# BAGS Dog racing forecast betting Calculator

1. In the course of the Commission’s inquiry into the Mecca/William Hill merger, complaints were received by the Commission that the Big 4 bookmakers had from time to time used their influence as members of the Betting Office Licensees’ Association (BOLA) to reduce returns to punters from BAGS computer forecasts by agreeing to changes in the formula used to calculate these returns. Grand Met told us that the formula in use was chosen by an industry technical committee. Recommendations by this committee are considered for implementation within the industry by a Joint Computer Committee consisting of representatives of the National Association of Bookmakers, the National Sporting League, and BOLA. The last elected Chairman of the Computer Committee was a representative of the National Association of Bookmakers.

2. Grand Met argued that it was necessary to have a common formula for simplicity of publication by the news services (SIS, Sporting Life, National Press, etc), for verification and to avoid confusion. It would be impractical if each company produced its own forecast. However, each company was at liberty to amend the particular returns as it desired (by adding general or specific bonuses, etc).

3. Calculation of the BAGS computer forecast is currently done on a race-by-race basis by SIS according to the Joint Computer Committee’s formula. The most recent formula was introduced in February 1986, when, according to BOLA, bookmakers believed that the formula needed changing to reflect more accurately the chances of particular forecasts occurring. The previous formula had been in operation since February 1983. Details of both formulas are given below, together with a worked example for the most recent formula.

4. When changes in the formula were introduced in February 1986, some forecasts were reduced, others increased, compared with calculation under the previous formula. Although one might compare bookmakers’ average gross profit on BAGS forecast betting during periods before and after the change in formula, such a comparison would not provide a measurement of long-run profitability for either formula, since the pattern of race results, race margins, and punters’ selections and staking patterns would not necessarily be, even broadly, similar as between two periods.

5. If one attempted to compare potential profits from operation of the successive BAGS formulae on a theoretical basis, for example by assuming that the pattern of results, margins etc was similar between the two periods, this would leave out of account factors such as that staking decisions will, for some punters, be partly affected by winning returns from previous bets. A further problem is that bookmakers’ gross profits may vary from one period to another, although the same formula is used, and the question of what is a suitable `long run’ over which to measure results is an arguable one.

6. If one considers the question of potential profitability at the level of an individual race, assuming, for example, a very closely graded race with all six runners at SP odds of 4-1 and a race margin of 1.20, then, assuming equal liabilities on all 30 forecast combinations, it can be calculated that the bookmaker’s gross profit from taking one bet on each of the 30 combinations at £1 each would be £5.72 after deducting £2.40 `tax’ (8 per cent of £30), and paying the winning punter £21.88. This would produce a gross profit margin for the bookmaker of 19.1 per cent.

7. In practice, however, punters rarely bet, in aggregate, in proportion to theoretical chances of each runner finishing first or second in a race, and in the case of races where the pattern of odds is uneven, eg the case used in the formula example below, with SP odds of 9-4, 3-1, 3-1, 4-1, 4-1, 8-1, there is likely to be disproportionately more staked on more favoured contenders than on others, other things being equal. At the same time the effective margin for each runner, ie the difference between its `true’ probability of winning and the probability as implied by the SP, are likely to vary with favourites’ effective margins tending in the long run to be smaller than those of the less fancied in the betting. The latter phenomenon has been the subject of a number of studies in connection with horseracing betting (see, for example, the Royal Commission on Gambling 1979 report) and it is reasonable to assume that a similar pattern is to be found with greyhound betting.

8. In forecast betting there is the added complication of assessing the chances of being placed second in relation to SP. This involves a probability conditional on which dog wins the racefor example, Grand Met told us that a survey of BAGS results (April to September 1985) found that when a dog 10-1 or over won the race, dogs priced odds-on to 15-8 finished second 55 per cent less than their SP would indicate but dogs priced 10-1 or over followed in 44 per cent more than expected.

9. Besides variability of results and punters’ staking, variability can be expected over time in race margins, and track racing managers’ grading practice. Race margins tend to vary with the strength of the on-course betting market, and margins are generally greater in weak markets where on-course turnover is low. Grading, or the selection of which greyhounds to put into each race (excluding open and inter-track events), is the responsibility of the track racing manager, and will be partly affected by the extent to which the running of greyhounds at a given track does or does not tend to match their previous form. Greyhounds vary in their ability to avoid baulking and checking in running, and in choosing which greyhounds to feature in a given race racing managers will have regard to this as well as to their recent times, performance from different traps etc. The National Greyhound Racing Club told the Commission that it believed that the BAGS tracks tended to feature very tightly-graded sprint and middle distance-type races, with mostly poor to moderate standards of greyhound, resulting in all six runners having near to equal chances of winning.

10. In view of the difficulty in determining prospective profitability from particular versions of the BAGS forecast formula, the Commission were not able to show the precise effect on bookmakers’ gross profitability of BAGS forecast betting.

11. Calculations can be made for individual races, comparing the size of dividends produced by each formula, but comparison of sequences of dividends alone does not necessarily provide an answer to the extent to which one formula is more profitable than another for the reasons stated above.

12. For comparison purposes the two latest formulae are shown below.

13. The formula in use from February 1983 to January 1986 was as follows:

Previous BAGS forecast formula

(in use from February 1983 to January 1986)

Let x:1 be the SP of the Winner

Let y:1 be the SP of the Second

Let q be the Betting margin on the Race

Let n be the Number of Runners

Then,

Let X = x, Y = y, Q = q, if q = 1.2, or if q < 1.2

Let X = 1/(1/(1 + x) – d) – 1

Y = 1/(1/(1 + y) – d) – 1

Where d = (q – 1.2)/n

(NB: A check is incorporated to ensure that an SP is not increased to more than 100:1.)

Q = 1.2

if q>1.2

DEFINE F AS Q / (Max (1.2, (1.2 + q)/2) – Q/20)

MULTIPLIED BY (1 + X) (1 + Y) [Q – 1/(1 + X)]

Then the BAGS forecast return, expressed in £s to a £1.00 stake, is given by

0.91

1 + Q – (1/(1 + X)) – (1/(1 + Y))

F 400

14. The formula in use from February 1986 has been as follows:

BAGS forecast

Revised formula (February 1986)

Let x:1 be the SP of the Winner

Let y:1 be the SP of the Second

Let q be the Betting margin on the Race

Let n be the Number of Runners

Define F as (1 + x)(1 + y)(q – 1 ) and M as MAX (1.17 + 0.04, 1.04)

1 + x q

1 + (n – 1)(1 + x)

Then let F1 = 500

1 + 1

F 500

1 + (n – 2)(n – 1)

and F2 = 1200 Multiplied by (1/M)

1 + q – (1/(1 + x)) – (1/(1 + y))

F1 1200

Then the BAGS forecast return, expressed in £s to a £1 stake, is given by

0.91 F2

An example of calculation of the current BAGS formula is as follows:

Monmore 4.48 pm race 1 July 1989

Trap 1 Won SP 8-1 0.1111

Trap 6 2nd SP 3-1 0.2500

Trap 5 3rd SP 3-1 0.2500

Trap 2 4th SP 9-4 0.3077

Trap 3 5th SP 4-1 0.2000

Trap 4 6th SP 4-1 0.2000

Race betting margin q = 1.3188

Number of runners n = 6

F = (1 + 8) (1 + 3) (1.3188 – 1 ) = 43.4769

1 + 8

M is the maximum of

(1.17 + 0.04) and 1.04,

1.3188

giving M = 1.04.

1 + (6 – 1)(1 + 8)

F1 = 500 = 43.5988

1 + 1

43.4769 500

1 + (6 – 2)(6 – 1)

F2 = 1200 Multiplied by (1/1.04)

1 + 1.3188 – 1 – 1

43.5988 1 + 8 1 + 3

1200

= 41.1875

Deduction of 9 per cent `tax’ is then made by multiplying the result of F2 by 0.91

= 37.4806

rounded to £37.48

BAGS computer forecast return for £1 stake.

It should be noted that elements printed in bold in the example above vary for each calculation depending on parameters for a given race.

15. Table 1 illustrates how returns to a £1 stake would have differed between the two latest BAGS formulae at three levels of race margin, 1.1, 1.2 and 1.3, over selected win/place SP odds combinations. For lower price winner combinations, forecasts at the margin points shown were virtually all reduced by the latest formula change. However, for higher price winners, such as the 16 to 1 ranges shown, forecasts were improved at the margin points 1.1 and 1.2 while they were reduced for all examples with winners at 4-1 or more where the margin was 1.3.

TABLE 1 BAGS forecasts to £1 stake

Race margin 1.10 Race margin 1.20 Race margin 1.30

SP SP Previous Current Previous Current Previous Current

winner second formula* formula** formula* formula** formula* formula**

£ £ £ £ £ £

4/6 2/1 2.18 2.12 2.87 2.70 3.06 3.14

4/6 4/1 3.63 3.52 4.76 4.47 5.26 5.20

4/6 8/1 6.51 6.28 8.52 7.97 10.12 9.25

4/6 16/1 12.20 11.68 15.90 14.76 22.20 17.08

2/1 4/6 3.35 3.28 4.14 3.93 4.37 4.38

2/1 2/1 5.99 5.86 7.39 7.01 7.98 7.80

2/1 4/1 9.90 9.65 12.17 11.53 13.60 12.79

2/1 8/1 17.53 16.97 21.42 20.19 25.60 22.32

2/1 16/1 32.05 40.64 38.70 36.19 53.25 39.73

4/1 4/6 6.52 6.49 7.91 7.63 8.63 8.38

4/1 2/1 11.59 11.50 14.00 13.49 15.59 14.76

4/1 4/1 18.95 18.71 22.75 21.88 26.10 23.86

4/1 8/1 32.88 32.15 39.00 37.36 47.41 40.49

4/1 16/1 57.93 55.68 67.26 64.03 91.23 68.65

8/1 4/6 12.79 13.10 15.32 15.23 17.94 16.54

8/1 2/1 22.40 22.82 26.61 26.42 31.60 28.58

8/1 4/1 35.88 36.28 42.11 41.77 51.02 44.91

8/1 8/1 59.91 59.79 68.86 68.16 86.43 72.56

8/1 16/1 98.86 96.65 109.94 108.49 146.07 113.75

16/1 4/6 25.01 27.00 29.61 31.11 40.45 33.51

16/1 2/1 42.58 45.57 49.61 52.12 67.22 55.71

16/1 4/1 65.63 69.46 74.92 78.69 100.49 83.31

16/1 8/1 102.72 106.79 113.52 119.20 149.95 124.38

16/1 16/1 153.84 156.15 162.90 170.98 211.07 175.20

Source: MMC using BAGS formulae.

*In operation from February 1983 to January 1986.

**In operation from February 1986.

16. A further point of concern on BAGS forecast betting, which was put to the Commission, concerned the calculation of multiple forecast betting, eg forecast doubles and trebles. Because the BAGS formula is used to calculate each leg of these multiple bets, a notional tax element is applied at each leg. As far as liabilities for the tax are concerned, these could be met by applying the tax deduction to the final leg only, with adjustments to BAGS forecasts for earlier legs. In some cases bookmakers have introduced `bonuses’ on winning forecast multiple bets, but these are effectively offered as a concession. Where these concessions are not offered, the NGRC claimed that the punter received extremely poor value for money with BAGS forecast multiple bets.

Source: MMC study, based on information from BOLA, Grand Met, NGRC and the Punters’ Association.