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‘1X2’ is an abbreviation of the three possible outcomes in a football match: home win (1); draw (X); away win (2).

This market is also known as ‘HDA’ (Home-Draw-Away), or sometimes simply ‘FT’ (Full-Time match result).

The act of 1X2 betting is referred to as “betting on the full-time result”, “match betting”, or can be termed a “three-way bet”.

Definition of ‘Full-time’

Full-time is reached in a football match at the close of the second half of 45 minutes’ regulation time plus the time added-on by the officials for stoppages. When the added-time has elapsed, the referee’s whistle signals the end of the game.

All 1X2 (HDA) bets relating to the result of the match then begin to be settled by the bookmakers.

In a fixture requiring an outright winner, in the event of a draw or tied aggregate scoreline at the end of the regulation match time, two periods of extra-time may then be played to break a deadlock.

It is important to reiterate that full-time 1X2 bets are closed and settled on the result at the end of a regulation period of 90-minutes’ play (2x 45 minute halves, plus added time), and after this, new markets will then appear in most bookmaker platforms for extra periods of play (extra-time) or penalty shoot-outs.

Placing a Bet

It is possible to place a match-result bet either before the kick-off (ante-post bet), or whilst the game is in progress (in-play bet).

In the English Premier League (EPL) match shown below (screenshot courtesy of Betdaq betting exchange), we have elected to back the draw at odds of 3.5. (Decimal or ‘European’ odds).

In this case, the bet was requested by clicking on the yellow-highlighted square bearing the odds of 3.5 in the ‘Back All’ column.

(Click on the image below to enlarge it in a new tab):

Betdaq: Example Bet Slip

Having clicked on the draw price, a bet slip opens up to the right of the screen, ready for insertion of our stake. Here, we have entered a figure of £10.

The profit due from our wager should the match indeed end in a draw is shown as £25.

In order to strike this bet, the next step would be to click the purple button ‘Place Bet(s)’.

What do Bookmaker and Betting Exchange Odds mean?

Just as a side note… When we write articles showing mathematical calculations we always prefer to use European odds, also known as decimal odds.

It would go too far to explain in this article the whole concept of betting odds but here’s an article on that topic if you are interested in learning more: Understanding Betting Odds – Moneyline, Fractional Odds, Decimal Odds, Hong Kong Odds, IN Odds, MA Odds

In short, betting odds show how much you will be paid out if your bet wins.

However, odds can also be converted into their ‘implied’ probabilities and here’s the formula:

Betdaq’s prices for our example match (at the time of the screenshot grab) were:

Theoretically, because there are only three outcomes to a match (home, draw or away), the probability percentages of each should add up to 100%.

But, in reality, the percentages on any one match with any single bookmaker will always be above 100%; using our example odds, it’s 101.09% (35.21% + 28.57% + 37.31%).

Why should this be?

Bookmaker vs. Betting Exchange Overrounds

The percentage difference over and above the 100% base probability figure is known as the bookmaker ‘overround’, ‘margin’, or ‘vigorish’ (or ‘vig’). This represents the bookmaker’s expected profit.

In its simplest form, for every 101.09 units the bookmaker accepts as wagers on the odds of our example match, if the wagers remain stacked in the same proportions as the implied probability percentages, then the bookmaker will pay out only 100 units, thus ensuring a profit regardless of the match result.

However, our example here is a betting exchange. Like all other exchanges, it guarantees a profit from every match by charging commission on all winning bets. Here, Betdaq’s commission rate is 2%.

The overround calculations now become slightly different because the commission amount has to be factored in.

You can see that at the same odds, the implied probabilities now add up to 102.45%. Because of the commission element, exchanges tend to have a larger overround than bookmakers, even if it seems at first glance that exchanges have better prices. In fact, rewards are generally higher with a bookmaker.

Here’s the formula to convert odds in an exchange into their ‘real’ odds (after commission) in order to compare directly with bookmaker odds:

So, in our example match, the ‘corrected odds’ were as follows:

What do the Implied Probabilities mean?

The important thing to remember is that converting odds into their implied probabilities is not an accurate indicator of the percentage chances of each outcome. Bookmakers adjust their odds (prices) due to demand, which leads to distorted ‘implied’ probabilities. These are normally very small and not easy to spot but enough for the bookmakers to stay in business and make consistent profits.

Implied probabilities reflect much more the public perception of the likely outcome (not the statistical likelihood), being a measure of the volume of money wagered on each outcome rather than its real chances of success.

And odds fluctuate throughout the ante-post and in-play markets according to the weight of money placed and other factors such as time elapsed in the match.

It is, therefore, not advisable to rely on the market odds (at any moment in time) as a totally accurate benchmark of the event probabilities.

In order to more accurately gauge ‘true’ probabilities, it is advisable to take a purely mathematical approach using historical results and statistics.

The very nature of selecting two variables in what is effectively a combination bet or ‘double’ means that the odds are multiplied creating an opportunity for higher returns than backing each outcome individually.

The attraction of higher odds and the perception that most games in modern football are free-flowing attacking affairs where both defences are likely to be breached have created a market for these types of combination bets.

You may also think that by ‘doubling’ the home or away result and BTTS, the wager is shrewder than simply picking the correct score of the match where the odds are higher but far disproportionate to the probability of a return?

Let’s take a look at these points in more detail.

Table 1: Winning & Losing – FT Result + BTTS Double

Goal-scoring Statistics

We have previously looked at FT score distributions using a sample of almost 11,000 matches from nine different leagues.

If you open the screenshot there you will find that clean-sheet victories (1-0; 2-0; 3-0; 4-0; 0-1; 0-2; 0-3; 0-4, etc.) by either the home or away team accounted for 38.22% of all results.

Draws (0-0 through to 4-4) made up a 25.33% quota of all results.

However, for the sake of this article, we are interested in home and away wins where both teams scored. When tallied, these accounted for precisely 33% (19.76% + 13.24%) of all results:

10,723 Match Sample: Home or Away Wins where both teams scored

A sample size of 10,723 matches is a statistically significant amount and a fair benchmark to gauge other leagues by.

In comparison, of the 1,900 English Premier League (EPL) games that took place in the five seasons from 2012/13, there were 646 matches (34%) when betting on one of the teams to win and both teams to score could have returned a winning bet.

From these indications, there will be ‘around’ a third (33%) of matches in a season in any top-flight league where the combination of BTTS and a decisive match result occur.

But, of course, this assumes that the right teams were selected to win. Without taking account of any assumed preference for the favourite, the probability is as low as 16-17% (50-50) for a winning return across those games.

Win and BTTS Odds on Offer

Typical odds in the market for the Win (home or away) + BTTS can be anything between 3.00 and 6.00 depending on the teams involved, but the average odds are around 4.00.

So, roughly speaking, there is a 1 in 6 chance (16% = 1 in 6.25; 17% = 1 in 5.88) of making a winning selection, which will, at average odds of 4.00, return winnings of three times your money.

But how does this compare with simply backing the correct score?

Correct Score Analysis

The EPL is considered one of the most exciting leagues in the world, but the most common result type, as it is in every league, is actually a (not very exciting) one-goal game (1-0 or 0-1).

One goal games accounted for 348 (18.32%) of the 1,900 EPL matches between the five seasons during 2013-18.

The second most common result is 2-1 either way. During the same five season period, the EPL recorded a 2-1 home win 142 times (7.47%), and a 1-2 away win 123 times (6.47%), equating to 13.94% of all results.

In comparison, adding the 2-1 and 1-2 occurrences in Table 2 above gives a total of 15.94%, but it is safe to say that, across the board, 1-0 and 2-1 score lines are generally the most common results.

Again, taking out any preference for favourites, and using the 50/50 measure to predict the right team winning the match 1-0 or 2-1, the probability of correctly predicting 1-0 either way are around 9% (half of 18.32% in our EPL example), and around 7% for predicting a 2-1 (half of 13.94%).

So, mathematically at least, there is a slightly lesser chance of winning with these bets. However, looking at the disparity in odds, the potential winnings in the Correct Score market are far, far greater.

Conclusion

Taking a typical weekend’s EFL Championship betting fixtures as an example, even allowing for favourites and serial 1-0 winners, the odds for correctly predicting a 1-0 win range from around 6.00 to 34.00, and average out at odds above 11.00.

So whilst there is statistically a 1 in 11 chance (9%) of making a winning 1-0 correct score selection, either way, the bet will on average return winnings of more than ten times your money, and potentially as high as thirty-three times the original stake.

All things considered, betting on the correct score market provides a much larger reward than betting on the combination of match result and BTTS.

You can bet on Over/Under 2.5, or Over/Under 2,25 or Over/Under 2. But what are Over 2.5 bets, or even 2.25? There are no half goals! Or quarter goals! It doesn’t seem to make sense. Does it?

We will explain what the different Goal Lines signify and after you’ve finished the article you will never be confused again!

Betting on .5 Goals

One of the most common bet types is Over/ Under .5 goals.

Obviously, there is no way for half a goal to be scored in a game. The expression .5 is just an aid to ensure that it is clear on what you are betting.

For example, if you place a bet on Over/Under 2.5 goals, then the .5 is the ‘turning point’. You win if there are at least 3 goals scored, and you lose if the match ends with less than 2 goals scored.

Here’s an example…

If you still have difficulties understanding the concept, here’s another article on the .5 bet: A Brief Introduction to Over Under Goals Betting.

Betting on Goal Lines with Whole Numbers

Bets on whole numbers are often called Goal Lines or Asian Goal Lines. Although, technically, this isn’t correct as all bets described here are ‘goal lines’, but we will be using the term as it’s widely used by punters and bookmakers.

They are somewhat similar to Asian Handicap betting on the 1×2 result. As the name suggests, the possibility of a refund exists if a certain result comes in, in this case the ‘Goal Line’.

Similar to the AH, if the match finishes in a draw result (= ‘goal line’), it’s a “push”. The punter gets their money back. Otherwise, if there are less goals scored than the goal line, the stake is lost, and if more goals are scored, it is a win.

In the above example, if you were to bet on Over 2 Goals then you get your stake back (push) if the final score is exactly 2 goals (e.g. 2-0, 1-1, 0-2).

All the other Goal Lines naturally follow the same pattern.

Betting on .75 Goals or .25 Goals – or – Whole Number, .75 or .25

If the .5 bets are combined with Asian Goal Line bets, then you get .75 or .25 Goals bets. Half of your stake is placed on the .5 bet whilst the other half is placed on the Asian Goal Line bet.

These bets are often shown as either Over 2.25 – or – Over 2, 2.5.

For example, if you place a bet of £20 on Over 2, 2.5 it means that you are placing a split bet. £10 on the 2 Goals Asian Goal Line, and £10 on Over 2.5 Goals.

If the match finishes…

• with 3 or more goals, then you will receive the winnings of both bets
• with exactly 2 goals, half of the stake will be returned as it was a push (2 Goals Asian Goal Line), and you will lose the other half (Over 2.5 bet)
• with less than 2 goals… your entire stake is lost

The same applies to the .75 bets, as shown below:

In this example you place a £20 bet on the Over 2.5, 3 goal line. Again, you would be placing a split bet. £10 on the 3 Goals Asian Goal Line and £10 on Over 2.5 Goals.

If this match finishes…

• with 4 or more goals, you will receive the winnings of both bets
• with exactly 3 goals, half of the stake will be returned as it was a push (3 Goals Asian Goal Line), but you will win the other half (Over 2.5 bet)
• with 2 or less goals… your entire stake is lost

To be honest, I would recommend keeping your hands away from these bets, although it may sound tempting to get half of the stake back. Although these are referred to as being a single bet they are actually two completely different bets rolled into one!

If you do not really understand odds calculation and probabilities, then it is definitely a bet which bookmakers love! They can adjust the pricing as they like, without the average punter fully understanding the maths behind it, ensuring that the mathematical advantage lies with the bookmaker.

Anyway, the silver lining is that it is quite unlikely to be exposed to the temptation as these bets are rarely offered by European bookmakers.

Here is another diagram to demonstrating split bets:

Betting for Profit on Goals

At the end of the day the goal of each punter should be betting for profit. Am I right?

Bookmakers make a living from betting by using maths. They analyse and calculate the chances of an outcome and then price their bets. Of course, they make sure that the mathematical advantage is on their side, just like anyone operating a game of chance (e.g. Casinos).

The punter who relies only on gut feeling does not have a chance against the bookmakers.

However, with Over/Under Goal bets the punter at least has a chance to start understanding the statistics behind the bet. It isn’t too difficult to calculate the probabilities of the various results and number of goals in a game and to then find value bets.

If you are interested in starting to bet for profit, then you should seriously consider buying our Fundamentals of Sports Betting course. For the first volume, we have chosen to write about the Over/Under goal market as this is the easiest betting market to teach the fundamentals of statistics and maths on, without the need to dive deeper into more advanced formulas and concepts. Give it a try!

There are all kinds of explanations on the Internet about various odds types, and the majority of them distinguish between fractional, decimal, and moneyline odds.

Image: paffy (Shutterstock)

Unfortunately, this is misleading and mathematically speaking, incorrect. There are only two types of odds, which are unrelated to their displays as fractions, decimals or, as in America, whole numbers.

Just remember those long ago school days (for some of us!)… A fraction, such as 6/5, converts into a decimal 1.2, or vice versa. Both numbers are the same, only written using different formats.

Here are the two main types of odds, including their formulas…

(1) Single-tier – (Net) Return Odds:

Fractional and Hong Kong odds are actually exchangeable. The only difference is that the UK odds are presented as a fractional notation (e.g. 6/5) whilst the Hong Kong odds are decimal (e.g. 1.2). Both exhibit the net return.

The European odds also represent the potential winnings (net returns), but in addition they factor in the stake (e.g. 6/5 or 1.2 plus 1 = 2.2).

(2) Two-tiered – Moneyline Odds: highlighting the amount of money risked, or the amount of money won:

Odds commonly referred to as ‘moneyline’ are mainly US bookmakers odds and also known as American odds. Moneyline means the money wagered either to win 100 units (e.g. -400), or money which will be won from a 100 units wager (e.g. +120).

However, both Indonesian and Malaysian odds, although displayed as decimals are, strictly speaking, ‘moneyline’ odds but their basis is 1 unit and not 100. Whilst the Indonesian odds closely resemble the American moneyline odds, Malaysian odds are a kind of “inverted” Indonesian style, combined with Hong Kong odds.

Although this may all sound pretty confusing, and the odds certainly look very different at first glance (see table below), just have a closer look at the above formulas – all odds are calculated using their net returns (formula for net return: 1/probability – 1) and change their formula at 50% probability (this is what is actually understood under by term ‘money-line’).

European, British, American, Malaysian, Indonesian, and Hong Kong Odds
BETTING ODDS CONVERSION TABLE

Fractional Odds (also known as Traditional or British/UK)

Fractional odds are favoured by bookmakers in the United Kingdom and Ireland.

Fractional odds quote the net return that will be paid out to the bettor, should he win, relative to his stake. Odds of 6/5 (“six-to-five”) imply that the bettor will cash £120 from a £100 stake. Should the punter win, he always receives his original stake back, plus the winnings.

So, if the odds are 6/5 and the stake is £100, then the total return is £220 (£120 winnings plus the original £100 stake).

Odds of 1/1 are known as ‘evens’ or ‘even money’. Not all fractional odds traditionally show the lowest common denominator. Perhaps most unusually, odds of 10/3 are read as “one-hundred-to-thirty”.

Hong Kong Odds (also known as HK Odds)

Image: Scott Maxwell (Shutterstock)

Hong Kong Odds are mainly used by people living in Hong Kong. Until 1997, Hong Kong was under British rule and therefore it should not be a surprise that HK odds closely resemble traditional British odds. The only difference is that HK odds are written in a decimal notation whilst the UK odds use fractions.

Hong Kong odds, as well as their UK counterparts, both quote the net return that will be paid out to the bettor should he win, relative to his stake. Odds of 1.2 in Hong Kong are the same as 6/5 (“six-to-five”) in the UK and both imply that the bettor will earn a net profit of £120 from a £100 stake. Should the punter win, he always receives his original stake back, plus the profit.

It follows that if the HK odds are 1.2 and the stake is £100 then the total return is £220 (£120 winnings plus the original £100 stake).

Decimal Odds (also known as European or Continental)

Decimal odds are standard on betting exchanges and they are favoured in continental Europe, Australia, and Canada.

Decimal odds are equivalent to the decimal value of the fractional odds, plus one. Because decimal odds are simply 1 divided by probability (= 1/probability) they are easier to use in calculations and we therefore favour them for our articles and explanations.

Thus, ‘even odds’ 1/1 are quoted in decimal notation as 2.0; the 6/5 fractional odds (1.2 HK odds) discussed above are quoted as 2.2. Decimal odds quote the net return paid out to the bettor PLUS the original stake.

So if the odds are 2.2 and the stake is €100 then the total return is €220 (€120 winnings including the original €100 stake).

Odds commonly referred to as ‘moneyline’ are the odds which are mainly used by US bookmakers. These odds mean the money wagered either to win 100 units, or the money which will be won from a 100 unit wager.

Please note that both Indonesian and Malaysian odds are also ‘moneyline’ odds although often wrongly referred to just as ‘decimal odds’, probably due to their decimal notation, whilst US moneyline odds are shown in whole numbers.

However, both Indonesian as well as Malaysian odds have the same underlying formulas as the US moneyline odds, only that their basis is 1 unit and not 100.

Even the term ‘Stake’, at least so long as it is money related, is easily understandable.

Whatever level your stake is, there are only two options: you either lose the bet and your stake, or you win the bet, retrieving your stake and adding to it your winnings.

However, the term ‘Odds’ is far more difficult for most bettors, especially as odds are connected to market prices, fluctuations, probabilities, expectations, etc.

Hand on heart, can YOU reliably define the terms “bet”, “odds”, and “stake”?

What is a BET?

Definition of ‘Bet’: Technically speaking, a ‘bet’ is an agreement between two parties that the one who makes an incorrect prediction about an uncertain outcome will forfeit something stipulated to the other – a wager.

Betting is all about risking something, usually a sum of money, against the money of someone else based on the outcome of a future event, such as the result of a race or other competitive event.

What are ODDS?

The term, ‘odds’, is somewhat ambiguous.

Here are two definitions from well-known dictionaries:

Macmillan Dictionary: The chances that are used for calculating how much money you will get if the person or thing you bet on wins a race or competition.

Oxford Dictionary: The ratio between the amounts staked by the parties to a bet, based on the expected probability either way.

The problem with the above definitions (and many other definitions found in dictionaries) is that odds are not necessarily connected to the real chances of something happening, not even to ‘expected’ probabilities.

Just think of British odds, European odds, and US Moneyline odds.

British odds show the net return of a bet, European odds display the net return of a bet plus the original stake, and US Moneyline odds exhibit the money wagered either to win 100 units, or the money which will be won from a 100 unit stake.

Another deviant example is that bookmakers adjust their odds to public opinion in order to balance their books.

Therefore, it is simply incorrect to say that ‘odds’ display the chances of something happening. Odds are not even necessarily based on expected probabilities.

Learning Point: There is NO connection between the market odds of a bet and the real probabilities of the event occurring.

What does the term STAKE mean?

Definition of ‘Stake’: Money or property risked on the result of a horse race, card game, match outcome, etc.

Stake (or ‘wager’ in America), is straightforward terminology.

You bet with your friend on a game of pool, and stake £5 each. Whoever wins the game gets £5 from the other party, and whoever loses is £5 poorer.

In betting, the stake (or ‘wager’) usually means money, which is countable.

The concept of stake becomes much more complicated if property is wagered, such as houses, cars, or in some countries even wives! If you gamble property then you not only have to calculate the true probabilities of a bet to compute the odds, but also convert the staked property into a monetary value.

In these cases bets are very often lopsided and unfair, with a huge advantage to the person who is better in maths than the other. (Read an example: Arsenal fan staked his house on a bet with a Manchester United fan, who offered his wife and Toyota car in return )

Bet, Odds, and Stake – Conclusion

The only honest advice I can give – Do not bet if you do not understand odds!

Unless money is no object, few people will go shopping and load their basket with goods without checking and comparing the prices of different brands. Most of us need to ensure we have enough money available to pay for the purchases, and some of us like to ensure we are getting the best value for the money we pay.

Understanding Odds is CRITICAL! If you constantly go shopping without paying attention to the prices (ignoring the significance of odds), or do not bother comparing brands before buying them (failing to shop around for the best odds), you will certainly end up paying more than others (failing to capitalise on your betting investments), and in the long run be able to buy fewer products for your money (losing more money than you win).

Always remember: Odds are the price for a bet, they very rarely stand for the real probabilities, or chances.

Of course, odds available in the market can be converted into their ‘implied’ probabilities, which can then be compared to your own calculations of the ‘real’ expected probabilities, and vice versa.

If you want to become a winner you MUST understand odds and be able to compare and distinguish between the implied probabilities suggested by the odds offered in the market and the real (or true) probabilities suggested by historical statistics. There is no alternative – a lucky gambler is never lucky all the time.

If you wish to learn odds calculation, please check out:

Soccerwidow’s Value Betting Store

This article is therefore a definitive guide to put the record straight…

Image: hightowernrw (Shutterstock)

Stake

The sum of money gambled on the outcome of an event. The amount of money played with, or placed as a bet.

In the online world of gambling, stakes are electronically placed on a desired outcome with another party that has agreed to accept your stake, whether this be a bookmaker or an anonymous person/group in a betting exchange.

These ‘adversaries’ are effectively backing with their own money against your selection, hoping to make a profit of your stake if your selection in the event turns out to be wrong.

Once the outcome of the event is decided, stakes are returned to you in full if your bet has won (plus the winnings), or, if you lose the bet, the stake is lost and either retained by the bookmaker, or transferred to the winning side in the betting exchange.

Technically speaking, stakes are guarantees! This means that they are short-term deposit payments to guarantee that the losing party can and will honour his debt obligation to the winner of the bet.

Yield

The Profit/Loss* ratio^† applied to the total capital employed (total staked)

*This is Profit or Loss, NOT Profit divided by Loss

^†ratio = the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

Literally translated, the term YIELD means profit, earnings, harvest, income, revenue…

When applied to gambling, Yield measures betting efficiency compared to total turnover.

If your aversion to risk is low, you will select bets with higher probabilities. Bets with higher probabilities of winning carry lower odds. Lower odds means a smaller yield.

If you enjoy higher risk strategies, the opposite will apply.

Generally speaking and depending upon the strategy employed, a good bettor will yield between 5 and 10 percent profit in the long run.

In football betting any yield over 7% is considered to be a very good result.

Yield Formula:

PL divided by ∑MS (written as a percentage):

PL = profit/loss (MW minus ML = net profit or loss); equivalent to your bank growth
∑ = the sum of
MS = money staked
MW = money won (purely winnings; returned stakes are ‘neutral’, not winnings)
ML = money lost (stakes lost)

We come across many forum threads with people talking about their betting strategies; It is also easy to find plenty of websites offering betting systems for sale.

What many of them have in common is claims of high yield results, probably intended to impress the reader.

If they are to be believed then this is an indication of high risk strategies employed.

It must be remembered that in the Yield formula, the sum of money staked (∑MS) includes all stakes, even those that have not been lost. (In other words, the refunded ‘guarantees’).

People tend not to understand this fully and as a result mistakenly overstate their yield results.

Yield is NOT the same as ROI (Return on Investment)!

Return on Investment (ROI):

The ratio of money gained or lost on an investment relative to the amount of money invested. In other words, the profit/loss ratio as a function* for investment^† (capital employed).

*function = a relation or expression involving one or more variables; in this case, investment, profit, loss.

^†investment = long-term employment of tangible, financial, or other assets that are not meant for immediate gains but are intended to generate benefits (normally earnings or profits) in the future.

ROI is also known as ‘rate of profit’ or sometimes just ‘return’.

ROI Formula:

If you bet systematically, your starting capital will be turned over again and again: It is effectively the same money you are investing. (So long as you don’t lose every bet!).

The ROI formula resembles the yield formula, but here, profit/loss is related to the actual investment (starting bank) instead of the total of all stakes (turnover).

For a more accurate ROI calculation, in an ideal world, you should also factor in to the investment all other costs of ‘setting up the business’. For example, hardware/software costs (computers). However, we will leave this out of our calculations for the time being for the sake of simplicity; you can always include these costs once you have mastered the concept.

ROI is always calculated for a certain predetermined amount of time; in finances usually for one whole year, but it is also common and acceptable to calculate the ROI monthly or, in a betting sense, for only the number of bets within a specific time scale.

The return on investment index is especially suitable when the amount of capital has a strong influence on the result (e.g. with arbitrage).

However, this is probably rarely the case for the majority of punters. Therefore, it is the next formula, profitability, which is the most important one for the normal bettor.

Image: Kristo-Gothard Hunor (Shutterstock)

When people talk about ‘value’ in connection with betting there are many different schools of thought.

This article therefore attempts to shed some light on this complex concept and its terminology…

Firstly, let us begin with a few synonyms for the word ‘value’: worth; usefulness; advantage; benefit; gain; profit; amount; rate; price…

You can see straight away that there is a plethora of different connotations.

The last two meanings in particular, ‘rate’ and ‘price’, are probably the reason why the expression ‘value’, when used in the context of ‘value betting’ is often unclear.

So, what is Value in relation to Sports Betting?

In order to really understand the concept of ‘value betting’, you need to grasp several connected aspects and I will tackle each of these individually for better comprehension.

Tip: Grab yourself a caffeine shot and read every section (re-read if necessary) until you are comfortable enough to proceed to the next. What I am about to say may initially be hard for some to digest, but don’t worry, you will certainly not be alone. Headache pills may be advisable for some…

(1) Betting Odds are solely the Market Prices for Bets

Anyone interested in sports betting knows that bookmakers offer bets on a multitude of match outcomes and sometimes the list of available bets on a single event can appear endless.

For example, the 1×2 market allows you to bet on a home win, a draw, or an away win, either at half- or full-time. Will there be more than two goals in the match or not (over or under 2.5 goals), will both teams score, or will the match end goal-less? Et cetera, et cetera…

Only very few bettors fully comprehend and understand the fact that betting odds are nothing more than the market prices of bets.

Betting Odds are Prices that Few Understand

Betting odds are not only all-inclusive prices for bets but to add to the confusion they are displayed, not in simple and easy understandable monetary units, but in different formats such as decimals, fractions, or moneyline.

When buying a bottle of beer, for example, you pay one Euro, Pound or Dollar and walk home with your purchase. When buying a bet, say, at decimal odds of 1.27 (27/100 Fractional Odds; -370 U.S. Money Line), the only thing you may understand is that if the bet wins you will receive your stake money back plus 27% winnings. Of course, if the bet loses all of the stake money is forfeited.

Judging ‘value for money’ from a bottle of beer is far easier than evaluating the same in a bet. Many bettors struggle to calculate the expected return of a bet or a series of bets let alone analyse why the big win they hoped for failed to materialise.

Even if sports betting odds appear to be genuine offers, the fact is that odds are frequently distorted.

Betting Odds cannot be priced by Gut Feeling or Intuition

Very few people are born with a sense of probabilities and ratios. Statistics and financial education are rarely taught in high school and touched upon in very few university courses.

To develop a ‘feeling for price’ is impossible, even for those of us who are born with a sense of probabilities.

To make matters worse, every bet is actually a different product, even if betting on just one particular type, for example, the “over 1.5 goals” market. Think about this bet in the context of a match between two evenly matched teams as opposed to, say, the team at the top of the table playing the weakest team in the league. The name of the bet is still the same but the two match situations are totally different.

There is no way but applying maths and statistics to decide whether the price of any bet offered is “too expensive” or “too cheap”. Gut feeling is misleading and may prove fatal. Probabilities are a subject too complex to succeed with guesswork, feeling and intuition alone.

For those of you who are really serious about understanding sports betting in depth and developing a value betting strategy, there really is no alternative to learning the calculations necessary.

In order to grasp the concept of value it is of uttermost importance to comprehend that betting odds are merely prices, and not ‘true odds’.

Before I address the term ‘value’ I must first plunge into probabilities… please stay afloat!

(2) The Broken Connection between Probabilities and Betting Odds

Once you have grasped that betting odds are nothing more than the price of a bet it should now be apparent that market odds cannot possibly “represent” the true probability (likelihood) of an outcome.

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It should be obvious that “making a book” is the business of bookmakers and they must ensure that the advantage is on their side. Common sense dictates that betting odds (price) can have little to do with true probabilities.

You must understand that bookmakers have no option but to manipulate odds in order to balance their books. They also construct odds to match public opinion, and use odds as a marketing tool to attract customers.

It is absolutely correct that betting odds can be converted into their implied probabilities. However, these probabilities seldom represent the actual ‘real’ chance that a particular outcome will occur. Though, the implied probabilities are very important for identifying ‘value’.

To reiterate: Betting odds are the prices of bets, not their probabilities!

Here, at this point, the huge advantage bookmakers hold over the uninitiated comes into focus:

• How many people do you know personally who were born with a good sense and acute awareness of probabilities?
• Do you actually know anyone who can demonstrate a sound training or exhibit a qualification in statistics and probability?
• Is this rare person actually interested in sports betting?

On the other hand, how many people do you know who collect money-off coupons, or chase after shopping discounts at summer or winter sales?

Do you wholeheartedly think that these people truly acquire decent quality with each bargain they come home with?

Or maybe they are tempted by these opportunities to spend more money than they actually had in their household budget, and may end up with a lot of things they didn’t really need, but which were “soooooo cheap” at the time?

I shall not delve any further into the mindsets of bettors or shoppers but I hope the analogy makes sense.

So, to summarise what I have discussed so far:

1. Betting odds are the price of a bet.
2. Betting odds can be converted into implied probabilities but these have hardly anything to do with the actual expected distribution of results.

Forgive me for preaching, but these are two vital elements you must fully internalise in order to have a chance of understanding the concept of value betting.

Now we finally get to the term ‘value’ of a bet… (And about time too, Soccerwidow!)

(3) The Term ‘Value’ in Relation to Sports Betting

When professionals speak of the ‘value’ of a bet, they are referring neither to the price of a bet (betting odds), nor to the probability of winning the particular bet. Value does not even mean betting odds for a particular bet being “too high” or “too low”.

The term ‘Value’ is used when a positive return can be expected. It is about the intrinsic value of a betting decision.

Please note that although this may be contradictory to common (non-entrepreneurial) sense, a purchase may hold ‘intrinsic value’ even if computations return a negative figure.

To compute value, formulas for the calculation of Profitability can be used.

It is possible to calculate the ‘mathematical advantage’ (value of a bet). The result is (nothing more than) a mathematical expression and technical declaration. The computed value estimates the expected return on investment. This information can then be used as guidance for betting decisions.

There are two different ‘Values’:

• Value I: Mathematical advantage of a bet. (Expected return = profitability)
  This ratio indicates if the offered price in the market seems too low or too high. It also computes how much investment increase can be expected if the same transaction (bet) is repeated over and over again.
• Value II: Relative deviation, being the ratio of the implied probability (market odds) relative to the mathematical probability expectation (true odds).
  This ‘value’ is used for further evaluation and statistical computations; for example, it is very helpful for correlation analysis, cluster grouping and portfolio construction.

Now comes the fun… Caution! It’s getting mathematical!

Introduction

The terms probability, expectation, likelihood, chance and hit rate are all closely related, and express more or less the same thing. The difference is that before a game one talks about ‘chance’, ‘probability’, ‘likelihood’ and ‘expectation’ but, after it has finished, these terms are replaced by ‘hit rate’.

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However, although often referred to, the term value has no place in this relationship. The literal meaning of ‘value’ is benefit, merit, worth and price.

Unfortunately, the latter meaning is probably the main reason why people find the expression ‘value’ rather confusing. Betting odds offered by bookmakers or exchanges are the market’s expectations (probabilities) converted into the price of a bet.

However, if the ‘value’ of a bet is discussed, this refers not to the actual price (odds) of the bet but to the merit or benefit of a particular price.

Strictly speaking, it would be more correct, instead of using the term ‘value’ to say “mathematical advantage” or “expected merit“, but these phrases are not usually connected with the mindset of football bettors.

Probability & Expectation

To give you an example, in the 2012 UEFA Champions League final between Bayern Munich and Chelsea the probability (statistical expectation) for Bayern to win was 64.6% (the calculation is explained here – Sorry! You’ll have to auto-translate it if you don’t understand German! ).

Please note that the terms probability, likelihood, chance and expectation are frequently used synonymously in scripts.

Technically speaking this is not entirely correct and real mathematicians probably groan indefatigably when they read betting forums or posts.

However, for simplicity, this is allowed and even we use these terms arbitrarily in some of our articles and explanations, but we mean all the time the same thing: The expected hit rate!

An expectation, probability, likelihood (call it what you will!) of 64.6% for Bayern to win means that in the long-run, placing 100 similar bets should see 65 winning and 35 losing.

Reality Check: Hit Rate

Hit rate has no connection with the quality of predictions.

High hit rates are often interpreted as a sign of a successful picking strategy. Unfortunately, this is a big and very common misconception! The only thing hit rate expresses is the number of winning bets compared with all bets. Hit rate is not a statement of any realised gains or losses.

Hit Rate is the number of winning bets in relation to all placed bets.

For example, if you bet on the full-time correct scores market, odds of 10 and over are normal. Based on such odds, any hit rate higher than 10% means profit, which in turn means if you manage to predict full-time scores with an accuracy of more than 1 correct in every 10 attempts, you will make a profit (despite a relatively small hit rate).

More examples… if you bet only on outcomes with probabilities between 60 and 70%, then the expected hit rate is between 60 and 70%. It follows that after 100 bets you should achieve 60 to 70 winning bets.

If you want to achieve a hit rate of over 80%, you must only bet on probabilities of 80% and above. These are back bets with odds below 1.25 and lays above 5.0.

If you prefer betting on odds between 1.8 and 2.2, a hit rate of around 50% can be expected and if you can achieve a hit rate of over 55% in this bracket, profit will be made.

At these odds if you expect to achieve an 80% hit rate from your own strategy or gut-feeling, or rely on a picking service to deliver, then you will be sorely disappointed as it is unrealistic.

A further example: If your strategy is to lay correct scores at odds between 7 and 12, then a hit rate of around 90% is realistic.

Hit Rate in Soccerwidow’s Context

Soccerwidow’s own régime relies on portfolio betting to spread risk and choose ‘value’ bets from the entire spectrum of probability groups (clusters).

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For example, up to the end of May 2012, the monthly evaluations of Soccerwidow’s match previews showed an average hit rate of 57% (Soccerwidow’s Match Preview Results: 6 Months, 207 Bets, Dec 2011 – May 2012).

However, as already mentioned, this number tells you nothing about the quality of the predictions, because to link these criteria would be comparing apples with pears.

Nevertheless, what it does say is that 57% of the recommended bets won. Nothing more. Again, this is not a statement of a good or a bad hit rate.

Soccerwidow’s recommendations encompassed all probability clusters (0-10%, 10-20%, etc.), and thus all possible expectations of concrete hit rates. Each cluster needs to be evaluated separately, since the average hit rate has no meaning whatsoever.

Remember: The hit rate, no matter how high, says absolutely nothing about potential and/or realised gains or losses. This leads us now to the concept of VALUE.

Value of a Bet

Betting profits can only be achieved in the long run if you ‘lay’ or ‘back’ at odds that do NOT exactly represent the average odds (expected outcome).

In other words, you should lay when the odds are lower than the expectation and back when the odds are higher.

To reiterate, a bet is called a Value Bet if the market’s back odds are higher than the expected odds, or the lay odds are lower than expected.

The ‘value’ of a bet is its mathematical advantage (‘edge’), being the expected profit from the betting transaction.

The concept of value is often mixed-up with the term hit rate. However, these two terms have no relation to each other.

Back to our example, Bayern Munich v. Chelsea: The chance (= probability, expectation) of a Bayern victory was 64.6%, which, translated into odds, is 1.55 (1 divided by 64.6%).

The betting odds in the market that day were 1.81, representing a probability of 55%. This meant that Bayern were 16.7% over-priced (1.81 divided by 1.55 minus 1), and therefore a back bet on Bayern held ‘value’ (= a mathematical advantage).

As it turned out, Bayern lost the match to the great disappointment of many German fans (Boo!), but to the professional gambler a loss such as this makes no difference because he/she knows that from 100 similar bets, ultimately 65 will win and 35 will lose. The profit from these transactions will be around 17% of the total capital employed (= Yield).

A professional bettor appreciates that not every bet will win. A 64.6% probability means a 64.6% expected hit rate; no more and no less! The value lies in the odds (price), not in the hit rate on the day.

Summary

The terms ‘hit rate’, ‘probability’, ‘likelihood’, ‘chance’ and ‘expectation’ are, more or less, synonymous. Ahead of the game one speaks of chance, probability, likelihood and expectation (future events), and after the match in the evaluation process it is then referred to as the hit rate (past events).

The value of a bet is its mathematical advantage or ‘edge’ over the market price (odds), and it is also the expected profit from the betting transactions. The term ‘value’ must not be confused with ‘hit rate’, ‘probability’ and ‘expectation’…

If you would like to learn how to calculate true probabilities and convert them into odds, identify cluster groups for betting, and understand value, then why not have a glance at Soccerwidow’s Fundamentals of Sports Betting Course).

When using odds in European format (decimal) you can be forgiven for thinking that average betting odds are simply computed by building the arithmetic mean of the data to be analysed. Unfortunately, this is the wrong approach and leads to a deceptive result.

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As a reminder, European odds are calculated as the reciprocal of the statistical probabilities of each event:

and vice versa … The implied probabilities are the reciprocals of the odds:

In effect, European odds are ratios/relations representing the likelihood of an event happening in comparison to each other event (e.g. a bet priced at odds of 4.0 is half as likely to win as a bet with odds of 2.0).

If these ratios are averaged using arithmetic mean (a common error), high data points are given greater weights than low data points. (e.g. working out the arithmetic mean of a set of 20 odds, 19 of them between 2.0 and 2.4, would be skewed if the 20th figure was, say, 15.0).

The correct approach is to calculate average odds by forming the harmonic mean!

The harmonic mean is defined as the reciprocal of the arithmetic mean of the reciprocals of x₁, x₂, …, x_n (the odds):

As the reciprocals of betting odds are the implied probabilities of the events, one can calculate the harmonic mean as a reciprocal of the average probability of the respective bets:

The above equations rearranged facilitates the harmonic mean calculation by dividing n (the number of matches) by the sum of the reciprocals of the odds:

Or alternatively… dividing n (the number of matches) by the sum of their individual probabilities:

The Result (Harmonic Mean) is the Accurate Average of the Betting Odds.

Excel users employ the following formula: =HARMEAN(number1,number2,…)

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For example, whilst the total number of goals in a match can be counted easily allowing various arithmetical interpretations, the inclusion of a certain team in the league cannot be expressed as a meaningful number and may only be used for categorising the respective data set.

It is very important to be aware of the scales of measurement and to assign the correct levels as they not only express how quantitative a response is, but also to what extent meaningful computations can be applied.


Table of Contents:

1. Nominal Scale
2. Ordinal Scale
3. Interval Scale
4. Ratio Scale
5. Scaling issues of variables
6. Think Before You Calculate
7. Synopsis & Summary Table

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Extent: 7 pages
Size: 122.6 KB

Think Before You Calculate

Given a list of shirt numbers of players, it is certainly possible to perform all sorts of calculations but none will provide any meaningful results. What is one shirt number divided by another one? A complete waste of your time as this data belongs to the nominal scale.

Unfortunately, it is not always as obvious which data will lead to meaningful results and which not. Therefore, when you are collecting data, think before you calculate. The level of measurement you are working with will determine what makes sense to do and what to leave well alone.

Probably the most prominent misleading data set is the order of teams in the form table. This data is ordinal scaled and exists purely to put teams in an order. However, in practice, punters pay a lot of attention to the form tables (often even just the last six results!), but unfortunately these data are pretty useless in terms of meaningful analysis and drawing conclusions for betting.