Calculating Each Way Value From Fixed Odds. Any help/links appreciated

Oddly enough, yesterday I was re-reading a book I bought around eighteen years ago which I remembered contains a section devoted to what the author called 'The Each Way choice'.  There are two pages of tables covering a variety of different scenarios, i.e. Number of runners, place terms and bookmaker's overround.  In fact, thanks to your enquiry I've finally succeeded in producing a spreadsheet to take all the hard work out of the calculations!   

I'll try and give you a brief overview of what he wrote.

He stated, disregarding the bookmaker's percentage for the moment, that it does not matter how many horses are in the race if the odds are 3/1 then whether the field has 8 or 12 runners, 3/1 are the chances of it winning.  He defined 'true place odds' using the formula below.

True place odds: (win odds +1/number of places) - 1

He went on to say that to see what advantage there may be in each way betting it is necessary to compare the real chances of coming placed with the odds that the bookmaker is offering.  This means that the advantage will change according to the percentage of the book.

The true win odds in a 110% book: ((win odds + 1) * 110%) - 1

The true place odds in a 110% book: (((win odds + 1) * 110%)/(number of places)) - 1

For convenience the bookmaker offers:  win odds/set figure

To assess the advantage:  ((true odds - offered odds) * 100%)/(true odds + 1)

He put forward the following scenario....

Take for example the eight runner race where the percentage overround is 115%.  At odds of 2/1 the place odds advantage to the punter is 21.74%, say 22%.  Where place betting is available, the whole of the bet is 22% in favour of the punter.  When the bet is struck each way, this 22% advantage only applies to the place half.  The bookmaker has an advantage of 15% through the overround figure in his win book.  Therefore the net advantage is 7% in favour of the punter.

Well, there endeth the overview.  In closing, here is the above scenario as it appears in my spreadsheet.

Win odds + 1	Book	No. of places	True place odds	Offered odds	% adv. to punter
2	1.15	3	0.77	1.20	56.52
2.5	1.15	3	0.96	1.30	35.65
3	1.15	3	1.15	1.40	21.74
3.5	1.15	3	1.34	1.50	11.80
4	1.15	3	1.53	1.60	4.35
4.5	1.15	3	1.73	1.70	-1.45
5	1.15	3	1.92	1.80	-6.09
5.5	1.15	3	2.11	1.90	-9.88
6	1.15	3	2.30	2.00	-13.04
6.5	1.15	3	2.49	2.10	-15.72
7	1.15	3	2.68	2.20	-18.01
7.5	1.15	3	2.88	2.30	-20.00
8	1.15	3	3.07	2.40	-21.74
8.5	1.15	3	3.26	2.50	-23.27

you may have an advantage on the e/w part of the bet but you will be giving the edge back on the win part alot of the time. The key to this type of betting is to get as close as possible to the 100% line win price. Your above eample is not correct either - the book may have an overall margin of 15% but you need to look at each runners margin as some may have more than others.

Here is a breakeven scenario

100% Line Win Price - 10/1
Bookie Price - 7/1

100% Line Place Price - 7/4
Bookie E/W Odds - 5/2

Get bigger than 7/1 and it then becomes a value bet assuming the % are accurate.

Thanks so much for taking the time to reply.

Sincerely appreciated

You cannot calculate place odds from win odds or vice versa.

Two simple examples. Both extreme but illustrate the point.

1.
A classy but tempermental horse over the jumps is rated at evens to win.

Previous race it has either won or refused/fallen.

The odds for a place should perhaps be around 1.8.

2.
A good horse with planty stamina that doesn't like to be out in front without hard work from the jockey.

Previous races has placed 2/3 mostly.
Rated evens to win. Odds for a place thould possibly be about 1.2

Also very short priced favourites inflate the win prices of
the other horses but not necessarliy their chances of being
placed.

you may not may be able to explicitly derive place odds from win odds but there will always be a price to place; included in the price will be all the elements that fred mentioned above  - you just need a good market line or strong pricing skills.

a good example is in Motor Racing where there will be derivative markets - Moto GP

Lorenzo is 4/1 to win 100% line
Bookie Odds: 7/2 - 1/5 1,2,3


100% Line to finish in the Top 3 - 4/9
Bookie Place Payout - 7/10

Edge on the bet is approx 4%

kenilworth

I'm pleased to see that your observation is in accord with the table I posted.  Namely, that the advantage to the punter decreases as the win odds lengthen.

By the way, I'm not a proponent of the method I described, I merely posted it because I thought it may be of interest to the OP.

no offence mate but that table is a load of rubbish. You can get great value e/w on outsiders. Every event has to be treated seperately.

comparing the place part of your bet with the place market on betfair would probably be more accurate ?

excactly lux.If there is not a market then you need to price it yourself - thats were pricing skills come in handy

max powers121

Re. your Moto GP example.

Can you kindly display the calculations, you know, the percentages and stuff, to show how you determined that Edge on the bet is approx 4% as I'm not sure I'm capable of doing it myself?

Thanks in advance.

Expected loss on the win part is 10%

Over a series of 100 bets(using £1 as a stake per bet) you will win 20 times and loss 80.
Your Profit on the winning bets = (4.5-1)*20 = 70
Your Loss on the losing bets = -80
Expected Profit/Loss over 100 bets = -10
Margin = Profit or Loss/Turnover*100 = -10/100*100 = -10%

Use the same principles for the e/w part and combine the two.

Place Part

Over a series of 100 bets(using £1 as a stake per bet) you will win approx 70 times and loss 30.
Your Profit on the winning bets = (1.70-1)*70 = 49
Your Loss on the losing bets = 30
Expected Profit/Loss over 100 bets = 19
Margin = Profit or Loss/Turnover*100 = 19/100*100 = 19%

Net Profit/Loss = 9

Margin/Edge = 9/200*100 = 4%

I would recommend getting to grips with Monte Carlo simulations in excel as it really shows these scenarios in black and white.

Take a look at calcodds dot com. You have to register to see the odds, but the service is free. 

14:10 Yarmouth sample:
http://www.calcodds.com/admin/testajax.php5?refid=51520