# Value Betting

Betting value, in a nutshell, is found where **the “true” chance of a win is greater than that estimated by the bookmaker as expressed by his odds**. In other words, if a bookmaker’s price is greater than that which a punter considers to be fair, then this would constitute a value price. As we know, sports are not like cards, and there is really no such thing as a ‘true chance’ in sports (hence the word is shown in quotes). The best that punters, tipsters and indeed bookmakers can do is estimate what they think the chance of a win for one side or another will be. There are all sorts of ways of doing this but most of them will involve looking at what is called the ‘form’ of a competitor, that is how it has performed recently, either in general or specifically against the opposition it is now facing. This can be done quantitatively by analysing numerical data that describes the form, such as goals or shots in soccer, points in basketball, and runs and wickets in cricket, or qualitatively by studying injuries, motivational factors and even the weather from various news sources.

Of course, **on a bet by bet basis the concept of value is really rather meaningless**, since something will either happen or it won’t happen, and a bet will either win or lose (or tie if it’s a handicap bet). Over the long term, however, it is far from that. Teams and players, unsurprisingly, are not able to win every contest against their opponents, and for every match there will always be an element of doubt as to whether a prediction will prove correct. For every contest random factors will have a significant influence on the outcome, but **over many contests these tend to average out**, leaving behind the “true” superiority level one competitor had over the other. If we can predict that “true” superiority better than the bookmaker, we have found what is called betting value and have a chance of making a profit.

So what actually matters here is not whether we think some team or player will win, but whether we think they have a better chance of winning than the bookmaker does as reflected in his betting odds, and whether our probability estimation is better than his. **Punters brought up in the ‘pick-winners’ tradition frequently lose sight of the fact that the betting price does actually matter.** Their argument goes roughly along the lines of “if I can pick a winner, any price will do since the bet will win.” We should not be fooled by this attitude. Anyone can pick a winner now and again, but only a **few punters are good enough to pick more winners than the bookmaker believes he should be finding**. Why? Firstly, because bookmakers have had a lot of experience at predicting the outcome of sporting events; and secondly, and perhaps more importantly because their overround protects them against any misjudgements that they make.

In the last lesson we introduced the concept of profit expectancy – that is how much profit we should expect to make on average from a bet. Recall, profit expectancy is just the probability of an outcome multiplied by the potential profit for that outcome, summed for all possible outcomes. When our net profit expectancy for a bet is negative, we have been unable to find value in the betting odds. Where it is positive, we have it. Of course, since we can’t know what the true chances are of a sporting outcome before the outcome happens, similarly we can’t ever know for sure whether we have or have not found betting value in the odds. **Only by retrospectively analysing our history of betting can we begin to find the answer to this questio**n. That is something we’ll pick up on in a later lesson (analysing a betting record). Here, let’s assume that we do know when we are better at assessing the odds than the bookmaker, and see how that plays out for different types of betting.

Let’s return to our singles and doubles from the last lesson. Suppose this time, our bookmaker has made a mistake and the true chance of Liverpool beating Manchester United and Arsenal beating Tottenham is both 50%. With betting odds of 2.50, we therefore believe that both teams have a 10% better chance of winning their matches than the bookmaker believes they do. Our profit expectancy for either single will be 0.50 (the probability of winning) multiplied by £1.50 (the profit if we win from a £1 stake) which is £0.75. Of course the probability of losing our £1 stake is also 50%, and hence the profit expectancy for that outcome is -£0.50. The total profit expectancy for this single bet is therefore £0.25 for a £1 turnover, or 0.25 expressed as a decimal. We could save ourselves all the bother of calculating all of this simply by dividing the bookmaker’s odds (2.50) by the fair odds (2.00), arriving at an equivalent answer, 1.25, which is simply profit expectancy (0.25) plus the unit stake (1). Essentially, then, we have another relationship for the profit expectancy of a bet, expressed as a decimal:

#### Profit expectancy = (actual odds / fair odds) -1

where odds are expressed in European decimal format.

#### Edge or return expectancy = actual odds / fair odds

Edge or return expectancy is profit expectancy + 1

Remember, our return is just the profit plus the stake. **Return expectancy is really just mathematical expression for “edge”, which is a measure of how much betting value we have found in the odds.**

For the two singles, both bets have an edge of 1.25, that is to say, on average we would expect to see a return of £1.25 from a £1, or £2.50 from £1 staked on each. Naturally, in the real world we will either see £5 returned (from 2 winning singles), £1.50 returned from 1 winner and 1 loser, or £0 returned if both lose. But in our mathematical world, our average expectancy will be £1.25 for every £1 staked.

What about the Liverpool/Arsenal double? In the same way as the overround percentage will be compounded for larger multiple bets, so, too, will be a betting edge. If the betting edge for each independent single is 1.25, that for the double will be 1.5625 (1.25 x 1.25). Alternatively, the actual odd for the double are 6.25 (2.5 x 2.5) whilst the fair odds for the double are 4.00 (2.00 x 2.00). 6.25 divided by 4.00 is 1.5625. Our edge is considerably bigger betting the double compared to the singles. Of course, we are still less likely to win the double (a 25% chance as compared to 50% for the singles and a 75% chance of seeing at least some profit from the singles), but we have nonetheless gained an additional betting edge by taking on that additional risk. **Betting a double in this way to achieve greater profit expectancy doesn’t make us better match forecasters, it just means that we can expect to win more money per unit stake taking a greater risk.**

Similarly if we now add Newcastle to make a treble, our betting edge increases to 1.953125 (1.25 x 1.25 x 1.25), meaning that for every £1 we wager we should expect to almost double our money. For a 10-fold accumulator with individual actual odds of 2.50 and fair odds of 2.00, our edge would be an astronomical 9.31 (rounded to 2 decimal places). Of course, such a 10-fold could be expected to win only once in 1,024 repetitions, so we are taking a much bigger risk in order to gain a much bigger advantage.

It would be easy to assume from all of this that all we have to do is bet large multiples to make ourselves a fortune. This thinking is flawed on two counts. Firstly, as has been repeatedly stressed, **the greater the profit margin we are aiming for, the bigger the risk we have to take to get it, and the longer we may have to bet before we have the winner we are looking for.** Risk is not just some theoretical construct; it has real life implications. Imagine betting a series of 10-folds priced 9536/1 with an edge of 9.31. If we have to place hundreds of bets before we have a winner, we might run out of money before we get there. Or more likely, our confidence in what we are doing will run out sooner. Secondly, t**he more matches we include in our accumulator, the greater the likelihood is that one (or more) of them lack the individual betting edge that we think we have calculated.** This lesson has assumed that we know what the true odds for each team should be. Of course, in reality we cannot possibly know that before the event. And the more estimates we throw into the mix, the greater the possibility that things can start to go wrong. Suppose, for example, that we are correct for Liverpool but Arsenal really have true odds of 2.5 (and not 2.00) whilst Newcastle’s fair price is 3.00. The edge for the treble is then just 1.042. In this instance this is still bigger than the aggregated edge for the 3 individual singles – 1.028 – but the advantage is much reduced and certainly not worth the additional risk of betting the treble as opposed to the singles.

**How much reward someone wants and how much risk someone is prepared to accept to pursue it, is very subjective. Each person is different**. Some prefer betting just low risk singles, accepting the lower payoffs and betting edges in return for less stress and a small probability of things going badly wrong. Others like to live life more on the edge and are prepared to take more chances in the hope of the bigger profits.

To summarise then: when our profit expectancy is positive we have found and edge, where it is negative we have not. Without an edge we can only hope to make a profit in the short term through a little bit of luck. Over the long term good and bad luck will even up leaving just an empty bank balance. Value betting is the key to overcoming the bookmaker’s odds and securing a long-term profit. Value betting encourages the informed punter to view all odds as probabilities, and to search for opportunities where the bookmaker may have underestimated the chance of a sporting outcome.