I wrote many articles on statistics over the years (Teaching a Grade 4 on Probability, Understanding the Market in a Statistical Way, etc.) and advocate traders to pay more attention to proper application of statistics in trading and model development.
I came across this educational video by Peter Donnelly from TED that explains several basic concepts in statistics clearly.
There is no point for me to repeat his work, so I will just include the video here.
In case your browser does not support HTML5 embedded video, here is the link directly to the lesson itself,
http://ed.ted.com/lessons/peter-donnelly-shows-how-stats-fool-juries
Relating to the Video
The HTH vs HTT occurrence frequencies – It is one of the most overlooked and misunderstood basic pattern recurrence behaviour.
Many rookie traders and trading model designers often assume that certain common patterns (price, indicator, geometry lines) are useless because of their potential frequent recurrences. What they have overlooked, is that, first the assumed common patterns are not that common (like HTH) and second, the importance of any recurring pattern is not how common or rare it is, but the consistencies in the expected outcome following the occurrence of such pattern.
Here is a good teaser – How often does S&P make new year high after the last occurrence has led to 1% (or more) drop in price?
The 99% interpretation issue – You think your trading setup has a 80% win rate is pretty good, think again.
Most successful traders know their own performance pretty well. They are often better than computers in analyzing real-time scenarios. In their heads, they can picture the possible scenarios and reduce that to actions that improves their profitability.
Such mastery is not just a plain 80% win rate or other simple measurement can do to discover or qualify a method.
80% win rate is an overall measurement. It does not take into account the separate performance of a correctly identified setup and a falsely identified one. Often traders cannot even distinguish the two scenarios for trading setups they use all the time.
For example, a 1-2-3 sell setup can fail and results in a bull flag upside breakout pattern. 1-2-3 sell setup works best if the trader can identify the strong resistance area to key off the setup.
A good combination can be 90% of the time you identify the trading setup at a good resistance zone where 90% of those identified setups result in profits, and that in the 10% of falsely identified setups, you still edge out 50% winners. The reason why this is a good combination is that your expected performance will likely to have good consistency.
A bad combination could be 50% of the time you identify the trading setup correctly and 90% profitable on those correctly identified ones. And then in the other 50% of trading setups, 70% of the time you edge out a profit. In this case, even though the historical performance is around 80% win rate, you do not really know why your setups are producing profit. In fact, that 70% winners out of the falsely identified setups could be just random outcomes. Worst yet, traders often try to improve the win rate by adjusting the stop loss which simply curve fit the trading setup to perform better on historical data. Those extra winners in the particular 70% is likely a result of that.
The rare case independency issue – Traders often make the mistake in thinking that since a (huge) losing trade based on a particular setup is very rare, why not double down, triple down, or bet the farm on the next occurrence of the trading setup. People justifying such measures are likely in a losing streak. In such stressed situations, bad ideas often pop up and this is one of them.
Even if the huge losses are rare and likely independent, that does not change the potential of the very next trade being a loser. Betting the farm or sudden increase in bet size in general will significantly affect the expectancies with your trading method. If it is not something you have anticipated and well planned out, it is just plain stupid doing that knowing the consequence can wipe out your trading account.
Professionals in various fields often misuse statistics – In the video Peter Donnelly pointed out this very important issue that infested our society.
Doctors, lawyers, economists, security analysts, etc. are not statisticians. Yet these professionals frequently try to draw conclusions and inference from data they have compiled. Often these inference are incorrect and misleading. Unluckily there is no rule or regulation to, say, revoke their professional licenses for misuse of statistics. At the receiving end of these analysis and conclusions, it is difficult for the public to protect themselves from these misleading information.
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