Variance is a key element in profitable sports trading. Learn how it works and improve your sports betting strategies today!Read More
If you've read our article on value betting, you've learned how edges occur in sports betting, and that good bets are characterized by a positive expected value. The question remains how to transform your edge into what is our ultimate goal: Long term profits.
Let’s take a look at a coin flip with 2.10 in odds of heads. The probability is 50 %, so the edge is 5 % (2.10/2.00 = 1.05). With a stake of $10 and potential return of $11, one trial give an expected value of $0.5 ($11*0.5 - $10*0.5 = $0.5). However, you won’t have $0.5 in profits after the first toss. You will either be $11 up or $10 down. To see how this looks, we can plot the different outcomes and their corresponding probability:
The chart shows the two only possible outcomes after the first trial, and that both outcomes are equally likely. In other words, after only one coin toss, there’s a 50 % chance that you’ll win money and a 50 % chance that you’ll lose. Strictly speaking, that is a risky investment.
When we flip the coin a second time, there are now four outcomes: $22 up (25 % probability), $1 up (50 %) and $20 down (25 %). The expected value can be calculated to be $1 (2 tosses * $0.5), and with more possible outcomes, the probability distribution would now look like this:
As illustrated, only one of the outcomes results in negative profits. In fact, the probability of losing money has gone down to 25 %, only half of what it was after the first trial. Then again, having a 25 % chance of losing money is still way out of our comfort zone.
The law of large numbers states that the mean of the results obtained from a large number of trials will get close to its expected value. This means that if we toss the coin many times, we should expect it to show heads and tails approximately the same amount of times.
Therefore, let’s see what happens if we keep increasing the sample size. Naturally, as the number of possible outcomes increases, winning every bet will become highly unlikely (prob = (1/2)^sample size)) and similarly it will become highly unlikely to lose all of the bets. If we map out the different outcomes and their probability after 1000 trades, we get the following bell-shaped curve:
Now, there are several observations to be made. First, we know that the expected value should be $500 ($0.5 * 1000 tosses). This is also reflected in the probability distribution, which is symmetric around 500. That means that you are equally likely to end up above and below $500.
Furthermore, the chances of negative returns is a lot less than before. In fact, we can calculate the probability of losing money after 1000 trades to be 7 % (You’ll have to trust us on this one). We can also plot the same probability for a number of sample sizes, which will turn out like this:
For example, if you want to be 98 % certain to make a profit, you would need a sample size of almost 1900. Increase the number to 5000, and you are theoretically going to make a profit with a certainty of 99.96 %. Moreover, you will earn more than the expected value of $2500 half of the time.
The lesson is simple. As long as your sample size is small, placing valuable bets is only part of the story and risk is still highly present. By increasing your sample size of +EV bets you will reduce the risk of negative returns and your results will converge towards its expected value.
That is the power of the law of large numbers.
In this article, I'll briefly go into the different parameters that ultimately decides your variance. If you are unfamiliar with what variance is and why it is important, start reading this section from the beginning. For the bettors out there that do not enjoy larger swings in your bankroll and deviance from your expected value, I'll also discuss what actions you can take in order to minimise those swings.
When placing trades - there are 4 main parameters that impacts your variance;
Time until the game starts
The edge %
Whether you place bets that are dependant of each other
Use a lower Kelly Percentage
Set a maximum bet
This is the most obvious one. The higher the odds you place on, the more swings you will see in your bankroll. The reason is quite simple; if you bet only on odds of 11 with an edge of 10%, you can expect the bet to be a winner one out of every 10 games, and you'll get paid back 11 times your wager. In theory, you'd then lose 9 bets in a row then win one and win back more than you lost in the previous 9 bets.
Time until the game starts
The time until the game starts is quite important. The reason is, if you place a bet a full day before game start with an edge of 3% - new information may occur that could swing the bet out of your favour. To be extreme, there is a chance that all the key players of your team might miss their flight, making your team lose the game. There is also a chance that the bet gets stronger, as the same thing could happen to the opposing team. The only thing we can say for sure is that this will increase your variance, as the lines and the information are not settled yet.
If you are unfamiliar with what an edge / value bet is, check out these articles. If you place on marginal edges (1-2%), chances are they can swing back if you place it a far from game time. The reason is that even the smallest piece of information may shift the market out of your favour. When you find higher edges, there is always a reason the market shifts so drastically - and the probability that it would shift back is higher. Most of the players in our community apply a rule of thumb that the longer it is until game time, the higher the edge threshold is. For instance, if it's less than 2 hours until game time, I'll place on my full range. If it's 2-6 hours, I'll only place on 5%+ edges. If it's more than 6 hours, I might place on 8%+ edges.
Multiple lines on same game
If you place multiple bets on the same game with dependant lines, you'll see huge swings. If you place bets on +0.25 Home, +0.5 Home, +0.75 Home, +1 Home as well as Home to win and you follow our bet sizing - you'll have a lot of money that the home team is going to win. Keep in mind that if you place on many lines on the same game you need to scale down the bet size. One could argue that decreasing the bet size and placing on multiple lines could decrease variance, for instance if there's an edge on Over 1.5 and Over 2.5 goals, you place half the bet size on both of them.
Use a Lower Kelly Criterion Percentage for your Stake Sizing
Set A Max Bet
Also, one should apply a max stake size. I operate with 1% of my overall bankroll. It is possible to set it higher and also to use a higher Kelly % if one wants to take more risk and increase the turnover. This could speed up the bankroll growth, but as Warren Buffet said it with regards to investing, "Rule No. 1: Never Lose Money. Rule No. 2: Never Forget Rule No. 1.". To take an extreme example, if one loses 50% of the bankroll, one will need to increase it by 100% to get back to the starting point. So the important aspect is to manage the risk so that one does not put oneself in a position where the bankroll has decreased to a point, which makes it difficult to recover, nevermind to make a solid profit.