There is a fine line and vital distinction between ignorance and stupidity. Foolishness is not lack of knowledge but a lack of intelligence, understanding, reason, wit or common sense.

We have collected together 50 of the finest and brightest quotes and sayings on the subject of ignorance and stupidity. Good luck on your journey through our collection!

Although professional arbitraging is one of the more secure methods of earning consistent profits through betting, there are several risks involved which must be avoided or controlled.

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(1) Disappearance of Arbitrage Opportunities

Arbitrage positions often have a very brief window of opportunity, perhaps between three and 15 minutes, before they disappear from the market.

Furthermore, the greater the number of ‘arbers’ finding and exploiting an ‘arb’, the shorter the arb’s lifespan becomes.

Once an arbitrage opening is identified speed and accuracy are essential to ensure that bets are placed at the required odds within the very short time window, the duration of which is fleeting and unknown.

Possible solutions:

Rapid disappearance of the optimum odds to attain profit from backing (or laying) all outcomes of an event is one of the largest challenges faced by professional arbers.

Experience in combating or avoiding loss making positions in sports arbitrage is the equivalent of possessing the betting equivalent of the ‘holy grail’, and every arber who has this high degree of market knowledge should be considered a master in his field.

• One path to attaining such heights is to specialise in cross market arbitrage, as these transactions are harder to identify for bookmakers and punters alike, reducing the risk they will be found by many others; hence the lifespan of the arb is protected or prolonged.

• Focusing on established bookmakers with both an online and high street presence is also a good idea. In this way, arbs can be compiled using a mixture of online bets from home, and walk-in transactions using the betting shops in your neighbourhood.

  Shops need to publish and make their prices available several days in advance as fixed odds coupons are printed and distributed for walk-in customers. This can certainly present arbitrage situations where all bets can be placed many days in advance of the event (although whether arbers mind having their betting bank tied-up for longer periods such as this is purely a personal and/or financial decision).

  Usually, only on the day of the event will punters be faced with the possibility of arriving at a shop with fixed odds coupon in hand only to be told that the price they have selected has dropped.

In summary, the combination of cross market arbitrage via the larger bookmakers will often present arbitrage opportunities with life spans of much longer than 15 minutes.

In the world of sports betting the art of arbitrage involves wagering on both or all sides of an event with the right combination of odds and stakes in place to make a profit whatever the outcome of that event.

Surely this is the closest you can come to attaining the “Holy Grail” in betting? Or maybe not?

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Despite the apparent rewards on offer the number of worldwide professional sports arbitrageurs is in the low tens of thousands, not more. In comparison, the German stock market employs over 3,200 staff, whilst one of the largest providers of automated arbitrage services, RebelBetting has even fewer subscribers than this number (as we write).

So, why such a relatively small group of customers taking advantage of the so-called ‘guaranteed’ gains averaging between 1.5% and 3.5% per bet (a typical ‘arb‘ provides around 2.5%), with perhaps 15-25% potential profit on the capital employed each month? That’s a far higher reward than any bank, building society, or share dividend offers!

High Capital Requirement and Personal Characteristics

Successful arbitrage betting ultimately guarantees small returns but the sacrifice is that the process requires large funds. The money is tied-up in the venture for a potentially long period of time.

Going after an average 2.5-3.0% profit per betting round and targeting a return of 15-25% of the capital employed per month, the ‘arber’ needs a starting bank of at least 25,000 € in order to make 5,000 € profit per month.

Huh! A lot of money, and for many, this will be an impossible barrier to even entry into the arbitrage arena.

Of course, arbitrage betting is a pretty safe investment, but in addition to substantial funds it requires not only great expertise but also some personal characteristics to make it possible at all:

• Many time-consuming calculations must be performed. Ouch, lots of maths!
• Clear and complete records of every transaction must be kept. How boring!
• Discipline and consistency has to be maintained at all times. Far too unsocial!

And lastly, a really stable, reliable and fast internet connection is essential without any limitations to any bookmaker or exchange world wide.

However, the average punter is perhaps not such a ‘professional’ investor, but bets for fun and/or the excitement of watching an event knowing that money is riding on the outcome. Of course, he too hopes to profit from the wager but his are gambles, not investments. Is that the reason why there are so few ‘arbers’ out there and active in the market?

Introduction to Combinatorics and Probability Theory

This article is a step-by-step guide explaining how to compute the probability that, for example, exactly 4 out of 6 picks win, or how to calculate the likelihood that at least 4 of 6 bets win.

To help your understanding of this topic you will need to comprehend the basics of football result probability calculations, which I explained in detail in the article Calculation of Odds: Probability and Deviation.

The Basics of Probability Computation in Football Betting

The following picks table (published on 22.03.2011 in the German language Soccerwidow site), contained 6 value bets including the calculated probabilities for each bet to win:

English Football: Picks 22.3.2011

Of the 6 published picks, 4 won and made a profit of 19.9% on the 50.00 € betting bank. I will now attempt to explain the mathematics behind the above selections.

The calculation of the probability that all 6 Picks will win is relatively easy and requires no knowledge of difficult formulas. You simply multiply together the given probabilities, thus:

The result of 6.3% is the probability that all 6 picks in the portfolio win.

Of course, the other end of the scale is that all 6 picks will lose. Again, this is a straight forward calculation: simply multiply the opposing probabilities to those used in the ‘win’ scenario, thus:

The result of 0.1973% is the probability that all 6 picks lose.

Summary:

• Probability that all 6 Picks win: 6.3%
• Probability that all 6 Picks lose: 0.1973%

If you divide 6.3% by 0.1973% the result is 31.93. This means the probability in this particular portfolio that all 6 picks win is almost 32 times higher than the probability that all 6 picks lose.

Practically speaking, there is a 32 times higher chance of winning all 6 bets and cashing 40.90 € profit than losing all 6 bets together with the entire 50.00 € starting bank.

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

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

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

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

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

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

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

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

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

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

The result (harmonic mean) is the accurate average of the betting odds.

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

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

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

Table of Content:

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

PDF file for download:

Extent: 7 pages
Size: 122.6 KB

Think Before You Calculate

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

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

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

Here are some of the most popular misconceptions…

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(1) Betting on low odds is not worth the effort because winnings are very little

This is absolute nonsense. Successful betting is not about the pay-out of a bet, but the main goal is to make a profit. Very often, especially in the small odds markets excellent value can be found.

In addition, low odds have the huge advantage that they stand for high probabilities and therefore losses are considerably fewer in number than with higher priced, lower probability events. Also, small odds experience shorter losing streaks and the patience of the gambler is never stretched too far.

However, what really matters is the price of the bet.

If, for example, the calculations for a match throw up an 85% chance that there will be under 3.5 goals (corresponding betting odds: 1.18), and the market is offering odds of 1.25 then this is a fantastically good value back bet opportunity.

(2) Betting on higher odds is more profitable

Again this is a very common misconception. Higher odds do not automatically hold more value and are therefore more profitable than lower odds.

Many punters believe that better returns can be achieved in the long run if playing at odds between 2.5 to 3.0. Of course, it is understandable that these bets are quite popular as the potential winnings are 1.5 to 2.0 times the stake.

However, what most gamblers do not consider (or perhaps simply do not know!) is that these betting odds represent chances of 33% to 40% of winning, meaning that on average six to seven out of 10 bets in this group will lose.

Since winning and losing bets are never evenly distributed it may well happen that, with a little luck, a few bets in a row may be won but, much more likely is that many, many consecutive bets will lose until the betting bank is depleted beyond recovery or is drained altogether.

To answer these questions we have sourced 50 intelligent value quotes, sayings and proverbs about the measurement of value and the value of money.

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The following value quotes and proverbs have been mainly sorted chronologically by birth year of the author to let you see how man’s perspective on value and the value of money has changed over the centuries, although it is noteworthy that many of the more ancient sayings remain valid today.

We have put together 50 of the best inspirational and motivational quotes, sayings and proverbs on the subject of valuing life and perhaps a few of them will make you think differently about the value of life itself.

Photo: Lobke Peers (Shutterstock)

The following motivational quotes about value in life are sorted mainly in chronological order by birth year of the author. This is a beautiful collection of thoughts by people from all walks of life who really understood the secret of a positive outlook on life itself or, who had their own personal recipe for success and measuring value.

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

Photo: Andrej Vodolazhskyi (Shutterstock)

The term value has no place in this relationship. The literal meaning of ‘value’ is benefit, merit, worth and price. Unfortunately, the latter meaning is probably the main reason why people find the expression ‘value’ rather confusing. Betting odds offered by bookmakers or exchanges are probabilities converted into the price of a bet. However, if the ‘value’ of a bet is discussed, this refers not to the actual price (odds) of the bet but to the merit or benefit of a particular price.

Strictly speaking, it would be more correct, instead of using the term ‘value’ to say “mathematical advantage” or “expected merit“, but these phrases are uncommon.

Probability & Expectation

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

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

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

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

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

The expectation, probability, likelihood is calculated by building the mean (average) of historic match data, correcting the results by a few factors, and then taking some of the latest trends into consideration (if you would like to learn how to do this, have a glance at Soccerwidow’s Value Betting Course).

Reality Check: Hit Rate

Hit rate has no connection with the quality of predictions. High hit rates are often interpreted as a sign of a successful picking strategy. Unfortunately, this is a big and very common misconception! The only thing hit rate expresses is the number of winning bets compared with all bets. Hit rate is not a statement of any realised gains or losses.

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

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

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