Expectancy: Why thinking like a casino will improve your trading

How many times have you been asked

Whats your Win / Loss ratio?

I get asked this question a lot and my response is often met with a confusing look.

I don't care what my Win / Loss ratio is. All I care about is whether my strategies make me money

Expectancy - The Secret of the Casinos

Here is why Las Vegas Casinos make so much money. Lets take a look at the parameters of the game of roulette (based on a single $1 bet on a single number)

• The Win / Loss ratio is 1/38 = 0.026 (or a 2.6% chance of winning vs a 97.4% chance of losing)
• The Average Losing bet is $1
• The Average Winning bet is $35 (odds of 35 to 1 against winning)

The expectancy of this system is [0.026*35] - [0.974 * 1] = 0.91 - 0.974 = -0.064 For every bet placed the Expectancy is a Negative $0.064 (for the punter) and so by having a small edge, the casino will always make money. Now obviously a trading system that had similar parameters to that of a game of roulette would be pretty hard to trade (imagine losing 97.4% of the time), but the concept remains the same.

A trading system does not need to have a great Win /Loss ratio in order to make money, it simply needs to have a Positive Expectancy.

Expectancy - The ONLY number EVERY trader MUST know

Put simply - If your system has a Positive Expectancy, then you can expect to make money with it. If it has a negative expectancy, then expect to lose. The formula for expectancy is;

[W/L ratio * Ave Profit per trade] – [(1- W/L ratio) * Abs(Ave Loss per trade)]

How to calculate your systems Expectancy

Your current trading system has the following metrics

• Number of winners = 60
• Number of Losers = 73
• Average Profit per Trade = $200 (Total value of winning trades / number of winners)
• Average Loss per Trade = -$120 (Total value of losing trades / number of losers)

Expectancy can be calculated as follows

1. Calculate Win / Loss ratio
   • 60/(60+73) =0 .45 (Only 45% of trades are winning trades)
2. System Expectancy is
   • [0.45 * 200] - [(1-0.45] * Abs(-120)] = $24

So even for a trading system that has a Win / Loss ratio less than 50%, over time this system will deliver a profit of $24 per trade. This can better be expressed in percentage terms. In order to make $24 we are risking $120 on each trade. So the expectancy of this system expressed as a percentage is: $24 / $120 = 0.2 or 20%

If you want to automatically calculate the expectancy of your current trading system, then download the FREE Trading Journal Software which includes an Expectancy Calculator

Finding a system that suits your personality

Balancing a systems Win / Loss ratio with your own personality as a trader is something that can take time to get right. Some traders are happy to trade a system that delivers fewer winners than losers (because they know the system will ultimately deliver a positive expectancy). However the majority of traders will prefer a system that wins more trades than it loses (it is human nature to want to be right more often than being wrong). However it becomes easier to trade a system with a Win / Loss ratio less than 50% if we know what our expectancy is.

Balancing Win/Loss ratio & Ave Win Size / Ave Loss Size

The graph below can be used to calculate breakeven points for systems based upon forecasted Win / Loss and Ave Win Size / Ave Loss Size ratios.

 

How to use the break even graph

Lets assume you are developing a system that has a Win / Loss ratio of 30% (eg more losing trades than winning trades). Using the graph above, in order to break even on that strategy, your Av Win / Av Loss size ratio would need to be greater than approx 2.2. If, however your trading system has a Win / Loss ratio of 70% (meaning more winning trades than losing trades) your break even Ave Win size / Ave Loss size is only approx 0.6 (meaning you can lose more on a losing trade, than you need to win on a winning trade in order to break even)