Understanding Odds

Rich had a comment on my "For Entertainment Purposes Only" post.

Discussing "value" as related to the probability of the result of a sporting event shows a fundamentally flawed understanding of what the odds on offer means. I quote "Odds makers will tell you their job is not to predict an event's outcome but, rather divide the public as to who it thinks will win. "When the oddsmakers have set a point spread properly," said Howard Martin, a noted expert on how odds are calculated, "there will be an equal number of people betting each side of the line."

Although that comment refers to US sports spreads, it's equally true of all odds.

I have to disagree, since it all rather depends on the source of the odds.

The odds you will find at a US Sportsbook or a UK bookmaker have a large built-in over-round which is not found on betting exchanges. No one would suggest that the price offered by a bookmaker could be translated directly into an implied probability, but when using prices from a betting exchange, you can often do this, especially in liquid markets. 

One study using the prices for the 2006 World Cup showed that "analysis of outright betting on the 2006 World Cup revealed that Betfair's book on the top twelve teams in the betting market was betting to an over-round of 100.92 against an average over-round of 112 elsewhere." 

Look at today's upcoming NFL game between the Baltimore Ravens and Kansas City Chiefs. A quick look at the current prices on offer from William Hill are 1.57 and 2.55 respectively, (102.91%) while on Betfair you can get 1.58 and 2.7 (100.33%). If you hold out for 1.59 and 2.72, the book becomes under-round. Betfair's implied probabilities for today's game have Baltimore at 63%, Kansas City at 37%. (At least William Hill know that Kansas City (a city) is the team's geographical location rather than Kansas (which is a state). I've written on this subject before, and it's pathetic that a company the size of Betfair can't get this right. And just so you all know, most of Kansas City isn't even in Kansas - it's in Missouri!)

Also, it's worth mentioning that a study by economist Steven D Levitt in 2004 actually showed that US sportsbooks do not set prices in the NFL to clear markets, as was commonly assumed, but set prices to maximize profits. "His data supported the theory that bookmakers are better able to predict both the outcomes of NFL games as well as bettors’ tendencies. This predictive superiority allows bookmakers to establish betting lines inducing uneven betting favoring the less likely outcome, increasing bookmaker profits despite the increased risk." I think it would be naïve to think that UK bookmakers didn't take a similar approach, at least in some sports.

Agreed that anyone who thinks that a bookmaker's odds reflect probability "shows a fundamentally flawed understanding of what the odds on offer mean", but the best prices offered on an exchange are, for the most part, from individuals who have no interest in building an over-round book.