# BetFair Digital Odds = BetFair Probabilities

Odds that Hillary Clinton gets the 2008 Democratic nomination = 1.56 (digital odds taken at 9:15 AM EST)

To get the implied probability expressed in percentage:

• Take the number &#8220-1&#8243–
• Divided it by the digital odds (here &#8220-1.56&#8243-)-
• Then multiply the result by 100-
• 64.1% = ( 1 / 1.56 ) x 100

BetFair-generated implied probability is not far away from InTrade&#8217-s 62.1%.

Psstt&#8230- This present post was prompted by Niall O&#8217-Connor, who puts all his faith in the BetFair instant &#8220-over-round&#8221- &#8212-which indeed doesn&#8217-t add up to the virgin and perfect &#8220-100%&#8221- that Niall is seeking (like the Monthy Python were seeking the Holy Grail). Good luck for your quest, Niall.

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External Resource: Interpreting Prediction Market Prices as Probabilities – (PDF file) – by Justin Wolfers and Eric Zitzewitz

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## 12 thoughts on “BetFair Digital Odds = BetFair Probabilities”

1. Niall O'Connor said:

I think you should slow down and read the piece again!

The probability calcualtion must always take the over-round into accound; something which you do not seem to get.

2. Chris. F. Masse said:

Shouldn’t you search for an averaged “over-round” over a long series, as opposed to an instant “over-round”?

3. Niall O'Connor said:

NO. You’re calculation is simply wrong! You have failed to understand both the concept of the over-round and probability (at its most basic). Your Clinton probability is a literal translation of a set of odds that do not sum up to 1! There is no debate – this is wrong!

I think you should put up some form of correction; and whilst we are it, perhaps you could confer your views on the point I make at the bottom of my article, regarding the fact that the Intrade Democratic nominee market does not sum up to one either. I would be particularly interested in hearing your views as to how this impacts on the notion of market efficiency.

Sorry to be so dogmatic as regards to challenging prediction market orthodoxy, but what hope is there, if at the very least prediction market advocates cannot master the simple notion of probability!!

4. Chris. F. Masse said:

Niall, I have just converted a digital odds into a probability expressed in percentage. It’s not like I have committed a crime.

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The Hillary Clinton event derivative market is independent of the others, right? You either buy long or short sell.

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Hillary Clinton has a 64.1% probability of winning the Democratic nomination, and a 35,9% probability of losing the Democratic nomination.

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Again, I’m just taking the BetFair digital odds and converting it to a probability expressed in percentage.

5. Chris. F. Masse said:

Economics PhD Michael Giberson:

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QUOTE

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Yes, I think you are right. I just looked at your exchange with Niall and Niall’s post, and haven’t thought through just how the over-round may affect things.

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But it seems okay to do it just the way you say, because the digital odds implies a precise numerical prediction and that prediction can be stated in the form of a probability. Call the calculated number an *implied probability* of the event, and then you don’t have to worry that a complete group of related market prices don’t add to 100 percent.

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If a trader believes that event X should be trading at 70 percent and sees current digital odds of 1.56 at Betfair ( => 64.1 percent), he should buy (considering fees, etc.). If the digital odds move to 1.4 ( => 71.4 ) then sell or at least don’t buy.

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Niall may be hung up on using a pure concept of probability. The purity is not useful; your explanation is useful. You win.

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(Feel free to quote from this email, should you wish).

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-Mike

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UNQUOTE

6. razhan miran said:

Hello Chris, my name is Razhan Miran and i have an MSc in Mathematical Trading (cass), and a PhD in Stochastic Calculus (Imperial). I am also an ex-employee of betfair. i was an in-play soccer market operator during my university days.

im afraid my friend your understanding of probability is very basic. you are correct but not very accurate, especially for a serious market trader. Converting a bookmakers odds into percentile probability would leave you with a set which sums to greater than one. Normalising it as Niall suggested does help, but a more rigorous normalisation scheme than he suggested would be appropriate for an accuracy of say a three decimal place local truncation error.

At the very most it gives you a clearer idea of how much of the market is made up of a single runner, but that is it im afraid.

to re-iterate, a rigorous normalisation scheme whereby the weight of each runner in a market is considered when normalising (each runner requires reduction based on its market share) is the only method by where your postulate may be successful. Indeed this is normal practice for many successful event derivitive traders, but not all. in fact if one can base a mathematical model on the decimal odds, accuracy will always be maximised.

7. Chris F. Masse said:

@razhan miran: Thanks for your comment.

8. medemi said:

Why don’t you just add the back price to the lay price, divide it by 2, and then tranlate it to a percentage probability. You can forget about any decimal being meaningful unless, maybe, liquidity is huge and the spread is minimal (1 tick). But it will still be meaningless, like the habits of your average wizkid, because we’d still be taking a snapshot from the market.

9. medemi said:

Isn’t anyone taking the bait ?