Pricing of odds
In the previous section we looked at how successful betting is all about probabilities and value: how if we can predict, with reasonable accuracy, the likelihood of a an outcome, we can then decide if the odds available represent good value and either place or decline the bet. If we follow this approach consistently, even though we can expect losers as well as winners, the wins should more than make up for the losses in the long term.
This is all very well except:
- Predicting probabilities is not as easy as it might sound
- Bookmakers don't like giving money away easily
Fortunately, if we know what we are doing and we're disciplined, then it is possible to overcome these problems. That's what the following two sections are going to look at. But before that it is important to appreciate how bookmakers make their profits and how betting exchanges fit into the bigger picture.
The 'over–round'
Bookmakers don't always set odds based directly on their perceived probabilities of the different possible results in an event. There are a number of factors they take into account but mainly they are interested in running a balanced book, so that they can make a profit regardless of the outcome of the event.
So a bookmaker might, in considering Manchester United at home to a lesser club, estimate the chances of the home win at 80%, the draw at 15% and the away win at just 5%. If they were to apply the fair value calculations we covered earlier, the odds would be:
Table 1| Outcome | Probability | Decimal odds | Fractional odds* |
|---|---|---|---|
| Home win | 80% | 1.25 | 1/4 |
| Draw | 15% | 6.67 | 17/3 |
| Away win | 5% | 20 | 19/1 |
*You won't often see fractional odds of 17/3 or 19/1 as the bookies tend to round to more familiar numbers, perhaps 11/2 and 16/1 in this case). We realise that some of you may prefer fractional odds but from now on we're going purely decimal as the calculations are much simpler. Sorry!
Remember that to get from probability to decimal odds we just divide the probability in to 100% (e.g. 100/15 = 6.67). Now lets say that these odds were offered and the stake money came in from the punters as shown in Table 2:
Table 2
| Outcome | Odds | Money staked £ | Potential payout £ | If result P&L £ |
|---|---|---|---|---|
| Home win | 1.25 | 425,000 | 106,250 | –31,250 |
| Draw | 6.67 | 62,500 | 354,167 | 83,333 |
| Away win | 20.0 | 12,500 | 237,500 | 250,000 |
This shows for example that if the game was a draw, whilst the bookmaker would pay out more than £350k on that result, they would keep the stakes received on both the home win and the away win. So their net position would be £83,333 profit.
The problem for the bookmaker is that this book is far from balanced and they are highly exposed to the home win. If that is indeed the result they will make a loss due to the weight of stake money on that result. If the bookmaker can pre–empt this bias towards the favourite in this case Man Utd then they can take this into account when setting the odds:
Table 3
| Outcome | Odds | Money staked £ | Potential payout £ | If result P&L £ |
|---|---|---|---|---|
| Home win | 1.1765 | 425,000 | 75,000 | 0 |
| Draw | 8.0 | 62,500 | 437,500 | 0 |
| Away win | 20.0 | 12,500 | 487,500 | 0 |
We've assumed the new odds haven't impacted the monies staked and this now gives the bookmaker a perfectly balanced book with no exposure for them to lose money. The problem now is that they don't make a profit either, regardless of the outcome. So, what might actually happen is something like this:
Table 4
| Outcome | Odds | Money staked £ | Potential payout £ | If result P&L £ |
|---|---|---|---|---|
| Home win | 1.15 | 425,000 | 63,750 | 11,250 |
| Draw | 5.0 | 62,500 | 250,000 | 187,500 |
| Away win | 17.0 | 12,500 | 200,000 | 287,500 |
The bookie has trimmed back the odds to provide a profit margin whatever the outcome! Not only will they trim from the weight–of–money adjusted odds in Table 3, but they will rarely allow them to be better than those based on their probability calculations used in Table 2 for fear that 'experts' like us will spot the value and move in heavily, thus unbalancing the book again.
Table 4 illustrates the bookmaker's 'over–round' or margin, which is calculated by dividing each of the decimal odds into one (the reverse of converting probabilities to odds) and then summing up the results to give us a percentage.
Table 5
| Odds | 1 ÷ odds |
|---|---|
| 1.15 | 86.96% |
| 5.0 | 20.00% |
| 17.0 | 5.88% |
| Total | 112.84 |
This gives up an over–round of 12.84% and this is fairly typical for match odds offered by bookmakers, though the range can be from about 8% or 9% up to as much as 16%. Betting exchanges tend to exhibit much lower over–rounds in popular markets, especially as the time to the event gets close, but it is worth remembering that the exchanges typically deduct a commission from your winnings. We look at this in detail later on.
Another way to think of the over–round is as the amount we would need to stake, in the right proportions, in order to be guaranteed a return of £100 not that betting like this would make any sense! Taking 112.84% as £112.84:
Table 6
| Outcome | Odds | Money staked £ | Potential profit £ | If result, overall P&L £ |
|---|---|---|---|---|
| Home win | 1.15 | 86.96 | 13.04 | 13.04 – 20 – 5.88 = –12.84 |
| Draw | 5.0 | 20.00 | 80.00 | 80 – 86.96 – 5.88 = –12.84 |
| Away win | 17.0 | 5.88 | 94.08 | 94.08 – 86.96 – 20 = –12.88 |
| Total | 112.84 |
Ok we've a small rounding error on the last line but basically £112.84 staked in the right proportions will lose us £12.84 whatever the outcome. Incidentally, the stakes were worked out by simply inverting the odds, e.g. 100/1.15 = 86.96.
A word on the street
In practice, most internet bookmakers will adjust the odds offered as the stakes come in just like the track–side bookies do – allowing them to keep a fairly balanced book without having to worry as much about how much money they are likely to take on each possible outcome. This is still fixed odds betting – in that you get the odds at the time you place the bet – its just that the odds aren't fixed at the same prices right up to the time of the event.
The exception to this remains the high street betting shops, especially in the case of football betting, where the punters like to pick up pre–printed coupons and the bookie can't afford to keep binning and re–printing coupons, so it is important that their judgement is right early on. Indeed the same bookmaker can quote different prices online to those quoted in–shop.
The next section looks at a number of tips we can use to improve the odds available to us and therefore reduce the overall effect of over–rounds and improve the likelihood of finding value betting opportunities.
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