Probability versus Expectancy

This blog has been prompted by a Twitter conversation over the last few days that requires me to respond in a much longer format than Twitter provides for. So I quickly set up this blog to accommodate that.

There is a fundamental concept that determines one of the major, if not the most important, differences between amateur traders and professional (successful) traders.

This concept is “Expectancy”.

I owe my discovery of this insight to Van K Tharp. Read his excellent books. I must also thank Mark Douglas for my further understanding of it, and the mindset associated with it.

This concept is essential to understand. All your trading must be based on this understanding as if your genetics included it.

For some reason that I cannot fathom, many traders do not grasp this concept. Many argue against it. But they are thinking in terms of probability rather than expectancy. There is a huge difference. If the difference is not apparent to you, stop trading. Why? Because you are not trading now – you are gambling.

When you throw the dice once, you have a 1 in 6 probability of getting a three. But you have no expectation of getting a three on that particular throw. The odds are against it. You have no way of predicting the outcome of that single throw. If you bet on getting a 3, you are simply gambling.

When you throw the dice one thousand (1,000) times, you expect to get a three 166 times. That is because probabilities start to approach certainty the greater the sample size. That is what studies of population trends and mass marketing are based on. This is very reliable.

In short, the result of the next throw could be anything. But the result of the next 1000 or 10,000 throws is reasonably predictable. Why? Because we know the probability associated with any single result, and that probability is a measure of the expectancy of an infinite number of events. If the number of throws was infinite, the probability of getting a three one-sixth of the time would be 100 percent. As the sample size gets smaller, the probability of that being true diminishes. But, although the probability of our expectation occurring is never quite 100 percent, it approaches 100 percent as the number of throws increases.

That is what trading is based on. You can never predict, with 100 percent certainty, the outcome of your next trade. Your expectancy is unmeasurable, although the probability is determined from the backtesting of your strategy. So, when we enter the next trade, we must assume that it will be a loser and we size our risk accordingly. This is called risk management and position sizing. The purpose of this, generically named “Trade Management”, is to ensure that, over the medium term, your account survives long enough to profit from your trading strategy.

Your trading strategy is your edge in the market. It includes the setups you have identified that you have found lead to a move in your favour a satisfactory number of times. This may be 50 percent of the time, or more, or even less than 50 percent of the time. This is not critical because the more important part of the strategy is not about being right, but about managing the outcome when you are wrong, and managing the outcome when you are right. If your loss is small when the trade goes against you, but very large when the trade goes with you, then, over time and many trades, a 30 percent success rate can lead to a 100 percent or so of profit versus risk.

This is a trading strategy. Trading is not about forecasting the market. Trading is about forecasting your equity curve. Forecasting your equity curve is possible. Forecasting the market, at least in a consistent manner, is impossible. There are too many variables for that to be done consistently. And why try to, when it is so easy to forecast the equity curve using expectancy.

If I have an entry criteria to a set up configuration that my backtesting has indicated results in a move in my favour about 50 percent of the time, and on average I can make a profit of 2 times the risk that I take then the arithmetic, leaving out costs and slippage, is very simple. Half the time I lose 1R, where R is the initial risk. The other half of the time, I make a profit of 2R. So, over many trades, I will average 2R – 1R = 1R for every 2 trades. Multiply that by the number of trades and that tells me the amount of profit I expect to make over those trades. If I take 1000 trades, I will lose 500R on the losing trades and make 1000R on the 500 winning trades. That gives me a net profit of 500R over 1000 trades. So my expectancy is 500r/1000=0.5R per trade over a large number of trades.

That is quite predictable. The probability of that outcome approaches 100 percent as more trades are taken but it never reaches 100 percent. But the probability of success on the next, single trade is always 50 percent. That never improves.

I can forecast my equity curve. That is expectancy.

I cannot forecast my next trade outcome. That is probability.

A successful, professional trader relies on expectancy.

A gambler relies on probability (and hope).

No exceptions.

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