness.