# Framing a Line Market: How Hard Can It Be?

This week, for the first time that I can remember, every line market has moved from its initial pricing on Wednesday at noon. More generally, I've noticed a greater sensitivity in the line market than in the head-to-head market and wondered why that might be the case.

Over the past five-and-a-half seasons, the handicap adjusted home team margin - the actual margin adjusted for the start given or offered by the home team in TAB Sportsbet wagering - has behaved like a Normally distributed random variable with a mean of about 2 points - the historical bookie home team bias - and a standard deviation of around 36 to 37 points. Even if we assume that the TAB Sportsbet bookmaker has a fairly large standard deviation in his expected margin of victory it's likely that the true standard deviation of victory margins about the true expected victory margin is somewhere around the 35-38 point range.

If we assume that the true handicap adjusted home team margin is Normally distributed with, by definition, a mean of 0, we can calculate the probability that a mishandicapped team wins on line betting given the size of the mishandicapping and an assumption about about the true standard deviation of the handicap adjusted margin in each game. Here's the detail:

At a price of \$1.90, any tipster who can predict line winners at a rate greater than 52.6% will make a profit. This equates, it transpires, to only about 2 points of error in offered margin. In other words, in any game where the bookmaker offers a price of \$1.90 and mishandicaps a team by 3 points or more, he is subject to being exploited by savvy punters who better estimate the true expected victory margin. That's right, just 2 points. No wonder the bookie's sensitive to changing information about player ins and outs, weather forecasts, and whether or not a key player enjoyed his breakfast on Wednesday morning. When you need to be accurate to within 2 points, I imagine that you fight on a daily basis the urge to consult chicken entrails for any clues about the weekend's matchups.

Even at \$1.85, a bookie can't afford to hide behind the overround. Generally, the move to \$1.85 only gives him an extra point of comfort, so now he can afford to be wrong by 3 points, or 4 if he thinks the victory margin for this particular game has a standard deviation of 39 or 40 points.

So, how might a bookie respond to new information or new perceptions about the expected victory margin? The TAB Sportsbet bookie doesn't change the offered margin, but instead changes the price. What then is a fair price on the line market for a given change in expected victory margin?

So, for example, this week on Friday night Hawthorn were at \$1.68 on the line market with 20.5 points start. Even if this pricing carries a zero overround, that means the TAB Sportsbet bookmaker now feels that this is about 9 points too much start for the Hawks. If you factor in a little overround, in truth he probably now feels that the correct start for the Hawks is about 8.5 to 9.5 points.

Frankly, no wonder the line market pricing changes so often and sometimes without apparent regard for the head-to-head price. My respect for the TAB Sportsbet bookmaker continues to grow - maybe that's just Stockholm syndrome.

Comment