It's all about the variance - part 1

A lot of newcomers to sports trading or betting may imagine that all they have to do is pick winners. They might think that getting as close to a 100% strike rate will guarantee millionaire status. It's just not as simple as that. For a start, we are going to pick losing bets or make losing trades. Nobody is perfect. Even if we could get close to a 100% success rate we would probably be betting or trading too little to make any serious money.

Risk and reward go hand in hand. The more we are willing to risk then the greater the potential for reward. That doesn't mean we should throw our money round and hope to get lucky. The key to success is money management, balancing risk and reward. To manage risk we protect our capital from the downside whilst making the most of the upside. We don't even have to have a 50% strike rate to make a profit. All that matters is that when we lose, we lose less than we win.

In the example simulation below (click to enlarge) on RiskSimulator 2, we see a trader who only has a 40% strike rate but who makes twice as much from winning trades as on losing trades.

This simulation models a trader who makes 2% profit on average from a 40% strike rate and who manages to keep his losses down to a 1% average. Intuitively, we know that if the strike rate falls below 33% (1/(2+1) = 0.333) then the trader will make a loss. Of course, all of these simulations can be calculated mathematically without the need for Monte Carlo methods. The point of the simulation is to show the variance graphically. A lot of novices have difficulty understanding the mathematics of gambling. A graphical representation can often aid the beginner sports bettor/trader.

The formula for expectation will tell you what you need to know about your bets without recourse to a simulation.

Expectation =  (prob of success * return) - (prob of failure * loss)

If the figure is negative then it's a losing system.

For our example simulation the expectation will be

(0.4 * 2) - (0.6 * 1) = 0.2% per bet

The simulation was pretty close (£19.46p average yield) to the expected £20 but we can see clearly in the simulation that we could have made more or less and in some cases there might have been a small drawdown before making a profit. The expectation is based on an infinite series and our betting will tend towards expectation. In theory when we calculate probabilities we are doing so from a distribution derived from an infinite series. However, we never get to place an infinite number of bets. A few hundred bets will be unlikely to produce smooth distibutions. A simulation helps us to understand short time variance very clearly.

In the example above, although all 100 trials yielded positive returns some were higher than others. The  highest yield was £32.40 and the lowest a little over £7. However, by trying to lose as little as possible we don't want to be so risk averse as to avoid any losses at all. Doing that can often prevent us from taking the risk of getting the right rewards. It's a matter of balance. Our winning bets or trades must overcompensate us for our losses. Do that and we will always be in profit.

Further Reading

It's all about the variance - part 2