http://www.avhf.com/html/Evaluation/HazardAttitude/Hazard_At...
Reduce your risk and improve your expectation values by rationally using decision theory and correcting the systematic sampling biases in your head.
When outside influences do come along that affect his expected outcome, he will be disrupted instead of scientifically understanding the situation, and his role as an individual who is not the center of the universe.
When you know there is sampling error (luck) it makes sense to blend a little bit of the distribution of the group in with each individual.
For instance, if you look at baseball hitters for a season ordered by batting average, probably the guy at the top of the list got lucky (sampling error) and the guy at the bottom of the list had bad luck. The real batting average is a hidden variable that we can only see through sampling.
A good estimator of an individual's batting average can use the group distribution as a prior against the individual distribution as an observation -- this regresses the individuals back towards the mean, which is a realistic way to perceive uncertainty.
In late 1990s, when Quinton McCracken first published DIPS theory, it was postulated that pitchers had zero control over their "luck based" factors (BABIP, in this case; expanded to include LD%, LOB%, HR/FB%, etc.)
Now there exists enough data to identify outliers, to whom the theory of DIPS (Defense Independent Pitching Stats) doesn't apply. Matt Cain, for example, is acknowledged to outperform his DIPS.
No matter what the statistics suggest, people will believe they're the Matt Cain. And some will be. By definition, they're the outliers that our statistical models do not account for.
For instance, as RyanZAG points out, if you are well prepared for a test, while you know others are 'just chancing it', then your chances of succeeding are much higher than the statistics would have you believe.
To state it more generally: the reason a statistic often cannot be used for an individual expectation, is that the statistic is based on persons completely unlike yourself. A relevant statistic would only include people like yourself. In his example: those that show themselves more aware of the difficulties that will be encountered, better prepared than average, etc.
As an example: my life expectancy is vastly different from the commonly stated 'average' life expectancy of people in my country. Firstly that is 'from birth' and I have already survived quite a bit. Secondly it includes smokers and I don't smoke. Thirdly it includes people that engage in all kinds of other risky behavior that I avoid. The average life expectancy may be 72, while mine is 87.