You are outside McDonalds. If there is a 20% chance of someone walking out with a Big Mac, and a 25% chance of someone walking out with some fries, what’s the chance that someone has a Big Mac and fries?
A first guess might be about 20% x 25% = 5%. But as you know my friends, there is a conspiracy within the arches to associate the two – hence my guess would be about 15%. The ghost of Ray Kroc lives on.
Which got me thinking about greyhound quinellas. Are there boxes that associate well and others which don’t?
Well let’s disregard railers, fast starters, common betting knowledge, and all other items that supposedly inform how a race shapes up, and for the sake of mathematical madness run an analysis.
I have a database of 1,474 races held at Manakau from 2010 through to mid-2012. Table 1 summarises the results of the relative performance of boxes. Boxes 1 and 8 have the highest frequencies of occurrence respectively for win and place.
Table 1: Frequency of winners and placegetters with market returns.
Column 6 (ratio) simply gives an indication of observed quinellas over what is calculated to be expected. To add a little statistical rigour the z score is calculated, being the number of σ’s the observed is away from the expected – e.g. Quinella 12: (67 – 54.7)/7.24 = 1.70.
Table 2: Expected and observed incidence of quinellas.
High positive z scores should give us suspicion of positive association between the boxes, and low negative z scores means they disadvantage each other. It’s not easy to see in a table so here it is colour mapped, yellow being no particular impact, green positive, red negative.
Looks to me like the neighbours at both ends of the street get on, but in the middle there’s an argument about a lawnmower.
Figure 1 Z score map
Moving on to the money, the TAB takeout for the quinella pools is 21%. Hence a market efficiently factoring box interaction effects into its returns would be expected to have a return of approximately $0.79 over many races.
As might be expected, the quinella combinations with decreased incidence over that expected generally achieved returns of less than $0.79 – quinella combinations 25, 28 and 47 had a particularly low return of around $0.50 on the dollar. This would indicate that the market overrates the chance of success, or alternatively stated, it is apparently not common knowledge that these are poor performing combinations.
Of particular interest is combination 68 – not only was it observed more often than expected, but its return suggests a positive expectation of more than 30%. A check for extreme data within the race results revealed a single win dividend of $131.40, however that aside, the result is outstanding.
Well while you bore yourself silly betting 6 and 8 for the quinella at Manukau for the rest of the year, I’m off for some Maccas… and I might just grab the fries.