Book Percentage
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- BTB System e-book - March 13, 2015
What Is “Book Percentage”?
The probability of an event happening can be expressed as a percentage, for example if you toss a coin the probability of heads or tails is 50% or evens for each. The book percentage here is 100% – it is a perfect book. In reality the correct odds of all the possibilities add up to make a 100% book (identifying the correct odds for each possibility is the tricky bit)…
When a bookmaker prices up an event, he factors his profit into the odds, and this is called the “overround”. If you calculate the book percentage on a bookmaker’s odds it will normally be over 100%. For an average race it is usually between about 110% and 125% depending on the number of runners – it will be lower for fewer runners or where there are only a couple of very fancied horses against longshots. For 2-way markets like tennis or football over/under a typical bookie might have 1.83 on each of the 2 outcomes, which is about 109.3%. This percentage varies a bit depending on the bookie.
How To Calculate Book Percentage.
Mathematically the book percentage equals the sum of the reciprocal decimal odds. This means that you have to take each horse’s decimal odds and divide 1 by it, then add all those numbers together. There is no quick shortcut – adding them all together and then dividing 1 by the result is not the same thing at all.
Taking a typical competitive race (real example at Paddy Power), to calculate the book percentage divide 1 by each of the decimal odds and add them all together:
1/6.5 + 1/7 + 1/7 + 1/8 + 1/9 + 1/9 + 1/11 + 1/11 + 1/13 + 1/17 + 1/19 + 1/19 + 1/26 for this 13 runner race.
Adding these together gives 1.248 which we then need to multiply by 100 for the percentage, so this is in fact a 124.8% book, typical of an evening all weather event and very stingy on Paddy’s behalf. Paddy’s takeout on this race, whatever wins should be 24.8% if they have balanced their bets correctly.
The back odds for the same race at Betfair were 6.4, 7.4, 8.8, 10.5, 12.5, 13, 13, 13.5, 20, 22, 22, 29 and 30.
This is a 101.4% book (Betfair do this calculation for you), which is much nearer 100% than 124.8%. In general the book % at Betfair will be slightly more than 100% on the back side and slightly less than 100% on the lay side, meaning that you can neither back all or lay all outcomes for a profit.
Being able to calculate book percentage at the bookie is useful – if you find a book which is under about 110% – 120% (depending on race type) which contains a non runner, it is extremely unlikely that the odds have been adjusted. You can therefore do a quick check if you find an arb in a race with a non runner, although this is not infallible by any means.
You will eventually learn how to recognize a dodgy looking book, but until then, here is a table of all the common odds and their inverses, so all you have to do is to add them together.
Table of Odds Percentages
| Odds Against | Odds On | Odds Against | Odds On | ||||
| Odds | 1/odds x 100 | Odds | 1/odds x 100 | Odds | 1/odds x 100 | Odds | 1/odds x 100 |
| evens (2.0) | 50 | 2.0 | 50 | 6/1 (7.0) | 14.3 | 1.167 | 85.7 |
| 21/20 (2.05) | 48.8 | 1.952 | 51.2 | 13/2 (7.5) | 13.3 | 1.154 | 86.7 |
| 11/10 (2.1) | 47.6 | 1.909 | 52.4 | 7/1 (8.0) | 12.5 | 1.143 | 87.5 |
| 6/5 (2.2) | 45.45 | 1.833 | 53.1 | 15/2 (8.5) | 11.8 | 1.133 | 88.3 |
| 5/4 (2.25) | 44.4 | 1.8 | 55.56 | 8/1 (9.0) | 11.1 | 1.125 | 88.9 |
| 11/8 (2.375) | 42.1 | 1.727 | 57.9 | 17/2 (9.5) | 10.5 | 1.118 | 89.4 |
| 6/4 (2.5) | 40 | 1.667 | 60 | 9/1 (10.0) | 10 | 1.111 | 90 |
| 13/8 (2.625) | 38.1 | 1.615 | 61.9 | 10/1 (11.0) | 9 | 1.1 | 90.9 |
| 7/4 (2.75) | 36.4 | 1.571 | 63.65 | 11/1 (12.0) | 8.3 | 1.091 | 91.7 |
| 15/8 (2.875) | 34.8 | 1.533 | 65.2 | 12/1 (13.0) | 7.7 | 1.083 | 92.3 |
| 2/1 (3.0) | 33.3 | 1.5 | 66.7 | 14/1 (15.0) | 6.7 | 1.071 | 93.4 |
| 85/40 (3.125) | 32 | 1.471 | 68 | 16/1 (17.0) | 5.9 | 1.063 | 94.1 |
| 9/4 (3.25) | 30.8 | 1.444 | 69.25 | 18/1 (19.0) | 5.3 | 1.056 | 94.7 |
| 5/2 (3.5) | 28.6 | 1.4 | 71.4 | 20/1 (21.0) | 4.8 | 1.05 | 95.2 |
| 11/4 (3.75) | 26.7 | 1.364 | 73.3 | 22/1 (23.0) | 4.3 | 1.045 | 95.7 |
| 3/1 (4.0) | 25 | 1.333 | 75 | 25/1 (26.0) | 3.8 | 1.04 | 96.2 |
| 10/3 (4.333) | 23.1 | 1.3 | 76.9 | 33/1 (34.0) | 2.9 | 1.03 | 97.1 |
| 7/2 (4.5) | 22.2 | 1.286 | 77.8 | 50/1 (51.0) | 1.9 | 1.02 | 98 |
| 4/1 (5.0) | 20 | 1.25 | 80 | 66/1 (67.0) | 1.5 | 1.015 | 98.5 |
| 9/2 (5.5) | 18.2 | 1.222 | 81.8 | 80/1 (81.0) | 1.2 | 1.013 | 98.7 |
| 5/1 (6.0) | 16.7 | 1.2 | 83.3 | 100/1 (101) | 1 | 1.01 | 99 |
| 11/2 (6.5) | 15.4 | 1.182 | 84.6 |
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