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How to Calculate Losing Streaks & Optimal Bankroll


In this article we will teach you to determine how large your starting bank needs to be to avoid bankruptcy by calculating the longest losing streaks that can be expected from your chosen betting strategy.

What is Bankroll Management?

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

Dollar notesImage: 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 Continual Importance of Statistics, and Lots of Them!

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…

What does ‘Optimal’ Really Mean?

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


Calculating the Optimal Bankroll

There are five vital criteria you will need to establish:

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


Example Calculation

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.)

Remember the five criteria:

(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:

Formula longest losing streak

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%.

LLSe = |(ln (17) / ln (0.67))| = |2.833213344 / -0.400477567| = 7.07
rounded down to 7.00

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.

Optimal Bankroll Formula

The formula is:

Optimal Bankroll = CS x LLSe x RC

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:

100 units x 7 LLSe x 1.5 RC = 1,050 units

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.

Calculate Your Own Longest Expected Losing Streaks & Optimal Bankroll!

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.


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Last Update: 21 December 2015

Categories:Betting Advice Investment Advice Money Management Odds Calculation



21 Responses to “How to Calculate Losing Streaks & Optimal Bankroll”

  1. Amy
    22 December 2015 at 10:47 am #

    I read your article and have a couple questions? I know this more applies to a system or set Strategy, but how can I apply this to betting teams to win at half time when the odds are lets say 60% or better? Would I just have to stick to a certain amount of games? Thanks

    Amy

    • Soccerwidow
      22 December 2015 at 11:59 am #

      Hi Amy,

      it doesn’t matter if your strategy is “betting teams to win at half time when …”, or any other strategy. The betting bank is determined by your expected hit rate, stake per bet and risk coefficient. I recommend to re-read the article, and then you should be able to establish what your ideal starting bank should be.

      Regarding the amount of bets… the more the better. It’s all about risk diversification.

      We provided in this article an example of 17 bets as we wanted to show something what actually works (betting on the underdog when Hamburg plays at home). Of course, this is an extremely low number of bets for an entire season. Ideally, one should have at least a dozen each week. But please don’t expect us to give away our portfolio of bets and provide free picks.

  2. Amy
    22 December 2015 at 12:12 pm #

    Apperixiate the reply and understand. Not sure why how the last statement of your response applies? I have never been a fan of free tips and plays because it doesn’t help the persons individual strategy and learning how to be profitable on there own.

    • Soccerwidow
      22 December 2015 at 1:16 pm #

      Hi Amy, I totally agree.. people have to develop their own strategy and learn themselves how to be profitable on their own.

      What I meant was that when writing an article like this one, we sometimes provide examples, but they are always only tiny fractions of a whole portfolio of bets. However, people have to be aware that large portfolios are required for successful betting.

  3. Teng
    23 December 2015 at 8:22 pm #

    Hi SoccerWidow,

    According to portfolio theory of Nobel prize winner Harry Markowitz. Do you think that n=30 is sufficient for a portfolio. As you provided in this article, an example of 17 bets (betting on the underdog when Hamburg plays at home). And when i look at the HDAFU table for Germany, i find out that I also can bet 17 bets on “the away team to win” when Hamburg plays at home. So do you think that whether i can put it into my portfolio (n=31) as i’m afraid duplicating. Eg: Hamburg vs Bayer Muchen ( Hamburg plays at home). What should i do in this case?
    I really appreciate if you can understand what i mean.

    Thanks so much.

    • Soccerwidow
      23 December 2015 at 9:45 pm #

      Hi Teng,

      To your first question: If you are having 30 bets each weekend like “back the underdog when Hamburg plays at home” then yes, this is a large enough portfolio.

      To your 2nd question:
      The example given is: Back the underdog when Hamburg plays at home

      So, Hamburg vs Bayern Munchen (Hamburg plays at home) – Hamburg is the underdog ==> back Hamburg

      However, please don’t expect every bet to win. The expected hit rate in this example is 33%! And winning (as well as losing) bets are not lining up in a nice row.

      This season so far was exceptional good (62.5% hit rate!), but please don’t expect it to continue like this (so far these selections finished well above the expected hit rate: 6-7 winning underdogs bets were expected for the 2015-16 season in total, and 5 already won and the season is just half over. There may be, or may be not, a long losing streak ahead.):

      22/08/2015 Hamburg vs Stuttgart (3-2) Underdog: Home (odds: 3.0) – won
      19/09/2015 Hamburg vs Ein Frankfurt (0-0) Underdog: Away (odds: 2.86) – lost
      26/09/2015 Hamburg vs Schalke 04 (0-1) Underdog: Home (odds: 2.9) – lost
      17/10/2015 Hamburg vs Leverkusen (0-0) Underdog: Home (odds: 4.9) – lost
      01/11/2015 Hamburg vs Hannover (1-2) Underdog: Away (odds: 4.35) – won
      20/11/2015 Hamburg vs Dortmund (3-1) Underdog: Home (odds: 9) – won
      05/12/2015 Hamburg vs Mainz (1-3) Underdog: Away (odds: 3.3) – won
      19/12/2015 Hamburg vs Augsburg (0-1) Underdog: Away (odds: 3.25) – won

      To get to your n=30 for each betting round you will have to purchase your own HDA tables (5 leagues should be sufficient) and identify the winning picks.

      Happy betting! 🙂

  4. paolo
    1 June 2016 at 7:59 am #

    Sorry,i didnt’ understand about risk coefficient..In the article you chose 1,5….but i’like to know,how could i chose a risk coefficient?and can you explain me,how many risk coefficiente are there? example risk coefficient 2 is for what kind of betting? or 3 or 1,7 etc etc are for…. thanks Paolo

    • Soccerwidow
      1 June 2016 at 8:45 am #

      Hi Paolo, the risk coefficient really depends on your personal risk aversion. How well you can sit out losing streaks without losing your nerves and start chasing losses.

      A low risk coefficient means that it may happen that a large chunk of the bank may be eaten by a losing streak. Can you live with it? Can you bear to see that 50% of your bank has gone and still stick to your chosen strategy?

      This article, for example, was co-written by our guest author Florian. He found a really good strategy (backing the underdogs in the German BL) which he used as the example in this article and chose a risk coefficient of 1.5. He believed that this was plenty. However, I recommended to go for at least 2.5 (as the probability of winning was only 38%). Never mind, it was his choice.

      What happened was that he couldn’t sit through a longer losing streak and his emotions became the better of him at some stage during the BL betting season. I wrote about his “Real Life Example of Betting Emotions” in the article The Gambler’s Worst Enemy: Emotions!

      The rule of thumb is:
      The lower the expected hit rate the higher the risk coefficient, and vice versa.

      Good luck with your betting!
      Soccerwidow

  5. paolo
    1 June 2016 at 8:47 am #

    thanks a lot

  6. Greger
    12 June 2016 at 11:11 pm #

    Hello!

    Can you explain how to calculate optimal bankroll when using a fixed win/risk staking system in percentage of the total bankroll (for instance 4%) as opposed to a constant stake (CS)?

    Best regards
    Greger

    • Soccerwidow
      15 June 2016 at 8:58 am #

      Hi Greger, the percentage to risk depends on the probability to win the bet.

      Here’s a staking plan which should work (of course only, if you play a winning system, meaning that the long-term mathematical advantage is on your side):

      Backing
      Probability to win – less than 40% (odds 2.5 and higher): 1% of your bank
      Probability to win – 40% to 65% (odds 1.5 to 2.5): 2.5% of your bank
      Probability to win – over 65% (odds lower than 1.5): 4% of your bank

      Laying
      Probability to win the lay – over 85% (odds 6.5 and higher): 0.4% of your bank
      Probability to win the lay – 70% to 85% (odds 3.5 to 6.5): 0.6% of your bank
      Probability to win the lay – less than 70% (odds lower than 3.5): 1% of your bank

  7. Jari Suomela
    8 July 2017 at 10:38 am #

    I have a question regarding to this. If I have bets ranging from 45% to 55% what size of bankroll I should bet on back and lay bets? I use risk coficient of 5. Should I adjust the stakes by the odds offered or my own calculated percentages? So do I look at the market odds and then calculate the hit rate based on that and then use the percentage for that? Can I use the average of the 45%,50%55% and backing and laying.

    Thanks
    Jari Suomela

  8. Jari
    8 July 2017 at 11:07 am #

    I cannot understand the calculus of the lay bets. When deciding the strike rate do my own estimations or odds dictate that for backing and laying? Calculate the expected strike rate from the odds or from my own calculations for the odds? How to calculate bankroll for only laying?

    Also I’d like to bet on 45%,55% and 50% market’s but what stake size percentages I should use for all of them. The average of three?

    • Soccerwidow
      8 July 2017 at 12:14 pm #

      Anything under 55% probability (strike rate) you shouldn’t risk more than 2.5% of you bank on each bet, maybe even less.

      The lower the strike rate the less you risk…

      55% strike rate: 2.5%
      45% strike rate: 2.0%
      35% strike rate: 1.5%
      25% strike rate: 1.0%

  9. Gabriel
    13 September 2017 at 1:08 am #

    Hi, SW!

    Here is my situation: I have a combined strategy of betting in 10 leagues at the same time. Here are my vitals:
    1) Expected number of bets per round (weekend): 36 (more or less)
    2) Average odds: 3,45
    3) LLSe: 11
    4) Hit rate: 38% (Y% of ~28%)

    Using RC = 2.5 (mid-low risk) I would have do bet ~2,2% (1/46) of my bank.

    That would be fine by me, but I make all bets at once for the weekend, on friday afternoon. Which means around 36 bets, sometimes more.

    I know it is almost impossible to loose all the bets in a weekend. But my question is: does this method consider that or I should use this only one bet at a time?

    Did you understand what I meant? Thanks a lot in advance!

    • Soccerwidow
      13 September 2017 at 6:22 am #

      Hi Gabriel, you can place all bets at the same time. No problem.

      The only thing what you may wish to do is to cluster your bets in different groups if you are able to group them by expected hit rate because then, the LLSe changes and with that your percentage of the bank.

      So, you could then have, e.g. one group of bets where you are risking 2.2% of your bank with each bet, and another set of bets, say, 1.5% of your bank.

      Feel free to report after the weekend if it worked. 🙂

    • acepoint
      13 September 2017 at 12:39 pm #

      A note to @gabriel and and the same time a question to @Ringht Winger whether I’m right.

      I think it is wrong to take the average odds for calculating streaks.

      1) The odds are no absolut but relation numbers (a bet of 1.5 and another of 2.5 doesn’t produce an average of 2 (= 50%)
      2) The formula including the natural logarithm isn’t a linear function.

      Depending on the low/high ends of your betting probabilities and the deviation of all bets within this interval the expected winning/losing streaks may deviate by a huge margin.

      • Soccerwidow
        13 September 2017 at 12:57 pm #

        Hi acepoint, thanks for your valuable input to point readers in the right direction. 🙂

        By the way, here’s an article I wrote a while ago on How to Calculate Average Odds in Football Betting. The correct approach is to calculate average odds by forming the harmonic mean! The article explains the how and why.

  10. Gabriel
    13 September 2017 at 9:47 pm #

    Hi again, SW! And thanks for the note @acepoint!

    My concern (and question) regards the fact that I might have to place 40 bets and the bankroll % is around 2,2% (1/46). Thats means I would have to put almost all my bankroll at risk in 1 weekend. Since I have calculated my LLSe of 15, that fact described above would then be controlled? Is that it?

    Or shall I work with a higher RC (lower risk)? Isn’t clustering the odds a much harder job?

    Gabriel

    • Soccerwidow
      14 September 2017 at 7:58 am #

      Hi Gabriel, if you feel uncomfortable to take the risk then simply increase RC from 2.5 (mid-low risk) to any factor which makes you feel more comfortable.

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