What is the ‘Overround’?

Friday, January 4th, 2013
By Racepedia

Introduction

You may have heard the phrase ‘overround’ within a few of the more knowledgeable betting circles. It is a very important concept in betting and is the foundation of a bookie’s business. Phrases such as ‘the bookies will be paying through the nose because of that 20/1 winner!’, or, ‘the bookies are hurting today’ are absolute rubbish and the ‘overround’ is the reason why.

The overround ensures bookies make a profit regardless of the outcome of an event. The concept they use to do this is simple, they offer all bettors lower odds than those they believe a horse is truly worth (our initial examples are based upon horse racing).  . If they believe a horse is 4/1 (5.0) they will offer 3/1 (4.0), the reduction in price ensures they will always return profit; especially when they do this across all the horses in a race. The idea is a simple one (overly simplified in this paragraph) but there is a bit of math behind it; the next section explains the math behind the overround and gives some examples of how it really works.

 

The Math behind the Overround

Example 1

Imagine a five horse handicap race; because the race is a handicap all of the runners theoretically have the same probability of success. To calculate the chance of success divide ‘1’ by the implied odds, in our example this is:

1 / 5.0 = .20

We then need to multiply this number by 100% to express it as a percentage.

.20 x 100% = 20%

The information for the race can be better displayed using the table below.

 

Horse

Probability of Success (%)

Fred

20

Ted

20

Jon

20

Bob

20

James

20

 

A bookie looking at this race may decide to give each horse odds of 4/1 (5.0).

 

Horse

Probability of Success (%)

Odds

Fred

20

5.0

Ted

20

5.0

Jon

20

5.0

Bob

20

5.0

James

20

5.0

 

Now imagine the bookie takes £20,000 upon each horse i.e. punters bet £20,000 upon each horse.

 

Horse

Probability of Success (%)

Odds

Amount Staked (£)

Potential Pay-out (£)

Fred

20

5.0

£20,000

£100,000

Ted

20

5.0

£20,000

£100,000

Jon

20

5.0

£20,000

£100,000

Bob

20

5.0

£20,000

£100,000

James

20

5.0

£20,000

£100,000

 

One of the horses has to win and therefor the bookie will be paying £100,000 to the lucky winners who bet on the correct horse (£80,000 profit + £20,000 original stake). The bookie in this example has not made a profit and is now scratching his head and wondering what he could do to change this…

 

Example 2

After thinking about the problem for a while the bookie decides to try a new tactic upon a similar race, he calls this tactic ‘The Overround’. Instead of offering the odds he would normally offer he decides to offer slightly less (4.5).

1 / 4.5 = .22

.22 x 100% = 22%

 

Horse

Probability of Success (%)

Odds

Jane

22

4.5

Freda

22

4.5

Rose

22

4.5

Dawn

22

4.5

Wednesday

22

4.5

 

He is again fortunate that punters bet exactly £20,000 upon each horse again.

 

Horse

Probability of Success (%)

Odds

Amount Staked (£)

Potential Pay-out (£)

Jane

22

4.5

£20,000

£90,000

Freda

22

4.5

£20,000

£90,000

Rose

22

4.5

£20,000

£90,000

Dawn

22

4.5

£20,000

£90,000

Wednesday

22

4.5

£20,000

£90,000

 

Notice now that the potential max pay-out for the bookie is £90,000 even though a total of £100,000 was staked. The £10,000 that is now ‘missing’ from the equation is the bookies profit and if you wish to know the profit on this market we need only calculate the overround. By offering lower odds on each horse the bookie is implying that each of the horses has a greater chance of success than is actually possible. If an event is certain to occur i.e. one of the horses winning a race, then the probabilities should sum to ‘1’ (as a percentage this would be ‘100 %’).

 

 

Horse

Probability of Success

Probability of Success (%)

Jane

.22

22

Freda

.22

22

Rose

.22

22

Dawn

.22

22

Wednesday

.22

22

Overround

1.10

110

 

Clearly the sum of ‘probability of success’ and ‘probability of success (%)’ is not ‘1’ or ‘100%’ respectively. This overestimation of true probability is called ‘the overround’ and for large events such as ‘The Grand National’ it can be incredibly high. Using the above example the bookie can expect to pay-out £100 for every £110 he receives. His profit is therefor:

 

10 / 110 = .09

 

.09 x 100% = 9% Profit

 

A Balanced Book

In example 1 there was no overround and consequently the bookie made no profit. An event that has been evenly balanced without an overround is called ‘a balanced book’; a balanced book yields no profit for the bookie.

We have seen how the overround works when punters bet an equal amount upon each horse but what happens when different amounts are wagered upon each horse (normally the case)? We discuss this in the next section.

 

Adjusting the Odds to Ensure an Overround

Example 3

The bookie is now becoming a bit more advanced with his overround tactic and decides to apply it on a normal race where the odds fluctuate before the event.

 

 

Horse

Odds

Probability of Success

Probability of Success (%)

A

2

.5

50

B

3

.33

33

C

3.5

.29

29

D

5

.2

20

E

5.5

.18

18

Overround

 

1.5

150

 

It can be seen here that the bookie has built-in a healthy overround which will yield him a large profit (50/150=.33, or, 33%). He needs to ensure though that the amounts bet upon each horse will yield him this profit regardless of the outcome of the event; he does this by adjusting the odds as punters wager their money.

If punters bet a lot of money on horse ‘A’ he will reduce the odds and thus decrease the attractiveness of the bet to other punters, if he simultaneously increases the odds of horses B-E he is also ensuring that horses B-E are more attractive and thus attract more new money than horse ‘A’. Using this method he ensures that the correct money is bet upon each horse and that regardless of the outcome he will retain a profit.

If you are watching a horse and the odds increase, it indicates that a bookie wishes to attract money to this horse.

If you are watching a horse and the odds decrease, it indicates that a bookie wishes to slow down the amount wagered upon this horse and make punters bet upon other horses.

At some point the odds may be greater than what you believe the implied probability truly is e.g. a 50/1 horse but you calculate it as having a 20% (.2) chance of winning, if this occurs you have found value. To learn more about value see our value article in the betting tips section; our value calculator is also available in the betting tools section.

 

 

Horse

Odds

Probability of Success

Probability of Success (%)

Amount Staked (£)

Potential Pay-out (£)

Bookie Profit/Loss (£)

A

2

.5

50

£20,000

£40,000

£60,000

B

3

.33

33

£20,000

£60,000

£40,000

C

3.5

.29

29

£20,000

£70,000

£30,000

D

5

.2

20

£20,000

£100,000

£0

E

5.5

.18

18

£20,000

£110,000

£-10,000

Total

 

1.5

150

£100,000

 

The bookie profit/loss column is calculated by summing the amount staked (£100,000) minus the potential pay-out of whichever runner won. If horse ‘A’ won, the bookie would have to pay-out £40,000 because £20,000 multiplied by odds of 2 is £40,000, the total amount staked upon the race was £100,000 and consequently the bookie has made a neat profit of £60,000 because:

£100,000-£40,000=£60,000 Profit

An important point to notice in the above table is that the bookie has not done a good job of spreading his risk, he has ensured a profit should one of the lower odds horses win but in the event a high odds horse wins he will either break even (Horse D, £0) or lose money (Horse E, £-10,000).  This is an unacceptable risk for a bookie, a bookie wants a fixed profit regardless of the outcome of the event and consequently the bookie is more likely to try and balance his books in the same fashion as the table below.

 

 

Horse

Odds

Probability of Success

Probability of Success (%)

Amount Staked (£)

Potential Pay-out (£)

Bookie Profit/Loss (£)

A

2

.5

50

£40,000

£80,000

£20,000

B

3

.33

33

£30,000

£90,000

£10,000

C

3.5

.29

29

£25,000

£87,500

£12,500

D

5

.2

20

£18,000

£90,000

£10,000

E

5.5

.18

18

£15,000

£82,500

£17,500

Total

 

1.5

150

£100,000

 

There will never be a perfect balance of profit across all horses but there will normally be a profit regardless of the outcome of the event. A good bookie will always retain a profit, if the bookie manipulates the odds well then a profit will exist and this profit will be roughly equal regardless of the outcome of the event. The constant price movement of odds indicates the willingness of a bookie to adjust prices in order that a profit can be equalised across all possible outcomes.

One more example should help illustrate how the overround works in other sports such as football (or ‘soccer’ for our non UK members!).

 

Example 4

A typical football match may have odds and money distributed similar to the table below.

 

Outcome of Event

Odds

Amount Staked (£)

Potential Pay-out (£)

Bookie Profit/Loss (£)

Home Win

1.4

288,000

403,200

19,300

Draw

4.0

88,000

352,000

70,500

Away Win

13.0

19,000

247,000

175,500

Total

422,500

 

The bookie has ensured there is a profit no matter the outcome of the event although normally he will try to equalise the money staked so that the profit is roughly the same regardless of which outcome occurs.

 

Influences upon the Overround

A normal overround for a horse race will be roughly between 105 and 120% but there are other factors that can influence how large or small an overround may be, a few of these factors are listed below.

    1. The fewer runners there are in a race, the less overround there is.
    2. A large number of runners in a race can increase the overround significantly.
    3. A large televised race where uneducated punters place bets without really knowing what they are doing will almost always have a large overround e.g. The Derby, The Grand National, Melbourne Cup.
    4. The overround for betting exchanges e.g. Betfair, Betdaq, WBX, is usually lower than a bookies. Betting exchanges earn their money via transactional commission, the Betfair starting price (BFSP) often has an overround of about 107% and this includes the average 3% commission paid by punters.
    5. The overround on betting exchanges is usually its lowest just before the event begins.

 

Conclusion

If you are going to get involved and expect to make any sort of money in the betting industry it is important to learn and grasp concepts such as the overround. For a quick conversion of odds to implied probability see our Odds to Probability conversion table. The conversion table will allow you to quickly convert odds to implied probability (chance of success e.g. winning a race) and thus quickly sum the probabilities to calculate the overround. Checkout the overround calculator in our betting tools section if you wish to have the math done automatically.

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