Value Betting: Gaining an Edge over the Bookie

[Cerebro]

Value Betting: Gaining an Edge over the Bookie If the bookmaker's odds are unfair, how can a punter ever win? Given the disadvantage the overround imposes, it is no surprise that as many as 95% of gamblers fail to win at fixed odds sports betting over the long term. There is no denying that most bookmakers, particularly the well-established firms, are very good at setting prices, estimating the true chance of sporting results and locking in a profit margin. <?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" />

Nevertheless, sports are not statistically quantifiable, in the sense that cards or other forms of casino gambling are, where simple laws of probability govern the outcome of games like blackjack, roulette and craps. I know that I have a 1/37 chance of landing a number 36 on a European roulette wheel (1/38 chance on an American wheel). But how can I know what the true probability is of Ronnie O'Sullivan winning the world snooker championship again? And if I think I know what his chances are, how can I be sure that my estimate is more accurate than the bookmaker's?

Unfortunately, the answers to these questions only come with time and experience, by acquiring a "knowledge" of a sport and its betting market, and a familiarity with the way bookmakers set their odds. The good news, however, is that whilst bookmakers are very good at setting odds for sporting events, they, like punters, can make mistakes, sometimes very glaring ones, which knowledgeable bettors will snap up without a moment's hesitation. William Hill, for example, astonishingly offered 200/1 on Primoz Peterka, the back-in-form Slovenian ski jumper, to win the opening ski jumping World Cup competition of the 2002/03 season at <?xml:namespace prefix = st1 ns = "urn:schemas-microsoft-com:office:smarttags" />Kuusamo, Finland, despite the fact that he had won the qualifying competition the night before, and had been double world champion in previous seasons. The true odds, by contrast, were likely to be nearer to 10/1, and most other bookmakers had priced accordingly. Peterka won, and William Hill ceased offering odds for the ski jumping World Cup thereafter. Of course, such large mistakes are relatively rare, but smaller pricing errors do and must exist to account for the few per cent of gamblers who are profiting regularly from fixed odds sports betting.

Punters differ in the methods they use to acquire a sports betting "knowledge". Some like to adopt a more mathematical approach by using rating systems based on past performance to predict future outcomes. Others spend hours each week poring over sports journals and Internet sites to glean as much information as they can about a particular event, including news about the weather, and team or player injuries and morale. Still others base their judgement on a subjective feel for the forthcoming event, relying on an inkling or a hunch about what may happen. And finally there are punters who simply pay others to do the thinking for them, by subscribing to one or more sports advisory services.

There is no right or wrong approach to seeking a betting edge. Ultimately, the best one is the one that works for you, one that returns a profit. However, what each approach has in common is a shared aim of finding "value" in the odds, where the true chance of a win is greater than that estimated by the bookmaker. Many punters fail to appreciate the importance of value betting, preferring to subscribe to the "back winners, not losers" school of gambling. Betting on Liverpool at Anfield to beat Sunderland at 4/11, it might be argued, is surely preferable to betting on Sunderland to beat Liverpool at 13/2, even if the bookie has restricted Liverpool's odds but been generous with Sunderland's. Liverpool, simply, are too good, however poor the price.

This analysis is confused because the punter has failed to assess Liverpool's chance of a win in probabilistic terms, but instead rather simply by whether he thinks they will or won't be victorious. "Winners" cannot win all the time, no matter how much a punter is convinced that they can. The important question a punter should instead be asking is whether the true chance of a winner is greater than that which the bookmaker has unfairly (in his mind), but potentially mistakenly (in the punter's mind), estimated it to be. In other words, is the bookmaker's price greater than that which the punter considers to be the fair price? If it is, then he has found betting value, provided he can estimate prices better than the bookmaker, of course.

A value bettor will be generally unconcerned about backing the underdog, or perhaps more relevantly backing a team which he thinks will not win (underdog or not), provided there is value in the bookmaker's odds. A value bettor estimating the likelihood for the Liverpool win to be 70%, with a 15% chance of a Sunderland win would back the away team, despite believing that Liverpool should win. According to these estimations, the fair odds for the two teams are 1.43 and 6.67 respectively. If the punter is right, and the game could be played 100 times, a 13/2 bet on Sunderland each time would, on average, return £12.50 profit from 100 £1 stakes. By contrast, backing Liverpool at 4/11 would, on average, lose him £4.55. He might believe that Liverpool should win each time, but in this case so does the bookmaker, who has cut his odds. Equally, however, the bookmaker has underestimated the chance of a Sunderland win, offering odds that the value bettor considers, in this case, to represent value.

Since odds are just probabilities, value betting offers really the only way to beat the bookmaker. A punter can back as many "winners" as he likes, but if he fails to take into account the bookmaker's prices, it may not be enough to return a profit. There will always be some losers. Really, the argument about value betting is a hypothetical one. The "back winners, not losers" philosophy is itself inherently all about finding a betting edge. If a punter is finding winners and making a profit with them, it means simply that he is winning more bets than the bookmaker believes the punter ought to be winning, according to the odds the bookmaker had set. If this is the case, the punter has found value and established a betting edge, whether he quantitatively set out to do so or just followed his hunches. Successful betting, then, is really all about understanding and managing probabilities. Know the true chances of a sporting win, and there may be profitable opportunities waiting at the bookmakers. As Geoff Harvey says in his book Successful Football Betting, "Find the value, [and] the winners will take care of themselves."

Betting Risks Every time a punter places a bet, he stakes a small proportion of his bankroll, the size of which may or may not vary, according to the punter's preferences and judgements about staking. Obviously, the smaller the stake as a proportion of the total bankroll, the less significant the impact after either a win or a loss. In terms of risk management, smaller stakes involve less risk of losing the bankroll entirely. For a punter with an edge over the bookmaker, the chances of ever losing it entirely are diminished. For a punter without one, that misfortune will unfortunately be unavoidable, but it will not come around as quickly. In terms of growing the bankroll, smaller stakes will naturally contribute smaller profits, and growth, if a betting edge is accessible, will take longer. Put frankly, the larger the size of the betting stakes as a proportion of the bankroll, the greater the chance of "bankruptcy" if things go wrong. Five consecutive losing bets at £20 each, for example, would eradicate a bank of £100. If the stakes had instead been £5, the punter could have afforded another 15 losses before bankruptcy. To most punters, this will seem intuitively obvious, yet it is surprising how many still insist on using stake sizes that a proper risk assessment would consider to be entirely unacceptable. Despite the greater overrounds, many punters like to increase the number of selections to a wager, attracted by the higher returns. The chances of winning a double, treble or accumulator bet, however, will always be less than for the individual selections which make them. It is not initially apparent, therefore, whether the longer-term return will be superior to singles, and perhaps more importantly, how the longer-term risks will compare. Much will depend upon the edge that a punter can on average achieve for his selections and the preferred size of his stakes. Where the punter fails to gain an edge, both singles and doubles lose money, but the doubles will always lose more, since their disadvantage is the square of that for the two singles considered separately. Conversely, the performance of a punter with an edge over the bookmaker will be superior for doubles than for singles. For singles, profit is proportional to the margin of success, and increases linearly as the prediction rate improves. For doubles, however, profit is proportional to the square of prediction success, and consequently increases faster for the same improvement in prediction rate. Where a punter has considerable confidence that he has achieved an edge over the bookmaker's odds, doubles are theoretically preferable to singles. By the same token, trebles will perform better still, with profit proportional to the cube of prediction success. As a general rule, the size of expected betting return will be proportional to the nth power of the betting edge, where n is the number of selections in an accumulator, assuming that each selection has the same edge. A punter should be cautious, however, before imagining that there are limitless profits to be won simply by enlarging the accumulator. Firstly, one must ensure that an edge has been secured for every part of the accumulator bet. Where this is not the case, the increased overround will begin to quickly conspire against the punter, eating into the expected return. Secondly, and more significantly, however, at greater odds, each bet is more likely to lose, regardless of the greater available returns. To be able to benefit from these superior returns, a punter must stake the same for his double, treble, or accumulator as he would for a single. The same is true for higher-priced singles - a multiple bet is really just like a single wager at longer odds, although the overround will be larger. The downside to this strategy will be a considerable increase in bankruptcy risk because of the larger and more frequent losing runs. Clearly, one way to limit risk exposure is to reduce the size of the stakes on multiple bets, or for that matter, on higher priced singles. Unfortunately, this also reduces the potential to gain at the same time. There always exists a trade-off between the impulse to achieve higher profits and the necessity to control risk. Herein lies the essence of gambling. Risk takers will win more in the short term, but must accept the greater prospect of severe misfortune. Risk avoiders must embrace a slower rate of return, but can potentially look forward to a longer betting "career". Whilst there is really no right or wrong way to bet, it may be argued that proactive risk management offers greater long-term security for a fixed odds sports bettor.

The Overround The fair odds for selecting any particular card from a standard deck of 52 are 51/1, with a probability of 0.0192 or 1.92%. As one might expect, the sum of probabilities for all cards will be 52 x 0.0192, which equals 1 or 100%. To gain an edge over the punter, a bookmaker will reduce those odds, for example to 48/1. These odds are then "unfair", since their associated probability is now higher, at 0.0204 or 2.04%, than the true chance of picking any particular card. The sum of the probabilities for all cards is now 52 x 0.0204, that is 1.061 or 106.1%. Mathematically, of course, the sum of probabilities for all possibilities must be 1.00 or 100%. The difference between this and the bookmaker's sum of probabilities represents the bookmaker's profit margin. A book with a total percentage over 100 is said to be overround. In the case just mentioned, the book is overround by 6.1%. This may be expressed by saying that the overround is 106.1%, or 1.061 as a decimal. That is, for every 100 units paid out to punters, the bookmaker can expect to take 106.1, or a profit of 6.1% on turnover. If a bookmaker offered 9/2 for numbers 1 through to 6 from a throw of a standard 6-sided dice, the overround would be 109.1% (1.091). Since the true probabilities associated with card drawing or dice rolling are mathematically fixed, a punter would be very unwise to bet at the unfair odds offered by a bookmaker. Initially he may be lucky, but over the long term he would find himself at a loss, the magnitude determined by the size of the overround. In view of this, it is remarkable how many gamblers are still happy to place bets on such games at a casino. When an edge is achievable, for example through card counting, the casino's regulations will usually prevent such a professional from benefiting from his knowledge. In sports betting, however, the fair odds of a particular event occurring cannot be known exactly, and this is perhaps why so many punters, with a belief that they know more than the bookmakers, are prepared to accept the disadvantage that they face through the overround. For his chosen bets, the punter will hope that the bookmaker has made a mistake in the estimation of the fair odds, allowing him to overcome this disadvantage.

With fixed odds for 3 possible outcomes in a football match bet - the home win, draw, and away win - a typical overround is about 111 to 112%, although some Internet bookmakers may go as high as 118% for the less popular European football leagues. Calculating the overround for any book is a simple task of summing the inverse of the home, draw and away odds and multiplying by 100%. Here, the inverse of the decimal odds for one result, of course, is the bookmaker's (unfair) estimation of the probability of that result occurring. Of course, whether the bookmaker's idea is accurate about what exactly the true chance of a particular result occurring is, is open to debate. If his customer disagrees, there may be an opportunity for him to make a profit, provided he is more accurate in estimating the true chance of an outcome than the bookmaker.

Other types of bets attract different overrounds, and it is usually the case that the greater the number of possible outcomes to a sporting event or one of its elements, the greater the bookmaker's overround. The correct score bet in football can have as many as 24 possible options on which to bet. A typical overround for this type of bet may be anything from 130 to 160%, depending on the bookmaker. In contrast to correct score betting, total goals betting in football, where there are usually only 2 possible outcomes (over 2.5 goals or under 2.5 goals), attract overrounds that are commonly less than 110%.

Punters with a keen interest in keeping the bookmaker's disadvantage to a minimum may very well be attracted to other 2-way betting opportunities. Asian handicap betting, where the draw is eliminated, generally has a low overround, sometimes as little as 106%. In addition to total goals betting and Asian handicap in football, match bets in tennis, snooker, darts, and in fact any two-player sport where there is no possibility of the draw offer excellent betting opportunities. Standard handicap and total points betting in American sports like basketball, ice hockey and American Football have some of the smallest overrounds available, sometimes even as low as 103 or 104%.

From 1X2Betting.co.uk and Fixed Odds Sports Betting: Statistical Forecasting and Risk Management by Joseph Buchdahl, published By High Stakes Ltd., London.

[Gingertipster]

Re: Value Betting: Gaining an Edge over the Bookie Excellant work Cerebro, value is indeed the only thing that matters. The table of odds and chances is the least talked about subject in betting. Never explained or publicsed in the British betting media. Why they are putting away punters by not doing so is beyond me. A punter who knows the table stands a far better chance of making a profit than one that does not. I do wonder whether you have over complicated things in the thread though. Maybe many PL members have been turned off by that, still in my opinion it's brilliant stuff.