**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.

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?

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 logarithm^{1}

**P** = probability^{2}

**| .. |** = absolute value or ‘modulus’

^{1}*Suffice 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.*

^{2}*For 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.

Choose two numbers that you do not want to roll (e.g. 5 and 6).

This means you have a 66.67% chance that one of the remaining four numbers is rolled.

In football betting terms, this equates to wagering on something like the full-time ‘Under 3.5 Goals’ market at odds of 1.50. (This experiment is just a little faster than waiting for 50 games to finish!)

Take a pen and paper and record 100 throws of the dice. If one of your four chosen numbers arrives mark a 1 on your paper; if the 5 or 6 are thrown, mark a 0. Count the number of winning and losing streaks you experience.

What is the maximum number of winning and losing streaks you experience in a sample size of 100 throws (bets)?

*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?**

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!

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:**

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

**Calculation of the starting bank:**

- A bettor pursues a strategy with a win probability of 60% per bet
*(e.g. Under 3.5 Goals)*. He places one bet after the other; in other words, he waits for the outcome of each bet before placing the next. In total he places 50 bets.What is the longest ‘losing streak’ (bad luck) that he can expect? How long is the longest ‘winning streak’ (luck) that can be expected?

- Same example as in (1): A strategy with a probability of 60% per bet; placing one bet after the other.
This time our punter is hoping for a ‘winning streak’ (luck) of 5 consecutive wins. How often does that happen?

- A gambler pursues a strategy with a probability of 20% per bet
*(e.g. ‘betting on the underdog’)*. Again, he places one bet after the other.With a total of 500 bets, how long is the longest ‘losing streak’ that he must expect? After how many bets can he expect the longest ‘winning streak’?

- Same example as in (3): Strategy with a probability of 20% per bet; placing one bet after another
The bettor was hoping for a ‘winning streak’ (good luck) of five consecutive wins. How often does that happen? After which bet number should he expect ‘bad luck’ of five consecutive losses?

- Following the above two strategies
*(one with a 60% chance to win, the other with 20%)*our bettor stakes 10 units per bet.How high should the starting bank be for the 60% strategy, and how much for the 20% strategy?

*Note: The initial bank should be approximately five times the maximum losing streak based on a total of 500 bets placed.*

*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.*

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.

]]>But which staking plan is the best?

The answer is: A simple and straightforward staking plan. Nothing complicated; just plump for **flat staking** with or without a **ratcheting** mechanism.

All other staking plans contain one or another problem and I can guarantee that there is definitely not a single staking method in existence, which makes a failing betting system work.

Therefore, firstly work out a sound betting system and then secondly, adhere to a modest and plain staking plan. Keep the money management as simple as possible because it is already difficult enough to keep up with everything that goes into **monitoring a betting system**. You will perhaps also have to think about juggling your bank between various bookmakers and exchanges if needs be.

In today’s article I’m going to show you a fuss-free staking plan using the example of our **2017-18 Winter League portfolio** .

As mentioned, it’s a combination of a **flat staking plan** and a **ratcheting mechanism**.

With the help of our HDAFU Tables and, in particular, their **Inflection Point** graphs, it is now easy to develop a portfolio of bets with a definite mathematical edge.

And in conjunction with our chosen staking plan, the portfolio of 2017-18 Winter Leagues performed as follows:

Image 1: 2017-18 Winter League Campaign – Profit Curve with Ratcheting

We started with a betting bank of 4,000 units and finished after 47 weeks and 518 bets with a total 38,925 units.

Of course, it wasn’t a smooth ride the whole time. Especially at the start of the season, the first 15 weeks (up to 27/10/2017) were very tough. 153 bets were placed but the result was pretty much a zero sum game. It did eventually rise to 5,562, but for all the time invested and work performed it was quite a frustrating experience.

From this point until the end of December, results were better and the ratcheting system helped the bank up to 13,792 units. But then another rough period started.

Nevertheless, it was worth it! A very long slog (47 weeks!) for a profit of 34,925 units. A great result vindicating the soundness of both the **portfolio of bets** and its staking plan.

Just as a side note, if you want to learn more about how the portfolio was originally compiled and how it performed in detail then you will find our report here:System Football Betting: 2017-18 Winter League Report – 35k in 138 Days

But let’s get back to the topic of the article:proper staking…

Image 1 showed you the performance of the portfolio using ratcheting, but if we would have applied a flat staking plan only *(without ratcheting)*, then the Profit/Loss curve would have looked like this:

Image 2: 2017-18 Winter League Campaign – Profit Curve Flat Stakes

You can see straight away that the simple flat stakes (without ratcheting) also produces profits, but the curve is much flatter – here, the betting bank *only* increases from 4,000 units to 13,909 units. Flat staking lacks the exponential element of a ratcheting system to grow a bank, but on the other hand, it is much easier on the nerves as I will show you later in this article.

But first here are a few definitions…

Flat staking simply means that you wager on every bet exactly the same amount of money, without any deviations. But this may include some consideration towards the risk of each bet. You may therefore wish to stagger your stakes according to the implied probability (odds) of winning each bet:

**VERY SIMPLE:**decide to stake a flat 100 units on every bet in the portfolio.**SIMPLE:**decide to stake a flat 100 units on bets with odds below 1.50, 50 units on bets with odds between 1.50 and 2.50, and so on.

But whichever of the two options you choose, you are in effect still ‘flat staking’.

Ratcheting is a progressive money management approach where the size of the stakes move by degrees, upward or downward, depending upon results.

With ratcheting the stakes are variable and depend on the size of the bank. However, the percentage of the ratchet (in our case 2.5%) always remains constant.

If at the end of a round of matches (or week) your bank has grown, all bets placed the following week should be adjusted to the higher bank.

For example, if the bank increases from 4,000 to 4,500, the stake increases from a flat 100 units to 112.50 per bet in the following round (i.e. stake remains at the base level set of 2.5% of bank).

**The percentage of the bank used per bet stays ‘flat’.**

Nevertheless, you also need to guard against bankruptcy. If your portfolio experiences a losing round, reduce the stakes for each bet but not before the bank drops to **75%** (or below) of its highest point.

You may think that this method is simply a stop-loss strategy, but it isn’t quite the same. I will explain further down in the article why we used 75% as the margin for our downwards ratcheting and not any other number.

Should you lose at the end of a round (week), continue to play each bet with the same, unchanged stake until the bank’s previous high has shrunk by 25%.

This means that in the event of a short-term loss, the stake continues to refer to the bank at the highest level it has reached so far and does not adjust to the lower bank until the bank has dropped to 75% of its peak size.

Only then is the stake recalculated (reduced) and the ratchet process begins again.

To be clear on this point, in the event of a run of losses, the stake size per bet always remains in relation to the highest bank to date and should not decrease until the threshold of 75% of highest bank ever is reached. *(If you have for example, a very bad start to a campaign, the 75% trigger point may well apply to your starting bank)*.

Only then will the stakes be adjusted (reduced) to this lower bank size. This will then be your new starting bank. All further bets from then on refer to this bank and the ratcheting process begins again.

**Example 1:**

The bank drops from 4,000 to 3,800: The stakes remain unchanged, flat 100.00 (= 2.5% of the starting bank of 4,000) for the next period (round/ week).

After the next round the bank closes with 3,520. Still, the stakes remain unchanged, flat 100.00, using the previous bank of 4,000 for its calculations.

Only if the bank closes with under 3,000 (75% of 4,000) will the stake sizes be recalculated.

**Example 2:**

Using the starting bank from our previous example, the bank has dropped to 2,800. This has now become the new starting bank and the stake is recalculated:

**2,800 x 2.5% = 70.00**

With the reduction of over 75% of the bank from its former highest level of 4,000 (100 unit stakes) to 2,800, the stake size is recalibrated and remains flat at 70 units.

Afterwards, if the bank starts to rise, you will need to begin increasing the stakes again.

Say, after the next round you bank has gone up to 3,150.

3,150 x 2.5% = 78.75

The adjusted ‘new’ stake is now 78.75 and remains in place until either the bank drops to 75% of 3,150 (2,362) or the bank grows above 3,150, when stake amounts will be 2.5% of the new, larger bank size.

We have seen that ratcheting is purely a method of ‘flexible flat staking’ to encourage exponential bank growth.

The idea is to start off with stakes of 100 units and, if everything goes according to plan, by the end of the season the stake sizes should hopefully be in the multiples of 100 units.

Looking at the other side of the coin, the losses during this time will be in the same proportions, and not everyone is comfortable when losing a few thousand units in an afternoon, even if its ‘just winnings’ from previous rounds.

Bear this in mind before you decide to try ratcheting. Are you a disciplined person? Are you able to function when you have a few thousand riding on a few matches?

If your answer to these questions is ‘no’, then please do yourself a favour and stick to flat staking only! Do not try ratcheting, at least not to the end, and stop increasing your stakes when you reach the limits of your comfort zone (or have achieved target).

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You may find it helpful to follow the explanations in this article with the help of our dedicated Excel workbook detailing our 2017-18 Winter League portfolio. Not only does it contain the match data and calculates the flat and ratchet staking results, but it also shows how the portfolio was composed and provides many other useful snippets of information.

We are sure that you will feel the nominal **£5.00 GBP** charge is a real bargain.

*The size of this .XLSX Excel file is 568KB:*

**>>> 2017-18 winter league campaign <<< **

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Even the soundest portfolio of bets will experience bad periods where one bet after another (or even one round after another) is losing. It happened to us from the 09/12/2017 (2017 week 50) – 11/03/2018 (2018 week 11). Three months of more losing rounds than winning ones! Tough indeed!

Here are two images that show the profits/losses together with the bank development during this rough period using flat stakes versus ratcheting:

Image 3: 2017-18 Winter League Campaign – Using Flat Stakes only

Image 4: 2017-18 Winter League Campaign – Ratcheting the Stakes

Both staking plans produced profits but, to put the choppy ride into even better perspective, you will need to note that the results summarised in Image 4 were by this time already based on a ratcheted bet size of 344.80 units *(as at 09/12/2017)*, and this has grown to 707.82 units by 11/03/2018.

The period spanned more than 15 weeks with nine losing rounds (60%). From the 23/12/2017 – 12/01/2018 there were many losses, not huge, but enough to be nerve-racking!

The biggest losing round of bets with flat staking was: – 578

The biggest losing round of bets with ratcheting was: – 4,091

**Tough!** This again highlights the difference in volatility between flat staking and ratcheting. Steel hearts only required here!

However:

The biggest profit round with flat staking was: 1,785

The biggest profit round with ratcheting was: 6,155

**Great!** But please don’t get carried away too much!

*Moral #1:* **If you are a person that finds it challenging to keep emotions under control, stick to flat stakes! The best laid plans fall to pieces if you can’t cope during the really rough times.**

**It is always better to be a modest winner than a brave loser.**

In the previous section you saw the monetary effects of winning and losing when using flat stakes only or when ratcheting. However, the differences become even more obvious if you look at the profits/losses in relation to the bank:

Image 5: 2017-18 Winter League Campaign – Profit/Losses in relation to the bank: Flat Stakes

When staking flat our example portfolio only produced a maximum loss of – 8.1 % of the bank. The winnings too were pretty ‘modest’: a maximum of 20.7%.

Ratcheting involves a far greater rollercoaster. The maximum loss was as high as – 15.2 % of the bank. The maximum winnings were: 52.6%.

Image 6: 2017-18 Winter League Campaign – Profit/Losses in relation to the bank: Ratcheting

*Moral #2:* **As I have already said, simple flat stakes (without ratcheting) are much easier on the nerves than ratcheting. The exponential growth a ratcheting system produces goes hand-in hand with exponential losses.**

In the article **Bank Management & Stake Size** I explained the ‘scientific’ calculation of the percentage of starting bank that should be used for betting.

It was based on the average of the three largest losing rounds (weeks):

12%, 15.2% and 14.6% >>> average: 13.9% (rounded: 14%).

We can use this figure of 14% to calculate the stop-loss margin. You see, everything is somehow connected. The stake size, the stop-loss margin, and much more.

To be able to sit through a run of at least two losing rounds in a row where the bank is depleted by 14% each time you need to calculate as follows:

86% x 86% = 73.96%

Let’s round this up to 75% to be more risk averse (safety conscious).

Hence, if your portfolio loses, reduce the stakes * but not before* the

Please bear in mind that all the calculations and explanations are based on a portfolio of just over 500 bets with an expected hit rate of around 50%. Should your portfolio be different (no two are alike), then you will need to carry out all the calculations using your own figures.

If you cannot calculate this for yourself in such great detail then either stick to the 75% threshold, or perhaps lower it to 65% *(if you have a lower risk aversion)* as advised in previous articles.

*Moral #3:* **Better to be safe than sorry. If you are new to ratcheting it’s probably better if you play with smaller stakes than the calculations actually permit (e.g. 1.5% of your betting bank instead of 2.5%) then you won’t reach the stop-loss margin too quickly. **

*I hope you’ve enjoyed this article and learned something about sound staking and ratcheting. However, if you are still unsure on any point, please feel free to ask any questions via the comment section below.*

Managing and following through with the plan is illustrated in the **2017-18 Winter League Report – 35k in 138 Days**, where the full performance of our selections is analysed and dissected.

But remember, the best compiled portfolio won’t work without proper bank management and staking.

Please have a look at the distribution of bets during the 2017-18 Winter League Campaign:

Image 1: 2017-18 Winter League Campaign – Bets per Week of the Year (per round)

Week 38 was the busiest with 24 bets in total, whilst week 50 saw 23 bets. Within a relatively small portfolio of just over 500 bets, the average number of bets per round was 11, but the observed spread was anything between 0 and 24 *(2 rounds without bets)*.

Even with a small portfolio, bank management poses challenges, especially when juggling numerous bookmaker/exchange accounts. Monitoring the balance of each account can become difficult, which may lead to liquidity issues (perhaps not enough in the account) and the constant hassle of moving money between your accounts (or playing with smaller stakes than intended).

Trying to get the highest odds possible in the market all the time becomes unrealistic as the total betting bank would need to be spread over many, many bookmakers.

As harsh as it may sound, you will have to accept that aiming to achieve the highest odds available in the entire market at any moment in time is virtually impossible, and the choice of bookmakers/exchanges has to be limited from the start. I recommend limiting your bookmaker/exchange accounts to a maximum of five or six, and simply choosing best price between them at the time you wish to place a bet.

Here is the list of bookmakers/exchanges we recommend to use in addition to Betfair: –

**BetDaq
Matchbook
Smarkets
Pinnacle
William Hill
888Sport**

It makes little difference to the results when limiting your accounts to just a handful and you will see evidence of this in our **2017-18 Winter League Report – 35k in 138 Days**.

The screenshot below shows the bet placement distribution by bookmaker/exchange.

Image 2: 2017-18 Winter League Campaign – Distribution by Bookmakers/ Exchanges

*Lesson 1:* **Limit your choice of bookmakers/exchanges!**

To determine the stake size there are a few things to consider. Firstly of course, the size of your starting bank. This is an easy one to call – You know what funds you have.

But once you’ve settled on the starting bank, things quickly become a little more complicated…

You can go to great length and once you have compiled your portfolio carry out following exercise:

- Go to the ‘data’ tab in the HDAFU Tables, copy and paste all applicable matches and amalgamate them in one spreadsheet.
- Go to any odds comparison site of your choice and check the bookmakers that would have been available for you in those matches; log them into your spreadsheet together with the name of the bookmaker/exchange
*(a hugely time-intensive exercise!)* - Sort the data into chronological order and group it by weeks/rounds.
- Count the number of bets with each bookmaker/exchange in each round.

Once complete, you will be able to use the data to come up with a similar graph to this one:

Image 3: 2017-18 Winter League Campaign – Distribution by Bookmaker/Exchange in more detail

In our example, you can clearly see that Pinnacle had the majority of bets (up to 15 in one round), Betfair and Matchbook were the next most used (up to seven bets per round), followed by 888sport (up to five bets per round), and lastly, William Hill (up to four bets).

Going forwards, the scientific split of our bank for the forthcoming new season based on experience from last season is therefore:

40% Pinnacle: 1,600 units

20% Betfair: 800 units

20% Matchbook: 800 units

10% 888sport: 400 units

10% William Hill: 400 units

But, if you have no past experience it may be harder to estimate which of your chosen bookmakers/exchanges are most likely to have the highest odds when you are ready to place the bets, and how future bets may be distributed between your accounts.

If you have no past figures to guide you, then it is probably best to distribute your betting bank equally between your chosen bookmakers/exchanges. In this case (five accounts), an even split of the starting bank of 4,000 units means 800 units in each account.

*Lesson 2:* **If you cannot calculate the most probable distribution of your bets between the bookmakers of your choice, then simply distribute funds in equal amounts between your accounts!**

The major question is how each betting round is going to perform. Is the portfolio going to make a profit or a loss? Which account will accrue the biggest proportion of profits? Which will be the most high-maintenance, requiring the most re-deposits?

Have a look at our profit/loss distribution over time:

Image 4: 2017-18 Winter League Campaign – Profit/Loss Distribution per Week (per Round)

In total, there were 47 rounds (weeks) of betting. 17 of these (36.2%) finished with losses. (Effectively one losing round in every three).

There were four months (15 rounds) between week 50 (9/12/2017) and week 11 (11/3/2018) where the portfolio experienced a seemingly never-ending rollercoaster ride.

During this time, eight rounds (over 50%!) produced losses as seen in the image above. Those three months were especially difficult on the nerves.

However, this still doesn’t tell us the best stake size. There is also no sense looking at which bookmakers incurred losses, as the past distribution will very likely not repeat itself during the forthcoming new season.

The best guide is to have a look at the profits/losses in relation to the bank size:

Image 5: 2017-18 Winter League Campaign – Profit/Loss in relation to the bank

As you can see, there were three occasions where the bank dropped by more than 12% of its total. In the worst single round (week) the size of the bank contracted by over 15%. Furthermore, we know from Image 1 *(distribution of bets per week)* that if we are going to employ a similar portfolio of bets in future, that there will be up to 25 bets in a week (round).

We have no idea which of the 25 bets will win and which won’t, and the intention of the staking plan not to be bankrupt after any one week of ‘bad luck’. Also, we don’t want to be in a position after experiencing a ‘bad week’ where we are forced to reduce the size of our stakes. Better to arrange the plan so that we can ride through any longer periods of ‘bad luck’.

We have distributed our funds between accounts but we don’t know which of the chosen bookies/exchanges are going to receive the bets.

**The ‘scientific’ calculation is as follow:**

The average of 12%, 15.2% and 14.6% = 13.9% (rounded: 14%).

Although very unlikely, there may be a run of losses (say three rounds in a row) where the bank is depleted by 14% each time, and should this happen, we still need to continue placing bets without having to reduce the stakes.

As mentioned, we are expecting a maximum of 25 bets in a single round.

25 divided by 86% divided by 86% divided by 86% = 39.3 (risk averse rounded: 40)

1 divided by 40 = 0.025 (= 2.5%)

So, if we risk 2.5% of our betting bank per bet, we will still be able to survive three hefty losing runs without having to reduce the stakes.

**The ‘short cut’ calculation is as follow:**

If you have no past figures or estimates, take a short-cut and use the following calculation:

- Estimate as best you possibly can the expected maximum number of bets in one betting round
- Double this number
- Divide 1 by this number

*Example:*

- Expected number of bets: 25
- 25 x 2 = 50
- 1 divided by 50 = 2%

*Lesson 3:* **Limit your stake to 2.5% if you have a portfolio of around 500 bets coming up for one season. If you have a larger portfolio, use your past experience or figures to calculate your maximum stake size as shown above!**

Yes, it can! Our portfolio produced a profit during and despite three very tough months:

Image 6: 2017-18 Winter League Campaign – Analysis of Most Challenging Period

Prior to week 50 the bank size stood at 13,792 units, but after enduring a really volatile period (where more than one round lost in every two) the bank had risen to 23,960 units.

This was only possible by using a strict staking plan in combination with stake ratcheting.

Please remember:

- Limit yourself to just a handful of bookmakers/exchanges: five or six is plenty
- Split your bank (more or less) equally between the chosen accounts
- Limit your individual bet stakes to 2.5% of your entire betting bank (or less if you are expecting more than 25 bets at any betting round)
- Apply and stick strictly to the set rules, and NEVER experiment and/or change your staking midway through a campaign! Once decided. Stick to it!

–

You may find it helpful to follow the explanations in this article with the help of our Excel monitoring workbook. Not only does it contain the match data and calculates the bet distribution, but includes many more Excel formulas and ideas to help you grasp how to record and control your own betting ventures.

We are sure that you will feel the nominal **£5.00 GBP** charge is a real bargain.

*The size of this .XLSX Excel file is 568KB:*

**>>> 2017-18 winter league campaign <<< **

–

*I hope you enjoyed this article and learned something about the unavoidable randomness of the distribution of bets within a portfolio and how to keep your bank under control despite the inevitable peaks and troughs. However, if you are still unsure on any point, please feel free to ask any questions via the comment section below.*

Despite a rocky start and other challenging periods throughout 2017-18, a starting bank of 4,000 units was eventually turned into 38,925.

Image 1: Winter League Campaign Development Graph

(Bank Development ↔ green profit curve; Profit/Loss ↔ weekly columns)

(Bank Development ↔ green profit curve; Profit/Loss ↔ weekly columns)

Regarding the selection of systems we will expand a little on our decision-making process in the league-by-league review below. For compiling this portfolio we used our **HDAFU Tables**.

How the systems were originally chosen, you’ll find a detailed explanation using the EPL pick as example here: **Finding a System Using the HO/AO Quotient**

To read about the compilation of the portfolio used for this article here’s a link to our analytical article: **Judging the Risk of a Football Betting Portfolio**.

There you will find explanations on how to calculate the overall probability/expected hit rate of a portfolio and how to judge the risk. You will also learn how to predict winning and losing streaks, and what kind of profit/loss curve to expect when compiling your own portfolio of bets.

Let’s now dive in to the performance report without further ado.

We start with a league-by-league review and then see how they all put together reduced the risk and finally produced a result as expected.

In Image 2 below you can see that hardly any individual system (league) within the portfolio met its expectations (predictions), yet the overall performance of the portfolio fully met the expectations, profit-wise, yield-wise and hit rate-wise.

Image 2: Final performance of the 2017-18 winter league portfolio

Risk Judgement: **HIGH RISK**

Hit rate expected: **31.94%** *(associated risk: high)*

Yield expected: **30.36%** *(associated risk: high)*

Despite its low hit rate this system was included because a healthy yield was expected. When judging a system fit for inclusion, healthy yield indicates that a profit can still be made even if something goes wrong, e.g. the hit rate is a little lower than expected.

Hit rate achieved: **30.67%** *(just below expectation)*

Yield achieved: **9.75%** *(far below expectation)*

The hit rate was more or less achieved, but the profit was 65% below budget. Perhaps the odds that were obtained were too low or there were just not enough larger priced winners in this cluster.

Risk Judgement: **LOW RISK**

Hit rate expected: **86.67%** *(associated risk: low)*

Yield expected: **13.85%** *(associated risk: low)*

Included because of the high hit rate indication to add reliability and stability to the portfolio, despite a low yield expectation.

Hit rate achieved: **80.95%** *(below expectation)*

Yield achieved: **7.90%** *(below expectation)*

The hit rate was below expectation and hence the yield too. However, a profit is a profit albeit small here, but no complaints. In the end, Belgium produced a profit and helped the portfolio to remain balanced over the season.

Risk Judgement: **MEDIUM RISK**

Hit rate expected: **41.67%** *(associated risk: medium)*

Yield expected: **21.18%** *(associated risk: medium)*

Another judgement call asking the anticipated yield of around 20% to buffer the expected hit rate and still turn a profit.

Hit rate achieved: **37.5%** *(below expectation)*

Yield achieved: **8.1%** *(far below expectation)*

The hit rate was below expectation and hence the yield too. But still a profit from a medium risk venture.

Risk Judgement: **HIGH RISK**

Hit rate expected: **39.62%** *(associated risk: medium)*

Yield expected: **38.62%** *(associated risk: high)*

Despite its low hit rate this system was included because a healthy yield was expected. It was felt that the risk was worth the potential reward.

Hit rate achieved: **38.18%** *(just slightly under expectation)*

Yield achieved: **26.73%** *(good, although far below expectation)*

The EPL is probably the most analysed league in the world and it is difficult to spot long-term value for betting systems that are reliable and come out to expectations. The hit rate was in line with expectations but the yield was not. Nevertheless, a healthy profit was achieved.

Risk Judgement: **MEDIUM RISK**

Hit rate expected: **50.00%** *(associated risk: medium)*

Yield expected: **24.93%** *(associated risk: medium)*

The yield looked slightly too high for an expected hit rate of 50%. This may have been an arbitrary positive result observed in the inflection point graphs, especially as the expected number of bets was only 36. Nevertheless, this system was included in the portfolio because of the risk-reward balance.

Hit rate achieved: **43.33%** *(below expectation)*

Yield achieved: **10.8%** *(far below expectation)*

Only 30 bets were played (from expected 36) and both hit rate and yield were much lower than expected.

Risk Judgement: **MEDIUM RISK**

Hit rate expected: **31.58%** *(associated risk: high)*

Yield expected: **29.83%** *(associated risk: medium)*

Normally, systems with an expected hit rate of under 35% (classified as ‘high’ risk) and with an expected yield between 15% and 30% (‘medium’ risk) get an overall risk judgement: HIGH RISK.

Although the combined expectations of hit rate and yield here would have labelled this system as ‘high risk’ we downgraded the overall risk judgement to ‘medium risk’ as it was Germany and the Bundesliga is probably the statistically most reliable league we are aware of.

Hit rate achieved: **37.04%** *(above expectation)*

Yield achieved: **55.43%** *(far above expectation)*

German underdogs (not sausage dogs) were a (woman’s) best friend, and proved to be the most successful of all our systems.

If the EPL is just about the most ‘statistically unreliable’ league, then the Bundesliga is at the other end of the scale. There is something typically German about the Bundesliga’s constant conformity to statistics, season in, season out – very correct and very efficient.

Risk Judgement: **LOW RISK**

Hit rate expected: 80.00% *(associated risk: low)*

Yield expected: 9.02% *(associated risk: low)*

The Greek system was chosen for risk diversification in our portfolio. Despite associated lower yields, bets with a high probability of winning break up losing streaks in the portfolio and add stability.

Hit rate achieved: **82.98%** *(slightly above expectation*)

Yield achieved: **8.06%** *(below expectation)*

Not a huge profit but a profit nonetheless. Low priced home wins are naturally odds-on favourites also. Better prices can be achieved on these by placing bets further back in time before the event.

Risk Judgement: **MEDIUM RISK**

Hit rate expected: **52.59%** *(associated risk: medium)*

Yield expected: **8.49%** *(associated risk: low)*

Like Greece, this one was chosen for risk diversification combining a relatively low yield with a probability over 50%.

Hit rate achieved: **61.11%** *(above expectation)*

Yield achieved: **17.51%** *(far above expectation)*

Italy was our second best performer with its mixture of odds-on and odds-against away teams. However, almost all of these were the favourites and just a 15% swing in hit rate (not unnatural with favourites), was enough to double the yield harvest.

Risk Judgement: **MEDIUM RISK**

Hit rate expected: **75.00%** *(associated risk: low)*

Yield expected: **32.23%** *(associated risk: high)*

The yield here stuck out as being too high for a system with such a high probability. This may have therefore been an arbitrary positive result observed in the inflection point graphs, especially as the expected number of bets was as few as 15. Nevertheless, this system was included in the portfolio and judged as medium risk.

Hit rate achieved: **73.33%** *(slightly below expectation)*

Yield achieved: **25.33%** *(below expectation)*

A very tiny system with only 15 bets expected and indeed, 15 bets played in the end. However, not 12 wins as ‘expected’ but only 11. With margins so tight it was no wonder that the yield figure dropped. Otherwise, despite initial indecision whether to include this system, a profit was made.

Risk Judgement: **HIGH RISK**

Hit rate expected: **25.00%** *(associated risk: high)*

Yield expected: **33.00%** *(associated risk: high)*

With such low probability on the table, unreliability was expected, but the reward (yield) was worth pursuing. Furthermore, only 40 bets were expected. This system therefore had all the hallmarks of ‘high risk’.

Hit rate achieved: **21.62%** *(slightly below expectation)*

Yield achieved: **16.22%** *(far below expectation)*

Betting on underdogs is notoriously volatile and it was lucky that the very last two bets of the season both won to avoid a deficit here. 40 bets were expected, but only 37 played that fitted the selection criteria. 10 wins were expected but only 8 materialised.

This was the only system in the portfolio with such a low hit rate expectation in connection with very few bets expected. It was always going to be a shaky, unreliable ride, and it didin’t disappoint.

There was not a single system that performed *as expected* within the portfolio. Of the 10 chosen systems illustrated here, eight underperformed, and only Italy and Germany overperformed (both ‘medium’ risk systems).

The expected hit rate for Germany was 31.58% and it achieved 37.04%

The expected hit rate for Italy was 52.59% and it achieved 61.11%

Although some of the other eight systems succeeded to surpass their expected hit rates, the profit at the end was less than expected. This indicates that perhaps the odds played across the board were a little below those used in the HDAFU simulation tables.

**Please remember!** Concentrate only on individual leagues whilst compiling your portfolio. Once you start placing bets shift your focus to the overall portfolio performance and bank management. Only after a set period of time, review the individual systems in your portfolio. There will be an article on that topic coming soon…

After you have compiled your portfolio with due care you need to trust your own judgements and follow through fully with your betting endeavour as planned!

The information contained in the spreadsheet is invaluable and we are sure that you will feel the nominal **£5.00 GBP** charge is a real bargain: It is an ideal template for your own portfolio structuring and monitoring processes, and in addition it provides the opening and closing odds for the 518 bets included in the portfolio.

*The size of this .XLSX Excel file is 568KB:*

**>>> 2017-18 winter league campaign <<< **

**Spreadsheet Features:**

- The spreadsheet details every bet in every system used.
- Includes tabs for the overview of the portfolio, match data of the 10 systems used, as well as their opening and closing odds, and finally the odds used and the staking plan.
- The most important feature is the
**Ratchet**staking tab, which will provide you with the ideas and tools to manage your betting bank professionally.

On the whole, the portfolio performed as expected:

- A hit rate of 48.32% was expected; 45.37% was achieved
- A profit (flat stakes of 100 units) of 11,253.60 was expected;
**9,909.00**was achieved (if using 100 unit flat stakes during the whole campaign)

Image 3: 2018-18 Winter League Campaign Portfolio Results

You might say that the portfolio underachieved. But this is betting! The only goal is to finish with a profit! Any achieved profit may be below expectations or above, but as long as there is a profit, the portfolio must be considered as having been successful!

Therefore, remember to look at the performance of the whole portfolio for judging if it was successful. Do not concentrate on the performance of individual systems; not even after the season has finished. Potentially fatal if your mindset is affected by worries about individual systems, especially whilst your campaign is in-play.

However, there are exceptions to this rule and I will write about this in another article and explain when a system can be abandoned in-play, or when a new system can (or should) be added during the season.

You certainly noticed that in the above chapter we wrote that the portfolio achieved a profit of 9,909 but stated in the title of this article “35k in 138 Days”.

To predict the most likely performance of a portfolio you only can simulate a profit/loss using flat stakes. The same applies to judging the performance of a portfolio. You can only use flat stakes to appraise the effectiveness of a portfolio.

It doesn’t matter what staking plan has been used; in order to evaluate *(and compare with predictions)* the performance of a portfolio, you will need to see what would have happened when using flat stakes. Otherwise you will be comparing apples with pears.

The sequence of winning and losing bets is pretty random and any staking plan applied would therefore skew the review process. Therefore remember always to use flat stakes for retrospective analysis.

However, the portfolio used to illustrate this article produced a final profit of 34,925 units using ratcheting *(= gradual increase of stakes when winning)*. More details you’ll find in the article: **Winter Leagues 2017-18: Bank Management, Staking and Timing** *>> This article will be published within the next few days.*

If you have read the article about judging the risk of a portfolio you may remember the following statement about **diversification**:

The rationale behind this technique contends that a portfolio constructed of different kinds of bets will, on average, pose a lower risk than any individual bet (system) found within the portfolio.

Diversification strives to smooth out unsystematic or anomalous risk events (outcome of matches/leagues) in a portfolio so that the positive performance of some bets (winnings) neutralizes the negative performance of others (losers).

Have another look at Image 2 for the losing streak sequences.

The expected individual longest losing streaks within the leagues (systems) were as long as 11 bets in a row.

All three ‘high risk’ systems produced, as expected, very long losing streaks: Austria, EPL, Poland.

Denmark produced an even longer losing streak than expected. It started on the 26/8/2017 and continued until 29/10/17 – more than 9 rounds of games! Nevertheless, they recovered to finish with a positive return, although far lower than expected.

However, the portfolio as a whole only experienced a losing streak of seven bets in a row *(chronologically)*.

But try and look at the portfolio as a whole and consider one round (week) as one ‘single bet’. This perspective reveals a longest streak of four *(out of 47 rounds)* – just about bearable!

*Please remember* that in order to judge the success of any betting portfolio it is necessary to evaluate the performance of all of its systems together as one, not just individual group members (i.e. bets in just one league or system).

*I hope you enjoyed this article and learned how to judge the performance of a portfolio. However, if you are still not clear, then please feel free to ask any questions via the comment section below.*

Have you ever wondered how bookmakers set their odds? They must be pretty good at it to remain trading in a high risk industry built on small margins!

Remember folks it’s all about finding the “edge”.

Image: Cartoonresource (Shutterstock)

Image: Cartoonresource (Shutterstock)

It is common knowledge that the gambling industry as a whole relies to a large extent on the ignorance of its customers and, only by understanding how bookmakers think and act, will you ever be able to compete with them on a level playing field.

This course is designed to give you the essential, fundamental knowledge necessary to understand odds calculation and the bookmaker market.

It deals with relatively simple descriptive statistics and teaches you how to look at data sets, calculate your own probabilities and odds, analyse the market odds on offer, and make informed decisions when predicting football results.

Amongst the topics you will work through are distributions, deviations, graphs and charts, odds calculation, financial terminologies, risk management, and of course, how to identify ‘value’ in the betting market.

You will gain a deep understanding of the many different elements required to understand the bookmaker market and odds calculation. Many false beliefs that the majority of gamblers and fans of football have about betting will be exposed and stripped away.

Readers will also be enlightened to learn about how odds are set in the market, where to find ‘errors’ in market prices, how to evaluate data and graphs, and much, much more.

The course comes in electronic format and the bundle includes the **course book (PDF*)** and a **Bundesliga cluster table (Excel)** for studying. This course employs a didactic method of teaching, which is an educational technique. It is a very structured style of learning and as such, each section of the course should be mastered before moving on to the next.

To further encourage you to learn, there is a plethora of exercises to practice what you have learned, and the solutions to the exercises are found at the end of the book, sometimes embellished with further explanations.

All of the course lessons are presented in a pragmatic, easy-to-follow, step-by-step fashion, with no more than passing respect towards the sport of football and the passion of its fans. After all, this book has been written by a lady who loves maths but dislikes football…!

In addition, you will receive **the very latest Bundesliga table for the current season**, so that you can put into practice what you have learned and within the course, you will find **a discount code** enabling you to download **for free the German Bundesliga sheet in future seasons**, meaning that you will always have access to the most current Bundesliga cluster table, **forever**: it doesn’t matter when you bought the course.

**By the way, the PDF is a professionally formatted document and if you have a double-sided printer you can print your own book for studying.*

Course with Cluster Tables for the German Bundesliga

Over/Under ‘X’ Goals

PRODUCT SUMMARY

- Format:
**PDF & XLS** - Download Size:
**Course (PDF): 5.2 MB & Excel file: 782 KB** - Publisher:
**Soccerwidow Ltd; 2nd Edition***(July 2016)* - Pages:
**169***(almost 38,000 words)* - Tables and graphs:
**70** - Example tasks:
**more than 80***(with solutions)* - Language:
**ENGLISH**

* 0% VAT to UK customers, 0% VAT to Non-EU customers **Read more:** EU VAT Legislation

For traditionalists, the PDF has been professionally formatted for double-sided printing. If you like, you can print your book in full-colour with a cover and add slick spiral binding.

Those who prefer to read the document on their computers will find the chosen font *(Myriad Pro)* easy to read on the screen. Myriad Pro has a clean sans-serif aesthetic which makes it highly accessible.

The electronic version also contains a plethora of easy-to-navigate links to help the learner find his way around the document.

**Probability, Betting Odds, Value, Yield, Profitability**

**Basic Statistical Terminology**

- Goal Distribution and Percentage Calculation
- Deviation from the Mean
- Standard Deviation – The Main Measure of Variability
- Precision, Trueness and Accuracy

**Betting Odds Calculation**

- Probability and Betting Odds
- Opening Betting Odds Range
- Calculation of ‘Zero’ (Fair) Odds

**Risk Management Control**

- Financial Terms: Yield, ROI and Profitability
- Risk Forecasting and Evaluation: Value of a Trade (Bet)
- Preventative Measures: Setting the Starting Bank

**Market Dynamics, Cluster Groups and Betting Tables**

**Market Dynamics**

- Betting Odds are Prices of Bets
- Falling Odds represent Price Increase
- Bookmakers adjust Betting Odds to Public Opinions

**Building of Cluster Groups**

- What are Cluster Groups?
- Clustering Depending on ‘Strength’ of the Team

**Betting Tables: Over/Under ‘X’ Goals**

- Goal Distribution by Team
- Team Calculation Tables
- Standard Deviation Tables
- Using Calculation Tables to Determine Betting Odds

**Finding Value Bets**

- Everything that Glitters is not Gold
- Method I: Value Betting using Cluster Group Tables
- Method II: Value Betting using the Value Calculator
- Cluster Groups, Value Calculator and Bets Identification

…or ask any questions in the comment section below. ]]>

**Do you know how bookmakers set their odds? We do! And we will happily teach you too!**

Image: Cartoonresource (Shutterstock)

The 2nd edition is not just a ‘revised’ version, it is a **total overhaul** answering many questions raised by our original audience such as deviations and correction factors, which are explained in great detail.

The updated version is now a hefty document at **169 pages** and **almost 40,000 words**, three times the length of the first course.

One enormous enhancement is that in this new version, we actually give away **two proven methods of bet selection**, making it as easy as possible to spot candidates for successful value betting portfolios.

Another substantial upgrade is that buyers of the 2nd edition will now automatically get the current, up-to-date German Bundesliga cluster table supplied with the course. In addition, you will find a discount code within the course enabling you to download **for free** the German Bundesliga sheet in future seasons, meaning that you will always have access to the most current Bundesliga cluster table, **forever**: it doesn’t matter when you bought the course.

**Attila**

The course is really very well done! Concentrated expertise that cannot be found anywhere else.

**Socrates**

Finally an unbiased contribution to football betting, which goes beyond a simple description of betting options and also explains bookmaker calculations as well as betting odds formation in detail.

What really surprised me is how easy it actually is to calculate odds and even predict Betfair market prices to find value bets. However, I will still need a long time to work through the entire course, but now I have some guidance about how to change my betting behaviour.

**Onheimlech**

Hello Soccerwidow,

Your course is written very well. My bet portfolio now considers mathematical formulas and somehow I like this.

It is amazing to see how close my own calculated odds come to the actual odds for different bookmakers. Without your course I wouldn’t be able to find value.

**André**

I just working through the Over/Under X Goals course.

The examples described are simply fabulous. When I look back and see what I have previously evaluated and what is recommended by you – they are worlds if not galaxies apart.

**Marcel Brand**

Dear Soccerwidow,

Firstly many thanks for the great Over/Under Goals course. I would already personally call myself an advanced bettor, but your course has brought me further forwards, especially in the topic of cluster grouping.

**Pete**

Just bought your guide, and learned a lot. Many, many thanks! I can recommend it.

Worth every penny!

**Ian**

I’ve just purchased the Over/Under course and Value Bet detector. They are both excellent products and bring together all the knowledge that I have accumulated over a few decades.

Unfortunately, it has taken me this long to figure out the simple fact that value bets + staking plan = steady profits

**Janice**

When I bought your course I was completely overawed by it and didn’t read it properly for a couple of months – in fact I stopped betting altogether…

But when I had nothing to do one day I re-opened it, gradually overcame my fear, and began making some satisfying progress.

The exercises and questions really are a great idea and help to commit the concepts to memory, and having the answers provided at the back of the book is hugely reassuring, especially when you get them right.

The course **Fundamentals of Sports Betting – Over/Under ‘X’ Goals** explains statistical applications required to calculate odds and find value in the market.

All the concepts explained apply basic maths, financial management, quantitative analysis, and statistics to football betting.

The course reinterprets maths covered in A-levels at school *(such as analysing graphs, calculating the mean, etc.)*, and also introduces some statistics from the first year of university studies *(e.g. standard deviation)*.

Bankroll management is one of the most important pillars for success in sports betting.

Image: Alex Roz

A portfolio of sports bets placed over time can be compared to investing in the money markets on a portfolio of stocks and shares.

Indeed, the term ‘bankroll management’ comes from the financial sector and describes the use of the *seed capital* (i.e. in betting terminology, the *initial stake*).

Bankroll is the ‘starting bank’, and the intention is to manage it and increase it at the same time.

Bankroll management therefore deals with how to properly manage your starting bank.

**The good news**: It is actually possible to calculate the required starting bank mathematically.

**The bad news**: The calculations are naturally dependent upon statistics, and the ‘significance’ of the results relies on the amount of data used.

For example, any strategy based on one German Bundesliga team’s home games during a season produces a sample of precisely 17 sets of data, which is a very small number, statistically speaking.

The **Law of Large Numbers** is omnipresent so far as statistical accuracy is concerned: The larger the data sample, the more accurate the final results are likely to be, although a line has to be drawn between sample size and an acceptable level of error.

One way of coping with small data sets is to incorporate a **risk discount** into the equation. More about this later…

On face value, you might assume that calculating the necessary starting bank for a betting strategy can be derived solely from the stake multiplied by the number of bets (n).

With the 17 matches from our example above, and a constant stake of 100 units per bet, the bank would then be: 100 x 17 = 1700 units. But is this maximal amount *really* needed?

Although this may be true where returns from winning bets cannot be immediately re-invested, such a bank can never be optimal because an inordinate amount of capital would be tied-up.

What you should look for is the most cost-effective bankroll where all the money you have at your disposal is working for you as efficiently as possible.

Optimal bankroll is characterized by two things:

- Cash holdings (i.e. money in reserve) is kept as low as possible
**Gambler’s ruin**is avoided

There are five vital criteria you will need to establish:

- What is the size of your stake per bet?
- How many bets does your strategy expect to be placed?
- What is the expected hit rate of your strategy?
- What is its expected longest losing streak?
- Determine the risk variables and incorporate a ‘risk coefficient’.

Okay, we will stick with the German Bundesliga for demonstration purposes and use a system gleaned from its latest full-time 1×2 **HDAFU Simulation Table**.

If you have already bought this table, you can see the full and detailed analysis of **backing the underdog whenever Hamburg plays at home**: This strategy has realised a yield in excess of 58% over the course of five complete seasons from 2010-11 to 2014-15.

In addition, there has been profit produced in every one of those same five seasons.

It’s an ideal candidate for incorporating into a large portfolio of other systems. (When we say ‘large’ we mean a portfolio that will generate at least 500 bets in a season.)

**(1) Size of Stake per Bet:**

This is determined by your own liquidity, and to keep this calculation simple, a **Constant Stake** (CS) of 100 units per bet will be used.

**(2) Number of Bets:**

For this mini portfolio of Hamburg home games, the **Number of Bets** (n) is 17 for the new season.

**(3) Hit Rate:**

The HDAFU Simulation Table reveals that from 85 Hamburg home games over five seasons, 32 underdogs triumphed: a **Hit Rate** of 38%.

The random selection of only 85 matches is a relatively small sample and the possibility of ‘random sample error’ is therefore relatively large.

To compensate, it is worth applying what is known as a ‘risk discount’ to reduce the actual hit rate experienced and to build-in an extra level of security if statistical expectations for the new season are not realised.

Taking a risk discount figure of 5%, the expected hit rate becomes: 38% – 5% = 33%.

[Have a look at **this article** for more information about hit rates].

**(4) Longest Losing Streak Expected (LLSe):**

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 logarithm*

**P** = (negative) probability^{†}

**| .. |** = absolute value or ‘modulus’ *(see Wikipedia if you would like to know more about these mathematical symbols)*

**Suffice 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: to make life easy, the formulas to use are included in the free spreadsheet download below*.

^{†}*For this calculation, the negative probability or hit rate is used. In this case, having adjusted our hit rate down to 33% using a risk discount, the probability that the bet loses (negative probability) is 67%*.

rounded down to

From a pool of 17 bets, you can therefore statistically expect that a maximum of seven in a row may be lost without winning one in between.

**(5) Risk Coefficient (RC):**

The determination of risk variables depends primarily on your **risk aversion**. Risk-averse bettors choose a high coefficient figure (e.g. 5), whilst gamblers who are happier taking risks choose lower coefficients (e.g. 2).

But why are we including a risk coefficient at all?

We can assume that the longest expected losing streak *(in our example, seven lost bets in a row)*, may already start with the first bet.

Although one bet may win after that, with the gains reimbursing the loss and allowing for reinvestment, there can still be a second stroke of bad luck directly after the first bet that you have won.

Neither winning bets nor losing bets ever line up in a uniform manner; they will always appear in a random pattern, so always better to be safe than sorry.

The formula is:

Our Bundesliga example is an underdog backing system, which by its very nature, is risky. However, as there are only a maximum of 17 bets in this mini system, we will choose a risk coefficient of 1.5: we are happy to take the risks!

It is not very likely that there will be two losing streaks of seven games in a row when betting 17 consecutive times. However, we are aware that it may be quite challenging for the nerves to sit through losing streaks watching the bank balance reduce before your eyes!

The optimal bankroll required to run this system for a season is as follows:

If you remember the sub-optimal bank strategy at the beginning of the article where we touched on a bankroll of 1,700 units (100 units per bet x 17), you can see we have now released 650 units for investing in another strategy elsewhere.

With this **free Excel table download**, you can easily and quickly discover what the longest losing streaks are for your own strategies. Just enter your stake, number of bets, and risk coefficient figures and let it calculate everything for you!

**>>> Excel Workbook – Losing Streaks <<<**

*Click on the above button – in the new tab click on the ‘Continue Checkout’ button. Enter your name and email address to allow our automatic shopping cart to deliver the file by email to you, free of charge. The .xls file size is 93 KB. When you receive your confirmation email, just click on ‘View Purchase Online’ (in the email text) to download the file.*

This is contrary to other forms of gambling loaded in favour of the house such as lottery and roulette, where success tends to rely more on luck than strategy.

Image: PhotoSky (Shutterstock)

With football betting, there are only three possible half-time and full-time outcomes (home/draw/away) for example, and sometimes just two sides to a football bet (e.g. over/under ‘X’ goals).

In contrast, the UK National Lottery has 45 numbers providing over 14 million combinations of the six needed for a jackpot, meaning the chances of winning are drastically low.

Indeed, football betting is a little like stock market shares where it is possible to select profitable investments, and traders can forecast with a deal of accuracy whether prices are more likely to rise or fall.

Whereas in stock markets prices sometimes rise or fall unexpectedly, freak results also happen in football as every fan will have observed.

I was fortunate enough to receive tutoring on financial and quantitative analysis of stock markets at university but of course, football betting is not on the syllabus. However, the more I study betting and its underlying statistics, the more parallels I can draw with stock market analysis.

The secret of long-term financial success in the stock market is not necessarily always about buying the right shares or options.

Obviously, a good selection of instruments naturally influences the profit margin in a positive manner but, long-term financial success is not guaranteed if the portfolio is wrongly structured. The same applies to football betting.

A professional stock broker would not dream of investing all of his clients’ money in just * one* share or option. Indices such as DAX, MDAX and TecDAX all include at least 30 companies in their portfolios. The DAX 100, as its name suggests, contains 100 companies.

Why, therefore, does the stock broker look to invest in a wide range of markets? The answer is obvious: This is done to reduce or spread the risk if one or another share price develops in the wrong direction. And, even in the very unlikely event that the whole stock market collapses, the indices will never totally drop to zero.

Translated into gambling, these principles indicate that you should **never ever put all your bank on one individual bet**, however ‘sure’ it appears. You must always bet on

One interpretation reads: …”A bundle of investments in the possession of an institution or an individual… Usually, an extensive analysis precedes the structuring of a portfolio… A portfolio is typically part of the strategy to reduce the risks of financial investments by diversifying”…

**Translated into betting language:**

…”A portfolio is a package of bets where extensive analysis has determined the choices (picks)…This is an essential part of the whole betting strategy in order to reduce the risks of losing by diversifying”…

This is an example of my portfolio of bets for 26.2.2011:

**Laying a considerably weaker away team (in terms of odds):**

- English Premier League: Aston Villa vs. Blackburn Rovers – Lay Away (5.3)
- English Premier League: Wolverhampton Wanderers vs. Blackpool – Lay Away (4.8)

**Backing at odds between 3.35 and 3.5:**

- English Premier League: Wigan Athletic vs. Manchester United – Back Over 3.5 Goals (3.35)
- English Championship: Hull City vs. Cardiff City – Back Draw (3.5)

**Laying the Draw:**

- English Championship: Barnsley vs. Norwich City – Lay Draw (3.4)

**Laying the home team in games between equally matched teams (in terms of odds):**

- English Championship: Doncaster Rovers vs. Watford – Lay Home (2.84)
- English Championship: Middlesbrough vs. QPR – Lay Home (2.88)
- English Championship: Millwall vs. Nottingham Forest – Lay Home (2.62)

I carried out an extensive statistical analysis before picking these games as my ‘value bet portfolio’ for the weekend and happily, seven out of eight bets (87.5%) won.

My calculations also revealed that had only five (62.5%) won, the profit would still have been in excess of 10%. If only 50% of the bets had been successful, the financial loss would have been limited to 10% of the bank.

The calculated probability that all eight of the selected picks lost was minimal at 0.0026% (38,428 to 1). The probability that all eight picks won was 3.53% (28 to 1).

The probability that seven or eight of the eight picks won was 20.77% (4.8 to 1).

In layman’s terms this means that assuming my trend analyses and calculations of the probabilities were correct (of course, there is always the possibility of calculation errors), statistically speaking with this type of portfolio structure, every 27th weekend is likely to produce eight out of eight winning picks, and on average, every 5th weekend is likely to finish with seven out of eight correct picks.

Based on my own statistical calculations for each event, the individual probabilities equated to:

- Aston Villa vs. Blackburn Rovers – Lay Away (84.69% probability of Blackburn not winning)
- Wolverhampton Wanderers vs. Blackpool – Lay Away (84.69% probability of Blackpool not winning)
- Wigan Athletic vs. Manchester United – Back Over 3.5 Goals (38.24% chance of happening)
- Hull City vs. Cardiff City – Back Draw (37.27% chance of happening)
- Barnsley vs. Norwich City – Lay Draw (81.07% chance the match is not drawn)
- Doncaster Rovers vs. Watford – Lay Home (75.28% probability of Doncaster not winning)
- Middlesbrough vs. QPR – Lay Home (75.28% probability of Middlesbrough not winning)
- Millwall vs. Nottingham Forest – Lay Home (75.28% probability of Millwall not winning)

If you multiply all the probabilities, 84.69% x 82.69% x 38.24%, et cetera, the result is **3.53%**. This was the calculated probability that all eight of the chosen independent events would occur (i.e. all eight bets win).

The opposite is of course to multiply the probabilities of the selected bets not winning: 15.31% (1 minus 84.69%) x 15.31% (1 minus 84.69%) x 61.76% (1 minus 38.24%), et cetera, for a result of 0.0026%. This was the probability of all eight bets losing.

Roughly speaking, the chance of winning all eight selected bets was 1,350 times higher than losing all eight of them (38,428 divided by 28 or alternatively, 3.53% divided by 0.0026%).

In this fashion, you can compute all the other probabilities for each permutation of events to structure the portfolio and organise its staking. However, an exact explanation of probability calculation and portfolio diversification would complicate this article just now.

If you would like further depth on this topic, then please read my articles on **combinatorics and probability** and also on **probability and deviation**, both of which offer a more advanced approach to the thinking needed before composing structured betting portfolios.

Please post any questions or comments in the Leave a Reply box below.

]]>You should not be dazzled by their mechanisms because * none* of these staking plans will work at all if your betting system has no mathematical ‘edge’. Indeed, with a blunt selection strategy the only mark even a highly sophisticated staking plan will make on your betting experience is how long it will be before your bank is lost.

Image: Ninell (Shutterstock)

In this article, I will not be analysing the myriad staking plans as there is plenty of information already on the Net. For example, just key in the words “staking plan”, or any of above names into the search engine of your choice.

I have said many times before on this blog that there is no way to make money in the long run from betting without having an edge over the market. Therefore, honestly, if you have arrived on this blog and you are reading this article because you hope to find a staking plan to turn your luck, then please forget it. First of all you need to find a * selection system* that works for you and which contains that magical ‘edge’!

If you have found your betting system then there is no need for any complicated staking plan, simply plump for a **level risk/stake**. All other staking plans contain one or another problem and please rest assured that there is definitely not a single staking plan in existence which makes a failing betting system work.

It’s only your **knowledge** of the market which will determine your success, and this means a * good understanding of probabilities and betting odds* and the knowledge of how to use them to your advantage.

**The benchmark for any betting system is the level risk staking plan.**

This means risking a fixed unit per bet. A selection system that does not produce a profit to level risk simply does not have a positive edge, and is doomed to lose in the long run.

There are two varieties of this staking plan:

This means risking the * same amount* of money with each and every bet. This applies to back as well as to lay bets.

**Back bets** are pretty easy. You risk, for example, 10 units per bet and it doesn’t matter how low or high the odds are.

**Lay bets** require some calculation as you need to calculate the stake for each bet individually in order * to risk* the same amount every time (e.g. 10 units) to minimise losses.

This strategy takes into account the probabilities (odds), meaning that there is a higher stake (i.e. risk) for bets with a higher chance of winning, and a proportionately reduced stake the lower the chance of winning a bet is (i.e. providing money for more attempts to get a ‘hit’ at higher odds).

This is an even more conservative approach than the “level stake” but in the end the outcome is more or less the same for most betting systems. The deviations are lower meaning that losing streaks (troughs) don’t reduce the bank as much, and winning streaks (peaks) are also levelled to some degree. The result is a less jagged performance with fewer heavy swings of misfortune and fortune. Evening-out the peaks and troughs makes the prediction of future performance also a little easier.

In essence fixed win/risk means the stakes employed depend upon the odds, but the risk and attainable profit remain constant. Wagers are always limited, for example to a maximum risk per bet of 10 units, or to a maximum win of 10 units.

**Back Bets at odds of up to 2.0:**Example 1.69; the stake (risk) is 10 units; if the bet wins, the winnings are 6.90 units; if bet loses, then 10 units are lost.**Lay Bets at odds of up to 2.0:**Example 1.69; winnings are capped at 10 units; if bet wins, the winnings are 10 units; if bet loses, the loss is 6.90 units.**Back Bets at odds over 2.0:**Example 3.5; winnings are capped at 10 units; if bet wins, the winnings are 10 units; if bet loses, the loss is 4 units.**Lay Bets at odds over 2.0:**Example 3.5; loss is capped at 10 units; if bet wins, winnings are 4 units; if bet loses, then 10 units are lost.

You may be surprised to hear but **that’s it!** There is absolutely no need to bother with any other staking plans.

If your system does not work either with “level stake” and/or “fixed win/risk” then you have a problem and seriously need to reconsider your strategy as being potentially flawed.

Please note that I have written * and/or* as it really doesn’t matter if you use “level stake” or “fixed win/risk”. Both staking plans are mathematically sound, and are more or less the same. Both staking plans will produce a benchmark for a betting system to test if it is working or not.

If you have found a betting system which works with “level stake” and/or “fixed win/risk” then the only thing you need to know in addition is * which percentage* of your bank to risk on an individual bet.

For this you need to calculate the **Expected Losing Sequence** meaning the maximum number of bets in a row which are likely to go wrong (lose), and from this, you will then be able to calculate the percentage of your bank to be risked per bet to ensure you never go bankrupt…

…But this is a topic for another day.

* One more thing though:* There are actually many people who have a

However, because these people are oblivious to the necessity for a controlled staking plan, they often do not stick to a set of rules, e.g. same risk per bet, and therefore they lose.

If you happen to be one of these bettors, please re-read this article and I urge you to start applying the same risk on all your bets. Your immediate reward for **just a little discipline** will be a gradually growing betting bank.

Be happy with “growing gradually”; don’t be greedy – and then you will be successful!

Of course, it certainly also helps if you have an idea **how odds are calculated**…

*Congratulations to those ‘mad’ scientists at the International School of Management (ISM) in Frankfurt and the German Sports University in Cologne whose predictions we followed throughout Euro 2012.*

Image: Pikoso.kz (Shutterstock)

*Those of you who also followed suit reaped the benefits of their statistical predictions realising a yield of between 19.7% and 25.5% depending upon which style of staking plan you employed (either fixed stake or fixed risk/win).*

However, some of their prophecies did not materialise…

For example, co-hosts Poland did not make the semi-finals.

There were plenty of goals in the England v. Sweden match but not a huge goal difference for England and in the end they struggled to win at all.

Alas, the scientists’ beloved Germany did not get a chance to dethrone the defending champions in the final despite saying, “chance, luck and statistics are favouring zis”.

Never-ze-less, ze predictions from ze Frankfurt and Cologne think-tanks produced handsome profits.

As mentioned in our original article * not all predictions will win*. Indeed, it would have been miraculous if they had all won as the mathematical likelihood was just 0.00000031% (326 million to 1 – that’s definitely the way to bankrupt the bookies!).

**Soccerwidow’s pre-tournament profit/loss estimation of the scientists’ predictions using a fixed risk/fixed win staking plan:**

*Total risk of all bets (stakes): 106.55 Units
Maximum potential profit: 140.52 Units
Realistically expected profit (10%-15% yield): 10.66 to 15.98 Units*

However, things turned out better than expected with profits of 27.22 units (25.5% yield) based on our favoured fixed risk/fixed win staking plan:

The second table represents the same bets using a fixed stake staking plan.

We feel that a **Fixed win/Fixed Risk staking plan** is the most solid and reliable form of staking for maximised profits and minimised losses, and we have just found this article **Raceadvisor.co.uk: Fixed Profits or Fixed Stakes?** which includes a mathematical experiment comparing a fixed stake with a fixed risk/win staking plan. It’s an interesting read and a similar outcome to our own findings.

However, the **Fixed Stake Staking Plan** tends to be a more popular method and although this would have also brought a nice profit of 22.65 units (19.7% yield), the **Fixed win/Fixed Risk staking plan** remains ‘smarter’ in our humble opinion.

*If you would like to analyse these calculations in a little more detail you can download our Excel spreadsheet which complements the above tables, free of charge. However, please kindly return the favour and either Twitter this article, like it on Facebook, or Google+ it.*

Excelspreadsheet Euro 2012 Simulation – Staking Plan Comparison

In our original ‘mad scientists’ article we recommended a fixed win/fixed risk staking plan and as we have seen, this method performed better than a fixed stake staking plan.

However, both staking plans produced fairly similar results due mainly to the fact that betting odds between 1.5 and 3.5 were in play. Especially at the lower odds the differences between the stake amounts in both plans were not huge, which ultimately led to similar results.

Whichever staking plan you choose is down to you and it then remains to follow it religiously without emotion and to never chase losses…

*If you now have a great void in your life following the completion of Euro 2012, instead of developing withdrawal symptoms or falling into post-Euro 2012 depression, remember that you always have therapy available by reading this blog from cover to cover. Then, if you are very brave you may wish to dive into Soccerwidow’s Fundamentals of Sports Betting course in order to learn the skills of professional odds calculation and prepare yourself for next season!*