How high should be a starting bank?
Is 5,000 units enough?

Well, there is no standard answer to this question. It all depends on the individual strategy.

Image: Sergey Novikov (Shutterstock)

However, what is possible, is to calculate bank fluctuations (i.e. winning and losing sequences).

With the help of knowing the best and worst case scenarios you can determine the ideal starting bank for any betting system of your choice.

At the end of the article you will find a few useful exercises to practise, with the solutions available as a free download to all of you who would like them.

Length of Winning and Losing Streaks

It stands to reason that the smaller the probability of an event occurring (i.e. higher odds), the longer the likely losing streak will be (in between winning bets).

However, the big question is how often and for how long will the losing (and winning) streaks transpire?

It is possible to mathematically calculate many things with statistics, including streaks of luck and bad luck. However, it is important to note that no matter how accurate the results may appear, they are ‘models’ (a formal representation of a theory).

In this article, we are talking about probabilities; what can we ‘predict’ about how things may develop in the future. Please bear in mind that any such hypothesis is always a “could happen” not a “will happen”.

Of course, the larger the sample size (i.e. number of bets), the more likely the prediction is to be correct. But apart from the bookmakers themselves, who else has a betting portfolio comprising thousands of bets every weekend?

Winning and Losing Streaks Formula

The longest expected losing streak (or winning streak) can be calculated using the following formula:

n = number of trials (i.e. total number of bets)
ln = natural logarithm¹
P = probability²
| .. | = absolute value or ‘modulus’

¹Suffice to say, explaining what natural logarithm is would be worthy of a series of articles. For the time being, use Excel to calculate this for you.

²For winning streak calculations use the positive value (i.e. the probability of winning). For losing streak calculations use the negative probability value. For example, if the probability to win the bet is 33% then the probability that the bet loses (negative probability) is 67%.

In practice, the formula is best applied to situations where you constantly bet repeatedly on the same probability, for example, on ‘red’ at the roulette wheel: its probability remains exactly the same with every new spin of the wheel.

For football betting the concept is much more difficult to apply as each bet is likely to have a different probability (e.g. one Over 2.5 Goals bet with a 55.3% chance, and the next with a 62.1% chance, etc.).

However, you can group bets in probability clusters – for example, bets with a 55%-60% expected hit rate, bets with a 60%-65% expected hit rate, and so on.

Longest Winning and Losing Streaks, depending on the number of bets (Examples for 50, 500 and 1,000 bets shown)

The tables above show the calculations of the expected maximum number of winning and losing streaks, depending on the expected hit rate (probability of the bet to win).

To read the tables, let’s explain the 70% line (odds in the region 1.4 and 1.45); in other words, bets with a 7 in 10 chance of winning.

The table on the left calculates the expectations of 50 tries (50 bets in a row, one after the next). You can see that the player will experience at least one streak of three lost bets in a row somewhere in the sequence.

On the other hand, he can expect at least one series of 11 winning bets in a row during the same sequence of 50 bets.

In contrast look at the 30% line (odds in the region of 3.2 to 3.4). In a series of 50 bets the bettor must expect at least one sequence of 11 consecutive losing bets, but will probably see only one set of three consecutive winning bets.

To develop a sense of probabilities and sequences, you can experiment with a dice. It has six faces; in other words, a probability of 16.67% (1 in 6 chance) of successfully landing on a chosen number.

Choose a number and count the number of throws until you succeed to roll it. Count also the number of consecutive successful rolls.

Having learned how to calculate the expected length of winning and losing streaks, the next question to ask is:

How many bets is it likely to take before I encounter ‘X’ losses in a row?

Timing of Winning and Losing Streaks

This formula is actually very simple:

= 1 divided by P, to the power of a

P = probability (expected hit rate or loss rate)
a = number of won or lost bets in a row

In the tables below you can see how many attempts (bets) it needs to experience a specific, expected length of luck or bad luck. Again, the assumption is that the bettor bets all the time on the same probability:

Expected time of occurrence of winning and losing streaks, depending on the hit rate

Looking firstly in the right-hand column at the Losing Sequences, if the expected hit rate is 45% (what you should ‘expect’ at odds of around 2.2), then it is likely that you will experience a sequence of three losing bets in a row by the time your sixth bet is settled.

After 20 such bets it is likely that you will have seen a losing streak as long as five bets in a row.

Looking at the Winning Sequences column: you will win three times in a row at some stage during a series of 11 bets.

However, winning five in a row may only be seen once in every 54 bets.

As we mentioned before, in football betting it is extremely difficult, if not impossible, to find bets, all with the same probability of success.

However, you should at least try to understand the theory behind winning and losing streaks, as it will be easier on your nerves when you do encounter the inevitable run of bad fortune.

In particular, a thorough understanding of losing streaks is of enormous importance when setting both the size of your starting bank and stakes per bet.

Example:

A bettor prefers bets within the odds range of 2.0 to 2.5 with a hit rate between 40% and 50%. He plans to place 50 bets (e.g. two bets per round on 25 rounds of matches).

After looking at the tables, he knows that the maximum losing sequence expected is likely to be as long as six to eight lost bets in a row. Therefore, he knows that there may be at least one sequence of three or four consecutive rounds (weekends) when all bets lose.

After every 5^th to 8^th bet, he is also aware that he is likely to experience a loss of three consecutive lost bets (e.g. one weekend loses both bets, the following weekend only one loses).

He also knows that every 13 to 32 bets there will even be a streak of five losing bets in a row.

The bettor is fully aware that he has to take this into consideration and plan the starting bank accordingly to be able to ‘sit through’ these losing streaks.

Of course, he also knows that winning sequences will arrive too. In his case, with some ‘luck’, he may experience a winning sequence of five bets in a row after 32 bets. Every eight to 16 bets he will have a ‘lucky’ streak of three wins in a row.

This is certainly quite a fluctuation. When these ‘bad luck’ and ‘good luck’ streaks actually happen, nobody knows. However, what we do know is: They will happen!

Starting Bank – Rule of Thumb

A starting bank should be approximately five times the maximum expected losing streak. The reason for this is that a losing streak can happen right at the beginning, immediately followed by another bad run of luck. We are talking statistics here!

So if a bettor wants to stake 10 units per bet, the starting bank must be nine times (expected losing streak) the stake of 10 units multiplied by five = 450 units. Then he can risk 2.2% of his bank each time he bets (10 divided by 450). If losing, the stakes will remain constant at 2.2% and, if winning, raised gradually.

Questions to ask before setting the starting bank:

1. What hit rate is expected (probability to win the bets)?
2. How many bets are planned for the season?
3. How long will the longest losing streak be?
4. What is the desired stake per bet?

Calculation of the starting bank:

Exercises: Losing & Winning Streaks

Answers to the Exercises

Just click on the button above and click on “Proceed to checkout” button in the new tab, then enter your name and e-mail address. Our automatic service will then deliver the file to you via e-mail, free of charge. The size of the PDF file is 320KB.

Optimising Your Bankroll

The factor 5 used in this article to determine the betting bank is a risk variable for risk-averse bettors. It is also the factor advisable for strategies with a 45% to 55% win probability (odds between 1.8 and 2.2).

Here is another article: How to Calculate Losing Streaks & Optimal Bankroll in which we provide a more detailed account of setting the ideal starting bank.

Risk management in sports betting is the foundation stone upon which all of your betting transactions should be built.

Risk management encompasses risk assessment, risk control and capital requirements, all of which cannot be addressed until you understand how winning and losing streaks are likely to impact upon your starting bank.

Image: archideaphoto (Shutterstock)

‘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.

Image: Gts (Shutterstock)

Over/Under is a great way for people new to betting to get their feet wet…

What Does Over/Under Mean?

With over/under betting, the first thing to understand is that you are betting in relation to the number of goals scored in the game. It doesn’t matter which team scores the goals or even who wins.

You just take the number of goals scored by each of the teams and add them together to get the total goals scored during the game.

The simplicity of this bet is what makes it such a common wager.

When you place an over/under bet, you have to choose two things:

It doesn’t matter how close the result is to the goal line either, the bet pays the same whether the end result is close to the bet’s goal line or far away.

Why the “Point Five”?

Over/Under bets that end in “.5” have only two outcomes.

You either win the bet and get paid an amount equal to your stake multiplied by the betting odds or you lose the bet and your stake.

Because you can’t score half a goal, every bet is either a win or a loss.

Let’s take the most popular goal line in football: 2.5.

If you think the total goals in the game will be three or more, you would want to bet “Over 2.5”. If you think the total goals in the game will be two or less, you would choose to bet “Under 2.5”.

Over/Under bets without the “.5” or with different fractions (such as 2.25) may return part or all of your stake to you even if you don’t win.

For example, with a Total Goals bet, if you bet “Over 2” and exactly 2 goals are scored, you will not win the wager but you will get your stake refunded.

The graphic below shows which bet (over or under) will win given a certain score in the game for various goal lines.

Attention Please! Some Goals Don’t Count!

When you are betting in football, the only goals that count towards over/under bets are the ones scored during the regulation 90 minutes of each match.

If the game ends tied after 90 minutes any goals scored in extra-time or a penalty shoot-out do not count towards the over/under goals tally.

The result of the match itself does not matter; drawn matches with scorelines like 0-0, 1-1, 2-2, etc., also contribute to over-under bet results.

Over/Under 2.5: The Most Popular Bet in Football

We are using 2.5 as an example here because although there are many possible over/under bets, 2.5 happens to be the most popular goal line for football bets.

It turns out that when you look at a long history of football games, even across different leagues, the average number of total goals scored per game is very close to 2.5.

As a result, you often have a similar number of punters backing each side of the 2.5 goal line where the odds are similar no matter which choice of over or under is made.

Choose Your Bet Using Statistical Information

Bookmakers set the odds of over and under for each available goal line using statistical information on the teams who are playing each other as well as football games in general.

Demand on each side of the bet can change the bookmaker odds and knowing what the statistics say can help you determine whether a particular bet is a good or bad one to take.

The best bet is not always the bet that is closest to the actual score you expect.

In fact, it is often the bets further away from expectations that offer the greatest difference between the betting odds offered in the markets and the true statistical predictions.

Making Money at Over-Under Betting

Some punters are surprised at how important the underlying mathematics are, but long-term success at over/under betting is much more science than art!

Continue to follow our blog to learn more, or check out our book: Fundamentals of Sports Betting.

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…

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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.

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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).