# A Line Betting Enigma

The TAB Sportsbet bookmaker is, as you know, a man to be revered and feared in equal measure. Historically, his head-to-head prices have been so exquisitely well-calibrated that I instinctively compare any model I construct with the forecasts he produces. To show that a model historically outperforms leads me to scuttle off to determine what error I've made in constructing the model, what piece of information I've used that, in truth, was only available with the benefit of hindsight.

Which makes the following all the more perplexing: why is it that over the past five seasons home teams have on average received about 2 points more start on handicap than they, in retrospect, should have? Further, as a consequence, why is it that home teams have won over 54% of all line bets, a rate high enough to overcome the overround and make wagering solely on home teams a profitable strategy?

First, a little explanation. If a bookmaker is handicapping games accurately, over time you'd expect that the handicap-adjusted margin - that is, the actual game margin plus the handicap - of any game type, however defined, should be zero. So, for example, on average over a long enough series of games, Geelong's average handicap-adjusted margin should be zero, as should Richmond's, the Swans', and so on.

More importantly, the long-term line betting winning rate of any strategy should be about 50%. In the absence of this there's an exploitable opportunity in the market place, which bettors should capitalise on and, in so doing, destroy.

But that isn't happening. Here's the evidence:

Each row of this table relates to a range of handicaps given (if they're negative) or received (if they're positive) by the home team, and shows the average handicap-adjusted result for games of that type. So, for example, this season, in games where the home team has been giving 42.5 points start or more, the average handicap-adjusted margin has been 8.5 points per game. In other words, the home team has tended to cover the spread by 8.5 points in these games.

When I first calculated the statistic showing the apparent 2-point home-team bias across all games, I immediately wondered if it was just the case that games with starts in the -6.5 to +6.5 range were the source of it, as the starts in this range might be distorted by the TAB Sportsbet bookie's reticence to post handicaps of less than 6.5 points. In effect what he does is deliberately give too much or too little start to one team or the other, for which he compensates by offering a price different from the usual \$1.90. So, for example, he might post a line of -6.5 for a narrow favourite but offer a price of \$2.00.

But this table demonstrates that this behaviour isn't the cause of the bias at all. In fact, with the exception of the rows for starts in the ranges -18.5 to -13.5 and -12.5 to -7.5, the bias permeates the table.

Hmm, well maybe this bias isn't really worth anything because it doesn't convert into a difference in the line-betting winning rate of home teams.

Nope. Again with just a few exceptions - the two earlier handicap ranges amongst them - home teams win at a rate in excess of 50% regardless of the start they're giving or receiving.

That's truly odd.

To be fair I should point out the fiction that I've been conveniently implying for some time, which is that the bookmaker sets prices and handicaps based on his view of how the game will pan out. That's only partly true, and perhaps not true at all in some cases: what he really does is respond to the weight of gambling dollars and set prices and handicaps that roughly balance his liabilities across every possible result. In that way, rather than being at the whim of outrageous football fortune, he can often guarantee himself a profit regardless of the outcome of the game. If, for example, in the line market, he sets a handicap that results in exactly 50% of all wagers on the favourite and 50% on the underdog then, because he only pays the winner bettors out at \$1.90, he guarantees himself 5% of all amounts wagered, risk free.

So the real question is not so much 'why do bookies set biased handicaps?' but instead 'why do gamblers wager in such a way that this is a profitable way for bookies to respond?'

I don't have an answer to this.

If that isn't perplexing enough, there's another, albeit smaller, apparent bias in football handicap setting. This time, consider the handicap-adjusted margin from each game from the favourite's rather than the home team's point of view.

Here, as you can see, there is also a bias, but it isn't as consistent or as large. Overall, favourites give about 1 point too much start, moreso for favourites giving 18.5 points start or fewer.

Again we need to consider whether this apparent bias leads to any exploitable difference in the rate of line-betting success of favourites (or underdogs).

The answer is that it does ... and it doesn't. Favourites do win on line betting at a rate lower than 50% and this is broadly true of narrow favourites (that give small starts) and of overwhelming favourites (that give large starts), but they don't win at a rate sufficiently different from 50% to cover the overround and so make betting on underdogs a long term profitable venture. (At a price of \$1.90 you need to win at a rate greater than 52.6% to make a profit.)

There's maybe some potential where the starts are in the 7.5 to 12.5 points range, but the anomaly here might be purely a statistical fluctuation. Or, of course, it might not ...

In any case the biases towards home teams and underdogs have persisted into 2010 and show no obvious signs of abating. That's good news for ELO-Line which, you might recall, wagers only on home teams in the line betting market. Long may the home team bias reign.

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