Does The Favourite Have It Covered?

You've wagered on Geelong - a line bet in which you've given 46.5 points start - and they lead by 42 points at three-quarter time. What price should you accept from someone wanting to purchase your wager? They also led by 44 points at quarter time and 43 points at half time. What prices should you have accepted then?

In this blog I've analysed line betting results since 2006 and derived three models to answer questions similar the one above. These models take as inputs the handicap offered by the favourite and the favourite's margin relative to that handicap at a particular quarter break. The output they provide is the probability that the favourite will go on to cover the spread given the situation they find themselves in at the end of some quarter.

The chart below plots these probabilities against margins relative to the spread at quarter time for 8 different handicap levels.

Negative margins mean that the favourite has already covered the spread, positive margins that there's still some spread to be covered.

The top line tracks the probability that a 47.5 point favourite covers the spread given different margins relative to the spread at quarter time. So, for example, if the favourite has the spread covered by 5.5 points (ie leads by 53 points) at quarter time, there's a 90% chance that the favourite will go on to cover the spread at full time.

In comparison, the bottom line tracks the probability that a 6.5 point favourite covers the spread given different margins relative to the spread at quarter time. If a favourite such as this has the spread covered by 5.5 points (ie leads by 12 points) at quarter time, there's only a 60% chance that this team will go on to cover the spread at full time. The logic of this is that a 6.5 point favourite is, relatively, less strong than a 47.5 point favourite and so more liable to fail to cover the spread for any given margin relative to the spread at quarter time.

Another way to look at this same data is to create a table showing what margin relative to the spread is required for an X-point favourite to have a given probability of covering the spread.

So, for example, for the chances of covering the spread to be even, a 6.5 point favourite can afford to lead by only 4 or 5 (ie be 2 points short of covering) at quarter time and a 47.5 point favourite can afford to lead by only 8 or 9 (ie be 39 points short of covering).

The following diagrams provide the same chart and table for the favourite's position at half time.

Finally, these next diagrams provide the same chart and table for the favourite's position at three-quarter time.

I find this last table especially interesting as it shows how fine the difference is at three-quarter time between likely success and possible failure in terms of covering the spread. The difference between a 50% and a 75% probability of covering is only about 9 points and between a 75% and a 90% probability is only 9 points more.

To finish then, let's go back to the question with which I started this blog. A 46.5 point favourite leading by 42 points at three-quarter time is about a 69.4% chance to go on and cover. So, assuming you backed the favourite at $1.90 your expected payout for a 1 unit wager is 0.694 x 0.9 - 0.306 = +0.32 units. So, you'd want to be paid 1.32 units for your wager, given that you also want your original stake back too.

A 46.5 point favourite leading by 44 points at quarter time is about an 85.5% chance to go on and cover, and a similar favourite leading by 43 points at half time is about an 84.7% chance to go on to cover. The expected payouts for these are +0.62 and +0.61 units respectively, so you'd have wanted about 1.62 units to surrender these bets (a little more if you're a risk-taker and a little less if you're risk-averse, but that's a topic for another day ...)

AFL Players Don't Shave

In a famous - some might say, infamous - paper by Wolfers he analysed the results of 44,120 NCAA Division I basketball games on which public betting was possible, looking for signs of "point shaving".

Point shaving occurs when a favoured team plays well enough to win, but deliberately not quite well enough to cover the spread. In his first paragraph he states: "Initial evidence suggests that point shaving may be quite widespread". Unsurprisingly, such a conclusion created considerable alarm and led, amongst a slew of furious rebuttals, to a paper by sabermetrician Phil Birnbaum refuting Wolfers' claim. This, in turn, led to a counter-rebuttal by Wolfers.

Wolfers' claim is based on a simple finding: in the games that he looked at, strong favourites - which he defines as those giving more than 12 points start - narrowly fail to cover the spread significantly more often than they narrowly cover the spread. The "significance" of the difference is in a statistical sense and relies on the assumption that the handicap-adjusted victory margin for favourites has a zero mean, normal distribution.

He excludes narrow favourites from his analysis on the basis that, since they give relatively little start, there's too great a risk that an attempt at point-shaving will cascade into a loss not just on handicap but outright. Point-shavers, he contends, are happy to facilitate a loss on handicap but not at the risk of missing out on the competition points altogether and of heightening the levels of suspicion about the outcome generally.

I have collected over three-and-a-half seasons of TAB Sporsbet handicapping data and results, so I thought I'd perform a Wolfers style analysis on it. From the outset I should note that one major drawback of performing this analysis on the AFL is that there are multiple line markets on AFL games and they regularly offer different points start. So, any conclusions we draw will be relevant only in the context of the starts offered by TAB Sportsbet. A "narrow shaving" if you will.

In adapting Wolfers' approach to AFL I have defined a "strong favourite" as a team giving more than 2 goals start though, from a point-shaving perspective, the conclusion is the same if we define it more restrictively. Also, I've defined "narrow victory" with respect to the handicap as one by less than 6 points. With these definitions, the key numbers in the table below are those in the box shaded grey.

These numbers tell us that there have been 27(13+4+10) games in which the favourite has given 12.5 points or more start and has won, by has won narrowly by enough to cover the spread. As well, there have been 24(11+7+6) games in which the favourite has given 12.5 points or more start and has won, but has narrowly not won by enough to cover the spread. In this admittedly small sample of just 51 games, there is then no statistical evidence at all of any point-shaving going on. In truth if there was any such behaviour occurring it would need to be near-endemic to show up in a sample this small lest it be washed out by the underlying variability.

So, no smoking gun there - not even a faint whiff of gunpowder ...

The table does, however, offer one intriguing insight, albeit that it only whispers it.

The final column contains the percentage of the time that favourites have managed to cover the spread for the given range of handicaps. So, for example, favourites giving 6.5 points start have covered the spread 53% of the time. Bear in mind that these percentages should be about 50%, give or take some statistically variability, lest they be financially exploitable.

It's the next percentage down that's the tantalising one. Favourites giving 7.5 to 11.5 points start have, over the period 2006 to Round 13 of 2009, covered the spread only 41% of the time. That percentage is statistically significantly different from 50% at roughly the 5% level (using a two-tailed test in case you were wondering). If this failure to cover continues at this rate into the future, that's a seriously exploitable discrepancy.

To check if what we've found is merely a single-year phenomenon, let's take a look at the year-by-year data. In 2006, 7.5-to 11.5-point favourites covered on only 12 of 35 occasions (34%). In 2007, they covered in 17 of 38 (45%), while in 2008 they covered in 12 of 28 (43%). This year, to date they've covered in 6 of 15 (40%). So there's a thread of consistency there. Worth keeping an eye on, I'd say.

Another striking feature of this final column is how the percentage of time that the favourites cover tends to increase with the size of the start offered and only crosses 50% for the uppermost category, suggesting perhaps a reticence on the part of TAB Sportsbet to offer appropriately large starts for very strong favourites. Note though that the discrepancy for the 24.5 points or more category is not statistically significant.

Waiting on Line

Hmmm. (Just how many ms are there in that word?)

It's Tuesday evening around 7pm and there's still no Line market up on TAB Sportsbet. In the normal course this market would go up at noon on Monday, and that's when the first match is on Friday night. So, this week the first game is 24 hours earlier than normal and the Line market looks as though it'll be delayed by 48 hours, perhaps more.

Curiouser still is the fact that the Head-to-Head market has been up since early March (at least) and there's an historical and strong mathematical relationship between Head-to-Head prices and the Line market, as the following chart shows.

The dark line overlaid on the chart fits the empirical data very well. As you can see, the R-squared is 0.944, which is an R-squared I'd be proud to present to any client.

Using the fitted equation gives the following table of Favourite's Price and Predicted Points Start:

Anyway, back to waiting for the TAB to set the terms of our engagement for the weekend ...