As anyone who has ever considered betting or even bets on a regular basis knows, placing money on bet raises a number of questions.
Questions like; who should I bet on ? What should I bet on ? When should I place my bet? Where to bet on? Why to bet on a specific event? How much should I bet ?
We understand, making a financial decision is never an easy task. The problem lies in finding the right sport to invest your money in and how much you should invest.
This is where the Kelly Criterion betting strategy comes in. The Kelly Criterion calculates the proportion of your own funds to bet on an outcome whose odds are higher than expected.
With the aim that your own funds will increase exponentially. The Kelly Strategy has proven to yield better results in the long run.
If your end goal is to maximise your bankroll as a punter, then this is the best possible strategy to achieve just that
Why the Kelly Criterion ?
The Kelly Criterion aims to calculate the optimum stake for any value bet. Basically, the Kelly Criterion will take into account both the size of your advantage, that is the value available.
As well as the size of your bankroll with the intention to minimise risk whilst maximizing your advantage.
When it comes to betting on sports, things get a little more complicated as the size of your bets increases.
What are the Issues in Using the Kelly Criterion?
As most things go, nothing is 100% flawless. The Kelly Criterion included.
John Larry Kelly who is the man behind this formula has stated that the formula is only valid “when the investment or 'game' is played many times over, with the same probability of winning or losing each time, and the same payout ratio”.
It’s common knowledge that in the vast world of sports, no two events are exactly the same. Each event will feature new players, new challenges and new outcomes.
For this criterion to work to it’s best abilities you will need both a positive edge and a value opportunity.
The million dollar question is, how can the Kelly Criterion help in the live world of sports, in the cases where probabilities are unknown?
To help answer this, let’s take a simple example of a game where the true probability is 50%, but the payout exceeds this. You have a value bet, but it should be obvious that betting the full bank each time is not the best way to approach this.
Your chances of going bust are extremely high. At the other end of the risk spectrum is the ultra-cautious approach of staking a small fraction of the bank each time.
While the chances of going bust are now very small, your bank isn’t going to grow very fast.
How Can You Calculate the Kelly Criterion?
So we know what the Kelly Formula entails and we know that you can apply to it to sports.
But how can you put this optimal strategy into play ?
Well, when you’re using the Kelly Criterion it is works on the premise of balancing out two extremes. Firstly the fraction of the bank to be staked and secondly the size of your edge.
Always keep this in mind, your stake should reflect the value of the opportunity.
For example, if the chance of a win is 51%, and the price available are odds of 2.00, you should bet your edge of 2% (51% -49%), 49% being the probability of losing.
If you have a bigger edge, for example your chance of a win is 53%, your stake should be 6% (53% - 47%).
The Kelly Formula in Action
There are two basic components to the Kelly Criterion:
Win probability - The probability that any given trade you make will return a positive amount.
Win/loss ratio - The total positive trade amounts divided by the total negative trade amounts.
- B = the Decimal odds -1
- P = the probability of success
- Q = the probability of failure (i.e. 1-p)
To see the Kelly formula in action, let’s take an example of a football match where the odds available on the draw are 3.50 but your estimate of the ‘true’ probability of the draw is 30%.
The formula for calculating the Kelly stake would be:
[(Probability multiplied by odds) – 1] divided by (odds-1)
Thus the Kelly stake is calculated as:
= [(0.3 * 3.50) – 1] / (3.50 - 1) =[(0.3 * 3.50) – 1] / 2.5 =[1.05 – 1] / 2.5 =0.05 / 2.5 =0.02
In this example, we should place 2% of our bankroll on this bet. If our bankroll is £1000, then our bet stake should be £20.
Whilst in theory the Kelly strategy is bulletproof, in practice it can be less precise. Punters tend to be more cautious and instead opt of ‘ fractional Kelly’.
This means that rather than bet the suggested percentage, you use a fraction of it, commonly a half (Half-Kelly) but it can be any fraction.
How are fractional Kelly Stakes calculated? It's fairly simple:
(((Probability multiplied by odds) – 1) divided by (odds – 1)) multiplied by your chosen fraction
So if we were to apply a Half Kelly staking strategy to our previous example, the Kelly Stake is calculated as:
= ((((0.3 * 3.50) – 1) / (3.50 -1)) * 0.50 = (((0.3 * 3.50) – 1] / 2.50) * 0.50 =((1.05 – 1] / 2.50) * 0.50 =(0.05 / 2.50) * 0.50 = 0.02 * 0.50 = 0.01
So in this example, applying a Half Kelly staking strategy would recommend betting 1% of our bankroll on this particular bet. So if our bankroll is £1000, then our stake should be £10.
This is a practical way of managing your bets, especially when they go south. Your bankroll will increase gradually at a slower pace but you will be reduce risk.
What Are The Benefits ?
The fundamental use of the Kelly Criterion will be that you will receive ¾ of your bets in returns. For the majority of gamblers,this is reason enough.
Betting is a lucrative hobby but takes a great deal of time to begin seeing profits. As any experienced bettor will tell you, this is a marathon not a sprint.
Using the Full Kelly, an average punter has about a 33% chance of seeing their bankroll cut in half before that bankroll will be doubled.
Applying a more conservative approach, such as the Half Kelly, the average punter has about an 11% chance of seeing their bankroll cut in half before it they see it doubled.
The Kelly Criterion also takes the size of your bankroll into consideration, which is another advantage. With that being said, any staking plan you choose to use should be based primarily on the amount of money you have to bet with.
This is a fundamental principle of bankroll management. What this particular betting strategy does that most other staking plans don't, however, is the application of the theoretical value of wagers.
The Kelly Criterion offers a distinct advantage over other betting formulas, especially since it works on providing a lower-risk bankroll.
Nonetheless, it requires precise calculations which at times will not provide an explosive boost to your bankroll.