Implied Probability of an Outcome –BetFair Edition
Chris F. Masse January 30th, 2008
“Does prediction market guru [= Chris Masse] understand probabilities?“, asks our good friend Niall O’Connor.
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Let’s ask economics PhD Michael Giberson:
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.
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.
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.
Niall may be hung up on using a pure concept of probability. The purity is not useful; your explanation is useful. You win.
(Feel free to quote from this email, should you wish.)
-Mike
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UPDATE: Michael Giberson precises his comment…
Niall, I agree that Professor Sauer’s presentation explains how to estimate true probabilities from odds that do not sum to one. I was taking Chris Masse to be explaining a related, but slightly different task: the conversion of the digital odds that Betfair quotes to an implied probability.
The point of my slightly snide comment concerning purity reflects the pragmatic view that a trader could use the method Chris describes to convert from digital odds to an implied probability (which may be easier for some traders to think with and trade on). A single quote of digital odds implies a particular probability estimate. Chris’s math gets the trader from the one number to the other. (=useful to traders)
To get to the estimate of true probabilities, as you have explained, a trader must have a complete set of odds for all possible outcomes for an event. This additional information requirement would completely stymie a trader wishing to arrive at the true probability estimates in cases in which some of the data is unavailable. (= not as useful to traders)
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Please note Professor Raymond Sauer’s analysis of how we derive true probabilities from odds that do not sum upto one;
http://hubcap.clemson.edu/~sau.....amp_04.pdf
“The purity is not useful; your explanation is useful.”
Useful to what - the cause of prediction markets??
Niall, I agree that Professor Sauer’s presentation explains how to estimate true probabilities from odds that do not sum to one. I was taking Chris Masse to be explaining a related, but slightly different task: the conversion of the digital odds that Betfair quotes to an implied probability.
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The point of my slightly snide comment concerning purity reflects the pragmatic view that a trader could use the method Chris describes to convert from digital odds to an implied probability (which may be easier for some traders to think with and trade on). A single quote of digital odds implies a particular probability estimate. Chris’s math gets the trader from the one number to the other. (=useful to traders)
.
To get to the estimate of true probabilities, as you have explained, a trader must have a complete set of odds for all possible outcomes for an event. This additional information requirement would completely stymie a trader wishing to arrive at the true probability estimates in cases in which some of the data is unavailable. (= not as useful to traders)
Niall and Mike, for Christ’s sake, go get each a gravatar.
http://www.gravatar.com/
So we can see how you look like.
Bettingmarket.com’s comprehensive guide to the over-round
http://www.bettingmarket.com/overround.htm
Raymond D Sauer on converting betting odds into probabilities
http://www.bettingmarket.com/oddsprobably.htm