Advanced Betting Theory
1 How To Convert Odds Into Their Implied Probabilities Knowing how to convert betting odds can be very helpful. In fact, if you don't know how to convert betting odds into their respective implied probabilities, you're not helping your chances of coming away as a long term winner in the competitive world of sports betting.
Understanding the implied probability behind the odds on offer is key to assessing the potential value in a particular betting market. And it is just as important when assessing the value that exists with regards to specific odds on a particular outcome. If the implied probability is less than your own assessed probability of a particular outcome occurring, that outcome represents a value betting opportunity.
1. Converting the 3 types of odds to their implied probabilities Typically, there are three kinds of odds you will come across in the sports betting landscape.
Decimal odds:
represented as
1.65 or 2.95 etc.
Fractional odds:
represented as
5/2 or 3 to 2 'on' etc.
Moneyline odds:
represented as
-120 or +140 etc.
They all reflect the same thing, the return you will receive on a given amount of money placed on a bet.
2. Decimal odds Decimal odds are a simple reflection of the return you will receive for each single unit placed. In other words, odds of 1.65 means that for every 1.00 you place on a particular outcome, you will receive a profit of 0.65 should that outcome prevail. To convert these odds to their respective implied probabilities we make a simple calculation. 1 divided by the decimal odds.
So for example, our odds of 1.65.
Implied probability
=
1 / 1.65
Implied probability
=
0.606
3. Fractional odds Fractional odds are generally the most traditional form of expressing betting odds. They are a simple reflection of the return you will receive for a particular amount bet. So for example, the odds of 5/2 (expressed as 5 to 2) means that for every 2 units that you bet, you will receive 5 back.
To convert fractional odds into their respective probabilities, we make the following calculation. Denominator divided by (denominator plus numerator)
So in our example of odds of 5/2.
Implied probability
=
2 / (5 + 2)
Implied probability
=
2/7
Implied probability
=
0.286
Multiplied then by 100 to express as a implied probability percentage of 28.6%.
4. Moneyline odds Moneyline odds, also known as American odds are probably the most foreign odds format to those of us outside of North America. And at first they appear a little confusing. But it is helpful especially when listening to Americans speaking about gambling odds in sports broadcasts or podcasts. So, let's see how we can convert Moneyline odds into their respective implied probabilities. There are two instances of Moneyline odds. The first are 'minus' moneylines. This is expressed as for example -120. But what does this mean exactly?
Well, it is essentially saying that to win 100 you have to make a bet of 120. In other words, if you place 120 on that outcome, you will receive a profit of 100. The other instance are 'plus' moneylines. This is expressed as for example +180. This means that if you bet 100, you will win 180. So how do we convert the 'plus' and the 'minus' moneyline odds into their implied probabilities?
For 'minus' moneyline odds, it's the following calculation.
( - (minus moneyline odds))
( - (minus moneyline odds)) + 100)
So let's take our example of a moneyline odds offer of -120.
Implied probability
=
(- (-120) / ((- (-120)) + 100)
Implied probability
=
120 / (120 + 100)
Implied probability
=
120 / 220
Implied probability
=
0.545
Multiplied then by 100, we get the implied probability percentage of 54.5%. Now the calculation for 'plus' moneyline odds, we make the following calculation: 100 divided by (plus moneyline odds + 100)
So let's use our example of moneyline odds offer of +180
Implied probability
=
100 / (180 + 100)
Implied probability
=
100 / 280
Implied probability
=
0.357
Multiplied then by 100, we get the implied probability percentage of 35.7%.
5. How do we convert one odds format to another? Knowing how to convert one form of odds to another can be helpful, especially if you have come into possession of a large amount of betting data that has odds formatted in an unfamiliar way. To do this, we first need to convert any odds format to their implied probability. Once we have done this, the calculations are fairly straight forward.
6. Converting implied probability into decimal odds. 100 divided by implied probability.
e.g. Implied probability of 75% would return decimal odds of 1.33.
Decimal odds
=
100 / 75
Decimal odds
=
1.33
7. Converting implied probability into fractional odds (100 divided by implied probability) - 1.
So an example of 25% implied probability would be calculated as:
Fractional odds
=
(100 / 25) - 1
Fractional odds
=
4-1
Fractional odds
=
3, expressed as 3 to 1.
8. Converting implied probability into moneyline odds
This depends on whether the implied probability is above 50% or below. If it is above, we make the following calculation. (implied probability divided by (100 – implied probability)) multiplied by 100.
So for example, the implied probability of 75%.
Moneyline odds
=
- (probability)/(100 - probability) * 100
Moneyline odds
=
- (75 / (100 - 75)) * 100
Moneyline odds
=
- (75 / 25) * 100
Moneyline odds
=
3 * 100
Moneyline odds
=
- 300.
If the implied probability is below 50%, the calculation is adjusted a little. (( 100 – implied probability) divided by implied probability) multiplied by 100.
So for example, the implied probability of 25%.
Moneyline odds
=
((100 - probability)/(probability) * 100)
Moneyline odds
=
((75) / (25) * 100)
Moneyline odds
=
3 * 100
Moneyline odds
=
+ 300
While there are many tools on the web that will help you convert odds to their implied probabilities and convert odds to other formats, it is still a good practise to understand the calculations behind these conversions. This will only help you better understand what the odds represent in terms of value as well as exercising your betting brain to think instinctively in terms of implied probabilities when odds are presented to you.
2 Understanding Bookmaker Commission It goes by many names: the Juice, the Vig, the Margin, The Take, The Percentage, The Cut, The Commission. Whatever you want to call it, it's that slice of action every bookmaker takes out of the odds so as to make their business worth their while.
And it varies from bookmaker to bookmaker and even from event to event with bookmakers offering special 'reduced commission' on particular leagues or tournaments to attract bettors, offering them higher odds and greater returns than at competing bookmakers. But what exactly is bookmaker commission? How do you calculate it?
1. What is Bookmaker Commission? It's sometimes thought that the odds a bookmaker offers are more a reflection of who the bookmaker thinks will win a particular contest and that in affect, bookmakers have a preferred winner in any given contest. However, this understanding is only half true. Yes, bookmakers might have a preferred winner in any given contest, but it's not in any way a result of favouring one side when framing the odds. A risk taker is exactly what a bookmaker is not. When framing odds for a particular event, bookmakers are attempting to compose odds that they think will attract betting on both sides of the market, therefore balancing the bookmakers liability given the possible outcomes. But if the bookmaker's liability is equal given any outcome, how does a bookmaker make a profit themselves? The answer is of course, the bookmaker's commission. Bookmakers take this slice of the full value of the odds offered, resulting in a profit, or 'commission' once their liability is balanced on either side of the odds. This is also known as the Theoretical Hold. In other words, the commission is the percentage of money taken from bettors that the bookmaker will claim should they balance their liability perfectly. And although it's unlikely that a bookmaker will achieve that perfectly balanced liability on each side of a specific event, by offering hundreds of markets each day on a wide range of sporting events, they can be confident that their overall liability will even out and they can take their cut of the money put down by bettors.
2. The 100% Market So what's an example of such a betting market. Well, the clearest example to offer is on so-called 'even money' events. This is where it is deemed by the bookmaker that both sides of the market will attract equal action from a betting public that considers each outcome as an even probability, 50-50. So let's use the example of tossing a coin. We can expect that over enough tosses, it is 50% as likely that a coin will come up heads as it will tails. Now if they were offering a full market without any commission, the odds would of course be an even 2.00 on both heads and tails. i.e. you bet 1.00 to win 1.00. This is what is known as a '100% market' or 'fair odds'. In other words, you're getting full value on your return. But bookmakers want their slice of the action. And so they offer us anywhere between 1.85 to 1.99 as 'even money.' They take out their percentage. This is the business.
3. Calculating The Market As we noted, a 100% Market is where 'fair odds' are being offered. It is where there is no advantage for either the bettor or the bookmaker. When the market is assessed as less than 100%, this places the advantage with the bettor, meaning there is greater value in the market than the probability of possible outcomes. And on the other hand, when the market is greater than 100%, as it typically is, this means there is less than full value in the market. So how do we calculate the commission? Well, it's a fairly simple calculation. Firstly, we need to convert the decimal odds to the percentage probabilities that they represent.
So let's take an example, the odds of 1.65. We convert these odds simply as 1 divided by 1.65 which equals 0.606. We do this for each possible outcome in the event, add them together, then multiply that by 100 and we get the market percentage also known as the 'overound'.
Here's an example. Let's take a football game, with 3 outcomes - either team wins or there is a draw. Team 1
odds:
2.00
Team 2
odds:
3.90
Draw
odds:
3.50
We make our conversions and we get: Team 1 probability:
1 div 2.00
=
0.500
Team 2 probability:
1 div 3.90
=
0.256
Draw probability:
1 div 3.50
=
0.286
=
1.042
Total
Overround
=
104.2%
4. Calculating The Commission There are a number of ways to calculate the commission on specific odds. A popular way is the following: (1 subtract (1 divided by overround)) multiplied by 100.
So let's take our example of the football game further to calcute the commission. (1 - (1/1.042)) * 100
(1 - 0.96) * 100
=
4%
So the odds for that particular football game have a commission of 4%. Of course, you're not going to want to have to do this each and every time you wish to make a bet, especially if you're trying to calculate the value in a horse racing market of 12 or so runners. Fortunately, betting exchanges such as Betfair display the Overound on each market. There are also a number of calculators on the web that will do it for you.
5. Find the lowest commission markets
While the conclusion is obvious, that it is far more beneficial to bet with bookmakers who offer better value markets, it's something that many novice bettors don't quite understand the full implications of. And with our ability now with online betting to play one bookmakers odds off against another, the opportunity to reduce the impact of commission is greater than ever, particularly with the advent of betting exchanges. It may seem like a slight percentage, and it may seem like the difference between a 1.90 even money offer is only 5 cents less than a 1.95 offer, but over the long run it makes a huge difference to your overall chances of success as a sports bettor.
3 Understanding The Kelly Criterion That some punters win consistently is not in doubt.
Bookmakers close, or severely limit, accounts and even the world's largest betting exchange has found it necessary to introduce a Premium Charge, implicitly acknowledging that a number of people have the ability to consistently identify favourable bets and the discipline to bet only, or perhaps mostly,when it is value for them to do so.
1. Maximising Your Advantage If the goal of these punters is to grow their banks as optimally as possible, how much should they stake on each individual bet?
It's the subject of much debate, but the answer to this is that stakes should be calculated according to the Kelly Criterion, but unfortunately when this solution is applied in the field of sports investing, there are a number of challenges.
2. Kelly Limitations As John Larry Kelly Junior's original 1956 paper makes clear, the criterion 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. This is unfortunate. In the world of sports, no two events are ever exactly the same. Bet on red on the roulette wheel and you know exactly what the probability is, but since the edge in casinos is in favour of the house, Kelly isn’t going to help you here. For Kelly to work, you must have a positive edge. If the edge is precisely zero, Kelly recommends no bet, and of course if the edge is negative, again there is no bet. So how can Kelly help in the real world of sports? To help answer this, lets 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.
3. Kelly In Action 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.
Clearly the optimal strategy lies between these two extremes, and Kelly calculated that the fraction of the bank to be staked equals the size of your edge. For example, if the chance of a win is 51%, and the price available is evens, 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%).
4. Real Examples To see the formula in action, lets take an example of a football match where the odds available on the draw are 3.50 (or 5/2 with an implied probability of 28.6%) but your estimate of the true probability is 30%.
The formula for calculating the Kelly stake is: [(Probability multiplied by odds) - 1] divided by (odds-1).
Thus Kelly stake: [(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, i.e. the stake should be 2% of the bank.
5. Fractional Kelly When applying Kelly, the consequences of over-estimating your edge are serious, and as we mentioned earlier, in sports the probability of an outcome is imprecise. It is for this reason that most punters err on the side of caution, and use the more cautious strategy 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. This is a sensible way of handling the inevitable losing runs which occur, even if you have a favourable bet. Your bank will increase in the long run, only more slowly, but the risk of blowing the bank are reduced. Progress and bank balance will not be a smooth upward slope, and will be interrupted by frequent drawbacks (losing runs) but by using the Half-Kelly bet, volatility is greatly reduced, yet returns 3/4 of the compound return. For many gamblers, that is a price worth paying. It can be shown that a Kelly bettor has a 1/2 chance of halving a bankroll before doubling it, and that you have a 1/n chance or reducing your bankroll to 1/n at some point in the future. For comparison, a Half Kelly bettor only has a 1/9 chance of halving their bankroll before doubling it.
4 Developing A Sense For Value
One of the hardest things to explain to people with only a casual (and often stubborn) understanding of betting, is the concept of value.
Understanding value is the key to long term betting success. It might seem like common sense to a seasoned betting veteran but to the inexperienced, it can be a difficult concept to adjust to. Learning to bet hard earned money on teams that nobody thinks are a chance to win can feel a little like learning to repel down the outside of a building. At some point you just have to let go and have faith in your preparation. The task is of course, developing a sense of value you can have confidence in. And it's not an easy thing to develop, but there are things you can do, to start developing your own intuitive sense for value.
1. Specialise At least in the beginning of your betting career, it's a good idea to specialise in particular sports or leagues. And it's a good idea to do so in a sport or league you already know well. Start with the leagues you know best in terms of team performance and history. Once you begin to investigate the leagues you know well, you can then apply what you have learnt to other leagues you don't know as well. Yes, baseball offers a tremendous number of betting opportunities each season. But if you know little about the sport, you're wasting your time and it's doubtful you will quickly develop a sense of for value. Bet what you know best first before you begin to expand your field of expertise.
2. Understand Probabilities
You don't need to be a maths wiz to be successful betting value long-term. But you do need to understand probability. After all, this is the business. Betting odds represent the probability of a particular outcome and we see far too often people betting in point-blank black and white terms. You'll often hear people declare that a team has no chance of winning or that there is no way another team is going to lose. The fact is, as far as professional sports is concerned, every team has a chance of winning and every team has a chance of losing. And identifying value is understanding what chance that is.
3. Pricing Up This is key to developing an intuitive sense for value. The task is to come to what we refer to as 'the uncomfortable compromise'. You're not composing the odds you would like to see the bookmakers post, you are composing odds that you would not feel comfortable taking yourself. We can't emphasise how helpful this task can be to an aspiring punter just starting out. It gets your head thinking in terms of probabilities and by checking the results of your own prices, it allows you to pit yourself against the shrewd and experienced bookmakers. It takes time to do. It takes effort. There can be weeks where you can't be bothered doing it. But doing this religiously each week of the season for the sport or league you plan to specialise in can quickly sharpen your nose for value.
4. Recognise that it's a Market Don't ever forget that it's a betting market. The pull and sway of general opinion is going to set the odds. Making this a habitual way of thinking is not only hard to do, but can at times reduce the sport you love so much, to a matter of mere economics. Sometimes you might wish you could just watch a football match and not be wondering about how the outcome may impact next week's odds or how the overwhelming number of casual punters might persuade the odds for an upcoming match in a particular direction based on what they have seen in this match. Will that persuasion offer value in the opposite direction? Will the market over-react?
Once your head gets wired in this way, it's very hard to undo. It might mean an end to your romantic notions of the noble purity of sport. But for understanding and identifying value, that's a good thing.
5. Review & Analysis You don't know where you're going if you don't know where you've been. Much of the work in developing a mindset for value is in reviewing how your previous assessments have performed. Where did you get it right? Where did you get it wrong? When you start out pricing up matches, you're prone to exhibit pre-conceived biases. Some may be accurate. Many will not. You can remedy this by reviewing your assessments at the conclusion of matches as well as undertaking analysis of how your sport or league has performed in recent years. For example, what is home-field advantage worth in real terms? Does the market over-value it? Does the market have a general and long-term bias for or against particular clubs or clubs playing in particular situations? All of this can help you tune your mind to value. Yes, it's work. What else did you expect it to be? Never think you know it all and always be prepared to reassess. It's this kind of study, review and analysis that will keep you one step ahead of the market.
6. Persistence Finally, recognise that it takes time. It's like developing any kind of craft. Even if you intend to develop sophisticated betting models for predicting the probable outcomes of matches, the development of an intuitive sense for value and 'gut feel' for the betting markets will often provide the basis for even such an abstract approach. Knowledge is power and the greatest knowledge is experience. Essentially, this is the task when developing a sense for value. In the end, it's a matter of developing rich and deep experience for the betting markets and experience worth anything is experience well earned.
5 Developing A Predictive Betting Model Building a sports betting model can be difficult work. We won't lie to you. It can mean long hours of tediously entering data, sorting spreadsheets, setting up databases, testing, re-testing and re-re-testing. All this, with no promise that you will eventually 'crack the code'.
Would you expect anything different? Bookmakers have the sharpest minds working for them day in day out, using everything at their disposal in order to compose the odds that millions of people are trying to beat. You think you're going to come up with a system to beat them in a couple of afternoons of analysis? It's not going to happen. It takes times and dedication, a sharp mind and persistence. But then, half the thrill is in the chase. More often than not, the end product is worth the time and effort, even if it's just for the many lessons you will learn along the way, both practical and theoretical. But we can tell you, while no model you build will be light work, the first model is always the hardest.
1. So where do you start? In this article we will discuss the fundamental things to consider before getting started on a sports betting model. And in doing so, try to impart to you some of the lessons we've learnt along the way in the hope that it saves you some time and frustration.
2. Understand what you're attempting to do
It's pretty elementary, but you would be surprised by the number of people who miss the point and don't quite grasp what a betting model is trying to achieve. And what is that exactly? Well, a betting model attempts to assess the current 'form' of a team or participant, which is then compared to its opposition in an attempt to gauge the likely outcome of the contest. What you're essentially trying to do with a model, in very basic terms, is create an independent point of reference from which you can ascertain the probability of all possible outcomes in a given match or contest. Ideally you want your model to be able to recognise value in a given betting market. In other words, you want it to give a truer expression of a teams potential or 'form' than what the bookmakers odds do. Once you've developed your model, you'll be surprised how often it can identify value in the market. Will it always get it right? Of course not. But a fully developed betting model will show you opportunities that the general betting public simply wouldn't consider.
3. Learn your probability theory Yeah it sounds like homework. Bor-ing. But you're not doing yourself any favours unless you understand the fundamentals of probability theory. And it's not so much about learning and grasping theory, although it's important. It's equally as much about inspiration. The more you read and understand about probability theory, the more imaginative you'll become with your models. You’ll come up with all sorts of interesting and creative things to do with the numbers, taking angles you hadn't even considered.
Sure you can probably get by making a model with basic arithmetic. Maybe. But it's not going to be the cunning bookie killing machine that you've always imagined having at your disposal.
4. Know how to manipulate a spreadsheet No you don't have to be a programming wiz to build a sports betting model. But the more you do know about spreadsheets and the like, the better off you will be and the more powerful your testing and analysis will be. And perhaps most of all, the more efficiently you will make use of your time. So at the very least, know how to throw a spreadsheet around and learn how to make the data dance. And from there, work your way into building databases and writing queries. Trust us. You'll be glad you did.
5. Know the sport and its betting markets If you're starting your first betting model or system, we would recommend you begin with not only a sport you know well, but a league you know well. And by knowing well, we mean like a ruthless expert. If you don't understand the fundamentals of the sport or league, it's very difficult to know where to begin in your analysis and very difficult to know how to assess the performance of the sports participants. And by understanding the fundamentals we also mean have a clear and comfortable understanding of the betting markets for that sport. The markets that you are going to attack is at the very core of your models identity. Is that market head to head betting? Is it line betting or handicap?
In other words, the manner in which you decide to assess a teams performance is going to be determined by the betting market you want to find value in. So know the sports betting markets as well as you know the sport itself.
6. Market Liquidity You must also keep in mind bookmaker limits and market liquidity. The amount of money you can get down on a particular league or bet type is something to consider before spending hours building your betting model. Sure, you might make a killer model for Polish 2nd Division football. But are you going to be able to bet at a rate that makes the time spent on the model worthwhile? We suggest staying away from the more obscure leagues. For one thing, bookmakers are far more sensitive to successful betting in these sorts of leagues. They will move quickly to restrict your betting if they feel you've got an edge in a league that they would readily admit to not knowing as well as they should. Plus bet limits in these leagues usually begin pretty low anyway. And even if you move your action to a betting exchange like Betfair, you're going to have trouble getting your money matched in the lower leagues. So aim high. Shoot for the big time. This is where the money is. And it's where the challenge is too. Build a model that will give you options and one that will provide for you long-term.
7. Data Data Data Your model is going to need data. At the very least that means final scores, but ideally it means meaty in-depth stats that you can breakdown and incorporate into an algorithm. And most of all historical odds for which to test your model on. Where can you get the data you need in the format you desire? Is it readily available in spreadsheet form? Well, that can be the tough part.
There are plenty of sources on the net for statistical data for a wide number of leagues. Some are free. Some will cost you a pretty penny. It's worth spending hours trawling the web for sources. You'll often find the best sources in places you'd never expect, tucked away in the far reaches of the internet. But you won't always find exactly what you are after, especially if you're looking to make a model for more obscure sports or leagues. So there is always the option of doing your own data entry, even if it's to augment a data source from another provider. Personally, we'd advise this only as a last resort. Because to be perfectly honest, data entry sucks. But if you are going to head down this path and begin your own data source from scratch, just remember to repeat this mantra:You only have to do it once. You only have to do it once. It helps. Oh, and remember to click 'Save' often.