Formula for back/lay odds conversion

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Namnam
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Namnam

Formula for back/lay odds conversion
« on: December 12, 2014, 08:18:53 PM »

Hey guys! Sometimes I need (or want) to know the equivalent back odds for my laybet. I have found a online calculator to help me with this (http://www.bettingtools.co.uk/back-lay-equivs) but its only 2 decimals and I would prefer to have the actual formula so I can insert it in Excel. I have found the following formula: LAYODDS = 1 + ( 1/(BACKODDS-1) ). However, this does not work well in excel, since it gives back the answer in % and not decimal odds. Does anyone have the correct formula that also works in excel? If I were a math pro, I'm sure I could just figure it out by myself, but unfortunately I'm not... :)
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ppintaluba
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Re: Formula for back/lay odds conversion
« Reply #1 on: December 12, 2014, 09:42:41 PM »

The formula is correct, and there's no need to be a math pro  :)
If it shows a % it may be a formatting problem in the excel.
Just select the cell with the formula, right click the mouse and choose format cells and then choose category "number" and select 3 or 4 decimal places.
Just in case, if you also want to consider commission, you can adjust the back odds like this:
1 + (odds - 1) * (1 - commission).
You will find out the real odds you get after commission.
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Namnam
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Re: Formula for back/lay odds conversion
« Reply #2 on: December 14, 2014, 02:19:35 PM »

The formula is correct, and there's no need to be a math pro  :)
If it shows a % it may be a formatting problem in the excel.
Just select the cell with the formula, right click the mouse and choose format cells and then choose category "number" and select 3 or 4 decimal places.
Just in case, if you also want to consider commission, you can adjust the back odds like this:
1 + (odds - 1) * (1 - commission).
You will find out the real odds you get after commission.

Thank you! You are completely correct, it was a setting in excel that was wrong! :) Could you help me change the formula to get the backodds also?
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ppintaluba
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Re: Formula for back/lay odds conversion
« Reply #3 on: December 14, 2014, 03:22:45 PM »

The formula is correct, and there's no need to be a math pro  :)
If it shows a % it may be a formatting problem in the excel.
Just select the cell with the formula, right click the mouse and choose format cells and then choose category "number" and select 3 or 4 decimal places.
Just in case, if you also want to consider commission, you can adjust the back odds like this:
1 + (odds - 1) * (1 - commission).
You will find out the real odds you get after commission.

Thank you! You are completely correct, it was a setting in excel that was wrong! :) Could you help me change the formula to get the backodds also?

What's the question? This formula is to get the back odds.
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Kynao
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Kynao

Re: Formula for back/lay odds conversion
« Reply #4 on: July 25, 2018, 08:16:25 AM »

Would you have the same formula for Lay odd ?

With Cv being the odd value to be found : Cv = C - ( C -1 ) * com

Does it look valid ?
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ppintaluba
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Re: Formula for back/lay odds conversion
« Reply #5 on: July 27, 2018, 02:33:35 AM »

If Lay is the lay odd (such as 2.5) and Com is the commission (such 0.05):

RealLay = (Lay - Com) / (1 - Com)
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Kynao
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Re: Formula for back/lay odds conversion
« Reply #6 on: July 27, 2018, 08:42:35 AM »

Thank you.
I try to compare with others formulas given on several websites and as they're different so i'm a little confused :))

For example, i have been given this formula for back odd : Cv = C - ( C -1 ) * com
While for Lay odd, for example here http://www.geekstoy.com/forum/showthread.php?7083-Lay-odds-formula seems different than yours.

To simplify things, i will forget all other formulas and concentrate on yours, so you have :

- RealBack odd = 1 + (Back odd - 1) * (1 - Com).
- RealLay odd = (Lay odd - Com) / (1 - Com).


Let's say we have :
- commission is 0.05,
- back odd value is 1.7   and back stake is 2€
- lay odd value is 1.5 and lay stake is 2.27€


Without commission, if players wins, my profit with the back will be :
back odd * back stake - back stake = 1.7 * 2 - 2 = 1.4€
while on the lay bet i lose lay odd * lay stake - lay stake = 1.5 * 2.27 - 2.27 = 1.1135€

Without commission, if players looses, my profit with the lay will be 2.27€ while on the back bet i lose 2€

Good point here is we have profit whatever the player win or loose.
Now what if we continue the example with the comissions ?

based on your formulas
- RealBack odd = 1 + (1.7 - 1) * (1 - 0.05) = 1.665

- RealLay odd = (1.5 - 0.05) / (1 - 0.05) = 0.07895. This one seems wrong

Could you continue with these (back and lay bets values examples) up to the profit (commission taken into account) based on your formulas ?
« Last Edit: July 27, 2018, 08:53:13 AM by Kynao » Logged
ppintaluba
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Re: Formula for back/lay odds conversion
« Reply #7 on: July 27, 2018, 06:41:24 PM »

Quote
While for Lay odd, for example here http://www.geekstoy.com/forum/showthread.php?7083-Lay-odds-formula seems different than yours.

This formula is the same I posted, but this site is using percentage commissions (such as 5), instead of 0.05. That´s why they divide commission by 100 in their formula

Quote
based on your formulas
- RealBack odd = 1 + (1.7 - 1) * (1 - 0.05) = 1.665
- RealLay odd = (1.5 - 0.05) / (1 - 0.05) = 0.07895. This one seems wrong


It is in fact wrong: (1.5 - 0.05) / (1 - 0.05) = 1.5263 (at least in my country :D)

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Kynao
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Re: Formula for back/lay odds conversion
« Reply #8 on: July 27, 2018, 07:13:18 PM »

Yes yes  ;D  Beer are stronger in my county :)

Coming back to the subject, would you complete the example ?

How is it used ? This means if the player wins, and if i back with 2€ with 1.7 as odd, my profit will be  2 * 1.665 - 2 = 1.33€ (instead of  1.7 * 2 - 2 = 1.4€)
Then i have to minus lay loss = 1.52632 * 2.27 - 2.27 = 1.19474€ (instead of 1.5 * 2.27 - 2.27 = 1.1135€)
So my final profit will be 1.33€ -  1.19474€ = 0.13526(instead of the previous calculated 2 = 1.4€ - 1.1135€ = 0.2865€)

Am i correct this time or i drink another beer ?  :o
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ppintaluba
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Re: Formula for back/lay odds conversion
« Reply #9 on: July 27, 2018, 07:23:03 PM »

But are you backing in the exchange with 5% commission? Or are you backing in a bookmaker without commission, and laying in the exchange with 5% commission?. If you have commission in the back bet, you should have included it your first example, so profit was not 1.4. It was 1.33 from the start.

2€ @1.7 (less commission): 2 * 1.7 - 2 (less commission) = 1.4 (less commission) = 1.33
2€ @1.665: 2 * 1.665 - 2 = 1.33
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Kynao
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Re: Formula for back/lay odds conversion
« Reply #10 on: July 27, 2018, 07:33:33 PM »

I were supposing to do back and lay in a betting exchange with a commission on both moves.

I feel what you just said is what is aid previously or i miss something ?
ie ie based on my understanding that :

1. the betting exchange shows odds which does not include commissions so we have to calculate them if we don't want the balance account shows us some surprises.
2. I modify the odds presented by the betting exchange with the help of your formulas to obtain "virtual odds" from which i can do my usuals calculations (which we did in our last 2 messages as i feel we said the same thing)
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Kynao
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Re: Formula for back/lay odds conversion
« Reply #11 on: July 27, 2018, 07:42:25 PM »

I think i will take a beer again :)
As on this commission subject, it seems hey are calculated differently here if we take the example of 2 betting exchanges : SMarket and Matchbook

So, How to calculate commission on a betting exchange ?

Answer from SMarkets here
https://help.smarkets.com/hc/en-gb/articles/115003370169-How-to-calculate-commission-on-a-betting-exchange

In short Commission charged = ((stake * odds) - stake) * commission rate

My understanding if my beer is not too strong, is :
what you should have in your pocket * commission rate.

Answer from Matchbook here :
https://www.matchbook.com/page/getting_started/howcommissionrateiscalculated/

In short : stake odds * odds * commissions

This is not the same thing.
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ppintaluba
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Re: Formula for back/lay odds conversion
« Reply #12 on: July 27, 2018, 08:18:08 PM »

Commissions in Matchbook are different!. This is just for Betfair, Smarkets, Betdaq, etc.

Back bet with commission, both formulas
2€ @1.7 (less commission): 2 * 1.7 - 2 (less commission) = 1.4 (less commission) = 1.33
2€ @1.665: 2 * 1.665 - 2 = 1.33
It's clearly the same.

But I don't know where did you get the lay stake and the lay formula. In generally I do the math using liability and back odds equivalent for the lay bet.

Lay bet equation profit: liability * back odds eq - liability
In your case: Lay odds is 1.5. So back odds eq = 3.
And the correct liability should be 1.15

Lay bet with commission (using back odds equivalent), both formulas
1.15€ @1.5(lay) (less comm) = 1.15€ @3 = 1.15 * 3 - 1.15 (less comm)= 3.45 - 1.15 (less comm) = 2.30 (less comm) = 2.30 - 0.115 = 2.185
1.15€ @1.5263(lay) = 1.15€ @2.9 = 1.15 * 2.9 - 1.15 = 3.335 - 1.15 = 2.185
It's also the same.

Your arbitrage:
2 @1.7 (back): profit => 1.33
1.15 (liability) @1.5 (lay): profit => 2.185

Arbitrage profit:
1.33 - 1.15 (if you win back bet) = 0.18
2.185 - 2 = 0.185 (if you win the lay bet)

I know it looks complicated, but I always do the math using back bets (converting lay odds to back odds equivalent and using the back bet formulas)
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Kynao
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Re: Formula for back/lay odds conversion
« Reply #13 on: July 27, 2018, 08:40:09 PM »

ok, so the formulas we are talking about don't work on matchbook, noted.

>But I don't know where did you get the lay stake and the lay formula.

The lay stake, i just gave is an example, so what not?
About the lay formula, i'm confused, you were the one to give it to me in this thread RealLay = (Lay - Com) / (1 - Com), i'm just using it.

>Lay bet equation profit: liability * back odds eq - liability. In your case: Lay odds is 1.5. So back odds eq = 3. And the correct liability should be 1.15

I'm sorry, i'm getting more confused, what's the point ?

> Lay bet with commission (using back odds equivalent), both formulas
>1.15€ @1.5(lay) (less comm) = 1.15€ @3 = 1.15 * 3 - 1.15 (less comm)= 3.45 - 1.15 (less comm) = 2.30 (less comm) = 2.30 - 0.115 = 2.185
>1.15€ @1.5263(lay) = 1.15€ @2.9 = 1.15 * 2.9 - 1.15 = 3.335 - 1.15 = 2.185

Ok, i'm lost  :o, would have been easier for me to rely on the previous example than starting on a new one.

At the end, whatever the kind of approach, i rely on formulas giving me the opposite stake amount i should look for,
=> ie for given lay and back odd and stake of one side, i calculate the stake for the other side so for the example of a back / lay calculation, i have a formula taking into account a ponderation coefficient (allowing you to define more a side against the other) but this formula does not take into account commissions.

This is the reason why at the end, instead of commissions formulas based on odd, i would prefer simpler commission formulas based on profit.
« Last Edit: July 27, 2018, 08:41:45 PM by Kynao » Logged
ppintaluba
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Re: Formula for back/lay odds conversion
« Reply #14 on: July 27, 2018, 08:55:07 PM »

OK. My confusion is because I don´t know this formula in your first example:

Quote
while on the lay bet i lose lay odd * lay stake - lay stake = 1.5 * 2.27 - 2.27 = 1.1135€
Where did you get this? You cannot use lay odds as if they where back odds and multiply them by a stake. I think this is the whole problem.

You must convert lay odds to back odds equivalent, and you must use a liability (given that 1.5 lay odds is equivalent to 3 back odds, the right liability should be 1.15 to have equal profit in both cases).

This is what I used in my previous post.
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