Understanding the Overround

Understanding the Overround

In a five horse race, a bookmaker may choose to price up each horse at odds of 4/1 (5.0). In such a scenario, were he to take an equal amount of money on eachrunner, he would break even, as each horse would have a 20% chance of winning. In that the five runners have combined implied "probabilities" of winning of100%, we are dealing with a "round" book.

Horse Odds PercentA 5.0 20B 5.0 20C 5.0 20D 5.0 20E 5.0 20

over-round - 100

If however, he were to price up each runner at 3/1 (4.0), the implied probabilty of each runner winning will change to 25% from 20%. If he were again to takean equal amount on each runner, he would receive five units and pay out four. The profitable extra unit amounts to 25% and 25% x 5 = 125%. His book wouldbe 25% "over-round".

Horse Odds PercentA 4.0 25B 4.0 25C 4.0 25

Understanding the Overround (The Betting Market's Pricing Mechanism). file:///C:/Users/Sergey/Desktop/overround.htm

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D 4.0 25E 4.0 25

over-round - 125

The over-round (Vigorish, or simply "vig", or "juice") is what gives the bookmaker his profit, his sun tan and his cigars. If the over-round is 120% thebookmaker will expect to pay out 100 pounds for every 12o pounds he takes in, yielding him an expected profit of 20/120 = 16.7%.

Our first example below, focuses on the 2006 Coral Eclipse Stakes, a Group One race run at Sandown Park on July 8 2006. We compare the over-round onBetfair, the world's leading betting exchange with that available with two of the main traditional bookmakers, Ladbrokes and William Hill. It can be seen that inevery instance the price on offer on Betfair is better compared with the two traditional bookmakers. No surprise, therefore, to see that the over-round on Betfairis 107.6 (including 5% commission) compared with an over-round of 118.1 at Ladbrokes.

Particular attention should be paid to the three outsiders in the betting market, where it can be seen that the prices being offered up on the Betfair exchange aresignificantly better than those available with the traditional bookmakers. This reflects the fact that betting exchanges tend to provide the punter with a betterestimation as to the chance of longshots compared with traditional bookmakers. Evidence of this fact is also supplied in our other examples below on the 2007November Handicap and the 2007 Paddy Power Chase.

Coral Eclipse Stakes

Teams Betfair William Hill LadbrokesOuija Board 3.10 2.50 2.62David Junior 3.30 3.25 3.00Aussie Rules 7.20 6.50 6.00Notnowcato 11.5 10.0 11.0

Blue Monday 11.0 10.0 11.0Snoqualmie Bay 23.0 21.0 17.0Notable Guest 38.0 26.0 26.0

Hattan 100.0 67.0 67.0


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Royal Alchemist 300.0 251.0 201.0Over-Round 107.6 116.6 118.1

In the world of football betting over-rounds of anything between 101% and 125% may be still seen.

Our analysis of outright betting on the 2006 World Cup revealed that Betfair's book on the top twelve teams in the betting market was betting to an over-roundof 100.92 against an average over-round of 112 elsewhere.

World Cup 2006

Teams Svenskaspel William Hill Ladbrokes BetfairBrasil 3.50 3.25 3.50 3.85

England 9.0 7.0 8.0 8.6Germany 9.0 9.0 8.0 9.8Argentina 7.50 9.9 9.0 10.0

Italy 9.00 9.0 9.0 12.0France 13.0 15.0 13.0 14.5Holland 12.0 13.0 13.0 18.0Spain 15.0 15.0 15.0 18.5

Portugal 20.0 23.0 23.0 27.0Czechs 30.0 34.0 26.0 40.0Sweden 30.0 41.0 41.0 42.0Croatia 75.0 67.0 51.0 110.0Mexico 50.0 51.0 41.0 60.0

Over-Round 112.9 111.6 112.9 100.92


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Prices were downloaded from the respective websites at 23.00 on 05/06/06. The Betfair over-round includes the 5% top-rate commission charge. Were we tohave used Betfair's average commission charge of 3% the market would actually have been betting to 98.92.

Our analysis of the World Cup Final and the third place play off match between Germany and Portugal highlights the extent to which the leading bettingexchange Betsson offers the punter value compared with the prices on offer from the German monopolist betting provider Oddset. A common feature in recenttimes has seen the development of a trend in cross betting exchange arbitrage, as shrewd punters take a price on Betfair and seek to lay it off on the Betssonexchange.

Germany vs Portugal

Bookmakers * Germany Draw Portugal Over-Round(%)Oddset 1.65 2.90 3.75 120.4Betsson 1.82 3.65 5.00 102.4Betfair 1.86 3.70 5.10 100.4

Italy vs France

Bookmakers * Italy Draw France Over-Round(%)Oddset 2.30 2.60 2.60 121.8Betsson 2.66 2.90 3.45 101.1Betfair 2.68 2.90 3.50 100.4

Monopoly rights have led to the Scandinavian betting market becoming distorted, such that punters in the Scandic countries are being openly ripped off. Theworst culprit is the Swedish monopolist operator Svenska Spel, which consistently bets to an over-round of 125% on football matches.

Our first example, concerns the fixed odds betting being offered on the Germany vs Italy 2006 World Cup semi final match.


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The Swedish monoply provider Svenska Spel offered consumers the least value on the match, trading to an astonishing over-round of 125% (compared with anover-round of 104.4% on the Swedish leaning betting exchange Betsson. Foreign companies are prevented from competing in the Swedish betting market. InJune, for example, Sweden's Gaming board reported the editors of four Swedish newspapers and magazines (Expressen, Metro, Slitz and Spray) to the police forpublishing adverts from foreign gambling companies.

Germany vs Italy

Bookmakers * Germany Draw Italy Over-Round(%)Svenska Spel 2.15 2.25 2.95 124.9Norsk Tipping 2.25 2.65 2.85 117.8

Veikkaus 2.10 2.80 3.30 113.7

A further analysis of the fixed odds betting being offered on the Portugal vs France World Cup 2006 semi-final match, sadly, reveals a similar picture.

The table below, which highlights the prices available on the match at 11.00 CET on the 05 July 2006, reveals that once more the Swedish monoply providerSvenska Spel offers its consumers the least value on the match, trading to a typical over-round of 125% (against a best-price over-round on the bettingexchanges of 101.5%).

Portugal vs France

Bookmakers * Portugal Draw France Over-Round(%)Svenska Spel 3.45 2.25 1.95 124.7Norsk Tipping 3.25 2.70 2.00 117.6

Veikkaus 3.85 2.85 1.90 113.7


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The disgrace of the Irish Horseracing betting market

In the UK, the profit margin built into starting prices fell from 2.07 per cent per runner in September 2000 to 1.45 per cent per runner in September 2006. Tosome extent this can be attributed to Betfair, which curtailed the ability of the big bookmarkers' to manipulate starting prices, through blowing money back intothe on-course market. Then, there were the odds-checking sites such as Oddschecker, which placed the big bookmakers on the same footing as numerous smallentrants, and served to put pressure on industry margins by making prices more visible and encouraging a greater intensity of competition.

Despite the arrival of internet betting and the betting exchanges, the same situation has not been mirrored in Ireland, where the over-round per runner continuesto operate at well over two per cent.

In the 2:25 at Clonmel, run on 1 November, the Powerstown Desmene Handicap Hurdle, the over-round per runner was 3.38. The 18 runner race was run bythe VP Donoghue trained Jamie's Boy at 10/1. The favourite was Asian Royale trading at 7/1, with the outsider of the field, Deep Spell, trading at 33/1.

In the www.punchestown.com Handicap Hurdle (4yo+,81-116), run over 2m run at Punchestown on 31 October, the over-round per runner was 2.73. The 15runner race was won by the Willie Mullins trained Viso at 6/1, with the biggest price on offer being shared by three horses at 25/1.

In the 4:15 at Down Royal, run on 2 November, the Archie Watson Memorial INH Flat Race (4-7yo), over 2m, the over-round per runner was 3.0. The elevenrunner race was won by the Even money favourite Chateau D'eau. The outsider of the field Mr Forgetful, traded at 50/1, and finished a distance last.

In the 12:45 BetChronicle.com Fillies Maiden (2yo), run over 1m, at Leopardstown on 3 November, the over-round per runner was an astonishing 3.81! Thefield comprised of eleven runners. The race was won by the heavily backed favourite Simawa, returned at 11/10. The outsider of the field Zennu traded at 66/1.Six of the eleven runner field traded at 8/1 or less.

Whilst Irish bookmakers have managed to convey an image of being great risk takers, the truth is, that the huge over-rounds pertaining on almost every horserace run in Ireland, characterise them as being infinitely risk averse. They seemingly spend their entire time shielding against real or imagined insiders, who theybelieve to be better informed than they are.

The existence of such uncompetitive offerings, would, one would imagine, drive bettors towards the betting exchnages in their numbers, but strangely, this hasnot been the case to date. It would seem that the informed insiders are happy to play in betting markets exhibiting huge over-rounds, rather than reveal theirhands on the betting exchanges. Accordingly, it is the punters in the Irish betting shops who suffer; many of whom know no better than to bet at SP.


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An interesting aspect of the Irish betting market over the past eight years, has been the reluctance of bookmakers to embrace online betting; a fear of margindepletion being the most likely reason. Cashmans of Cork, one of the most high profile Irish bookmakers, shows no sign of making the leap online. Sean Grahamcame online and then went back off again. Eastwoods remain offline. Terry Rogers recently entered the fray, and Hacketts are coming back online, havingdipped their toes in the water some time ago. BetChronicle now also have an online presence. The betting exchanges Betdaq and Betfair both operate in theIrish betting market.

The extent to which Irish punters are being ripped off when it comes to betting on horse racing, has been one of the great untold stories of recent times. Untilnow, something akin to a conspiracy of silence has reigned. Everybody knows the shocking over-rounds in operation in the Irish betting market, but everybodyjust puts up with it for fear of rattling the boat. Even Betfair and Betdaq seem somewhat reluctant to capitalise upon the issue. And as for the irish journalists.....

In the tables below we look at four recent horse race meetings in Ireland. In the first table we look at the over-round per race. In Table two we break this downfurther and look at the key metric over-round per runner.

Table One:Over-round per race

Race Punchestown Clonmel DownRoyal LeopardstownFirst 119 139 139 149

Second 151 146 146 142Third 137 161 131 131Fourth 140 128 117 150Fifth 143 148 132 116Sixth 142 131 133 148Seven 136 151 133 163

Average 137.2 143.4 133 142.7

Prices were taken from the Punchestown meeting held on Wednesday 31 October 2007. Clonmel prices were from the meeting on 1 November 2007. Theprices for Down Royal were collected from the meeting there on 02 November 2007. The prices for Leopardstown were collected from the meeting there heldon 03 November 2007.


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Table Two - Over-round per runner

Race Punchestown Clonmel DownRoyal LeopardstownFirst 2.11 2.30 2.05 2.88

Second 2.31 2.70 2.30 3.21Third 2.31 3.38 2.82 2.21Fourth 2.73 2.33 2.42 2.38Fifth 2.38 2.66 2.66 2.28Sixth 1.95 2.58 2.75 2.18Seven 1.95 2.83 3.00 2.86

Average 2.24 2.68 2.57 2.66

Prices were taken from the Punchestown meeting held on Wednesday 31 October 2007. Clonmel prices were from the meeting on 1 November 2007. Theprices for Down Royal were collected from the meeting there on 02 November 2007. The prices for Leopardstown were collected from the meeting there heldon 03 November 2007.

The case of Betfair

In the table below we look at the November Handicap run at Doncaster on November 10 2007, and compare the official SP with the "Betfair SP". The horsesare listed in market order and not order of finish.

The first thing to note is that the SP over-round on Betfair, including commission, totalled 108.5 against an official SP over-round of 127.9.


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It is notable that not in one instance did the offical starting price returned on each runner, beat the "Betfair SP". On only one occasion, the case of LundysLane, did the official SP match the "Betfair SP".

The biggest discrepancy of all, can be seen with regard to the six outsiders in the field. Taking the six runners collectively, we get an average over-round perrunner on Betfair of 0.74, compared with an official over-round per runner of 1.48.

Table One:Betfair SP vs Official SP

# Horse Betfair SP Official SP1 Pippa Greene 5.7 5.52 Malt or Mash 6.6 6.03 Sanbuch 7.6 7.504 Heaven Knows 8.8 7.505 Tropical Strait 15.5 13.06 New Guinea 17.5 17.07 Heron Bay 21 15.08 Bandama 24 17.09 Dzesmin 25 17.010 Philantrophy 29 17.011 Akarem 34 21.012 Rampallion 34 26.013 Inchloch 36 26.014 John Terry 36 2315 Lundys Lane 34 3416 La Estrella 75 5117 Night Crescendo 95 5118 Chicken Soup 120 5119 Turn of Phrase 200 101


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20 Realism 220 10121 Bazart 410 10122 Over-round 108.5 127.9

In the table above we look at the November Handicap run at Doncaster on November 10 2007,The "Betfair SP" was the final price available to back fromwithin the last minute before the event closed. The Betfair over-round includes the average commission paid on Betfair of 3%.

Paddy Power Chase Cheltenham November 17

# Horse Betfair SP Official SP1 Granit Jack 4.2 4.02 Lantartique 8.4 7.503 Vodka Bleu 11.5 9.04 Copsale Lad 11.5 9.05 Knowhere 13.0 11.06 Private Be 15.0 13.07 Bob Hall 16.5 12.08 Crozan 16.5 13.09 Idole First 20 17.010 Ponmeoth 27 21.011 Three Mirrors 28 17.012 Palarshan 44 26.013 Il Duce 50 34.0


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14 Ballyagran 46 3415 Black Hills 60 3416 Patman Du Charmil 66 6717 Bambi de L'Orme 80 5118 Kings Brook 120 6719 Too Forward 150 6720 Billyvoddan 170 6722 Over-round 107.8 130.0

In the table above we look at the Paddy Power Gold Cup Chase run at Cheltenham on November 17 2007,The "Betfair SP" was the final price available to backfrom within the last minute before the event closed. The Betfair over-round includes the average commission paid on Betfair of 3%.

Odds and Probabilities

Amidst the hype currently surrounding the prediction market industry, some commentators have called for betting exchanges like Betfair and TradeSports totranslate their odds into probabilities. Behind this call, one suspects, lies the common error of misinterpreting bookmaker and betting exchange odds as winprobabilities.

In practice, bookmakers and betting exchange odds do not sum upto one. The sum of the odds is called the over-round and the sum exceeding one reflects thebookmaker's/market maker's margin.

Let us look at one of the markets most favoured by the prediction market advocates - The 2008 US Presidential Elction Democratic Candidate market. Betfair'smarket on this event is currently trading as follows;

Candidate CurrentOdds

HilaryClinton 1.55

Barack 2.86


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Obama

Al Gore 70.0

JohnEdwards 110.0

Others 1000

Over-Round 103.2

To go along with the odds into probabilities camp, we have in the table below translated the current odds straight into probabilities. Surprise, surprise, the oddsdo not sum upto one! This is because there is "excess probability" whenever a book is over-round.

Candidate Probabilities

HilaryClinton 0.6451

BarackObama 0.3496

Al Gore 0.0142

JohnEdwards 0.0090

Others 0.014

Total 1.0319

In order to obtain normalized fair probabilities, we must return to the over-round. We saw that the market on Betfair was trading to an over-round of 103.2. Thetask that we now face is how to allocate the excess probabilty across our range of prices so as to obtain normalized fair probabilities. To achieve this, we mustdivide each of the probabilities in the table above by 1.032 This leads us to obtain the following probabilities.


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Candidate Probabilities

HilaryClinton 0.6250

BarackObama 0.3387

Al Gore 0.0137

JohnEdwards 0.0087

Others 0.0135

Total 1.000

Of course, in the case of Trade Sports and Betfair, the situation is complicated further, by the fact that market commissions should actually be factored into theover-round. In the case of Betfair, commission rates vary from between 2% and 5%. Any attempt to translate odds into probabilities, would of course, have totake into account the commission rates faced by each individual trader. The small matter of the favourite longshot bias also raises problems when one isattempting to obtain normalized fair probabilities.

Calculating the Over-Round

Decimal odds are quoted as a positive number greater than 1. It represents the number of pounds returned if the bet wins, including the initial stake. Hence, aone pound bet at decimal odds of 2.0 would return two pounds to the bettor; the one pound initial stake plus one pound in winnings. Decimal odds of 6.0 implythat if a one pound bet were to win, six pounds would be returned to the bettor; the one pound initial stake, plus five pounds in winnings.

Fractional style odds, which are still the most common used by traditional bookmakers in the UK and Ireland, are quoted as a fraction, and again indicate theamount that would be paid out relative to a given stake. Fractional odds of 1/2 infer that a winning bet would pay out one pound for every two pound risked,whilst fractional odds of 3/1 imply that the bet would pay out three pounds for every one pound risked. Under fractional style odds, an even odds bet is quotedas 1/1.

To calculate the over-round we utilise the implied probabilities, expressed as percentages (%) in the table below. Let's take the example of Betfair's bettingmarket on the African Nation Cup match between Ivory Coast and Guinea, played on 3 February 2008.


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Ivory Coast vs Guinea

Outcomes DecimalOdds

FractionalOdds

ImpliedProbabaility

(%)

Ivory Coast 1.50 1/2 67%

Draw 3.75 11/4 27%

Guinea 10.0 9/1 10%

Over-Round 104 104 104

Odds as Fractions and Probabilities

Fractional Decimal % Fractional Decimal % Fractional Decimal %1/10 1.10 91 11/8 2.37 42 16/1 17.0 61/9 1.111 90 6/4 2.50 40 20/1 21.0 51/8 1.125 89 13/8 2.265 38 25/1 26.0 4 2/15 1.133 88 7/4 2.75 36 30/1 31.0 3 1/7 1.140 88 15/8 2.875 35 33/1 34.0 3 2/13 1.154 87 2/1 3.0 33 40/1 41.0 2 1/6 1.166 86 9/4 3.25 31 50/1 51.0 2 2/11 1.182 85 5/2 3.50 29 60/1 61.0 2 1/5 1.20 83 11/4 3.75 27 66/1 67.0 2 2/9 1.222 82 3/1 4.0 25 80/1 81.0 1 1/4 1.25 80 13/4 4.25 24 100/1 101.0 1


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2/7 1.285 78 7/2 4.50 22 125/1 126.0 1 4/13 1.30 76 15/4 4.75 21 140/1 141.0 1 1/3 1.33 75 4/1 5.0 20 160/1 161.0 1 4/11 1.364 73 9/2 5.50 18 200/1 201.0 - 2/5 1.40 71 5/1 6.00 17 250/1 251.0 - 4/9 1.444 69 11/2 6.50 15 330/1 331.0 - 1/2 1.50 67 6/1 7.0 14 400/1 401.0 - 8/15 1.533 65 13/2 7.50 13 500/1 501.0 - 4/7 1.571 64 7/1 8.0 13 660/1 661.0 -8/13 1.615 62 15/2 8.50 12 1000/1 1000.1 - 4/6 1.66 60 8/1 9.00 11 5000/1 5001.0 - 8/11 1.73 57 9/1 10 10.0 7500/1 7501 - 4/5 1.80 56 10/1 11.0 9 10000/1 10001 - 9/10 1.90 53 11/1 12.0 8 50000/1 50001 - EVENS 2.00 50 12/1 13.0 8 - 10/9 2.11 47 14/1 15.00 7 - 5/4 2.25 44 15/1 16.0 6 - 100/1

To cite this article: Niall O'Connor "Beting Market Lessons No 1: Understanding the Overround." (All Rights Reserved).


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Understanding the Overround