Today another dive into the scoring event data provided by Paul over at afltables, specifically to look at the patterns in successive Scoring Events. How likely, for example, are we to see a Home team Goal as the next Scoring Event after another Home team Goal?
Here, firstly, are the figures for all Quarters and all Seasons in the data (ie from Round 1 of 2008 to the end of the 2014 Home-and-Away Season). Each entry in the table represents the frequency with which a given pair of Events occurred in the course of a game.
For example, the 6.7% in the top left corner tells us that about 1 in 16 of all pairs of successive Events (which I'll call Event Pairs) in all games were a Home team Goal followed by another Home team Goal. This is the most common Event Pair in the table, the second-most likely Pairs being an Away Goal followed by a Home Goal, and an Away Goal followed by another Away Goal, both of which represent 5.8% of all Event Pairs.
Note that, in creating this table I've treated the starts and ends of quarters, as well as the scoring of points by either team, as Events. The SOQ row relates to Event Pairs where the first Event was the Start of the Quarter, and the EOQ row to Event Pairs where the second Event was the End of the Quarter.
From the SOQ row we can deduce that the most common first Scoring Event in a Quarter has been a Home Goal, and from the EOQ row we can similarly deduce that the last Scoring Event in a Quarter is also most often a Home Goal.
Rushed Behinds are relatively rare events, Event Pairs involving successive Rushed Behinds rarer still, with less than 1% of all Event Pairs being of this type.
A comparison with the same table produced using only 2014 data reveals that back-to-back Goals by either of the teams has been a less frequent occurrence this season than it has been during the period as a whole. Back-to-back Home Goals represent only 6.6% of Event Pairs (down from 6.7%), back-to-back Away Goals only 5.3% (down from 5.8%), and back-to-back Home then Away or Away then Home Goals represent only 10.8% of Event Pairs (down from 11.4%). In aggregate, back-to-back Goals are down from about 23.9% of all Event Pairs to about 22.7%
These declines can be partly attributed to the increase in Rushed Behinds (up from 8.8% to 9.5%) but also due to the general decline in Scoring Events per game (EOQ Events represent 7.7% of all Events in 2014, up from 7.4%).
In 2014, Quarters have also been significantly more likely to start with an Away Goal - indeed, more likely than they've been to start with a Home Goal - and they've also been more likely to finish with a Goal, especially a Home Goal.
INDEPENDENCE OF SCORING EVENTS
One obvious question to ask of the Event data is whether or not it supports the statistical notion of independence or, in lay terms, whether the next Event is or is not influenced by the previous Event.
The table at right records the difference between the actual frequency of a particular Event Pair and what would be expected if Events were statistically independent. For example then, if the likelihood of a subsequent Home Goal were independent of whether or not the previous Event were a Home Goal we'd expect that the joint probability of a Home Goal / Home Goal Event Pair would be equal to the probability of a Home Goal as the 1st Event multiplied by a Home Goal as the 2nd Event. The table suggests that these two Events are nearly independent, the excess frequency being only 0.1%.
A Home Goal, however, is followed by a Home Behind more often than would be indicated if independence were in play, and is also followed by an Away Goal or Behind less often than such an assumption would imply.
Similarly, an Away Goal (or even an Away Behind) slightly depresses the likelihood of an ensuing Home Goal or Behind and slightly enhances the likelihood of a follow-up Away Goal or Behind.
All of which is much as we might have expected were we subscribers to the notion that there is some momentum in AFL Scoring behaviour, albeit only a mild form.
A look at the same table but only for Season 2014 reveals that a Home Goal here too elevates the relative likelihood of a follow-up Home Goal or Behind (especially the latter) and depresses the chances of an ensuing Away team Goal or Behind, moreso than it's done more widely across the entire period.
An Away team Goal makes an Away team Behind more likely as the next Scoring Event, but also makes an Away Goal marginally less likely. In addition, an Away team Goal reduces the likelihood of an immediately subsequent Home Goal or Behind moreso than has been the case across the period as a whole.
Returning to an all-season view but now considering each Quarter in isolation, we find that the profile of Event Pairs differs only slightly across the Quarters.
The Home Goal / Home Goal sequence is the most common in all four Quarters, but most common of all in 4th Quarters and least common in 2nd Quarters. Away Goal / Away Goal sequences have being most frequent in 3rd or 4th Quarters and least frequent in 1st Quarters.
Rushed Behinds have been commonest in 2nd Quarters where they represent about 9.2% of all Events, and least common in 4th Quarters where they represent only 8.3%.
Home Goals are the last Scoring Event of the Quarter most often in 2nd Quarters where they fill this role 32% of the time (ie 2.4% / 7.5%). Conversely, in 4th Quarters, they assume this status only 27% of the time (ie 2.0% / 7.3%).
Another way of presenting this data is to have it answer the question: if I've just witnessed Event X, what's the likelihood that I witness Event Y next?
So, for example, in the table for 1st Quarters below, the first row provides us with the frequencies of the various possible Event Types given that the previous Event Type was a Home Goal. Home Goals follow Home Goals in 1st Quarters, therefore, 26.5% of the time. And, perhaps most importantly for those who like to wager on the First Scoring Type market, Home Goals follow the Start of 1st Quarters 28.6% of the time meaning that, absent any other relevant data, a fair price for this Event is about $3.50.
Looking down the columns we can infer after which Event Type a particular Event Type is most likely. In 4th Quarters, for example, a Home Goal is more likely to follow the Start of the Quarter than any other Event whereas a Home Behind is more likely to follow a previous Home Behind than any other Event. Similarly, a Rushed Home Behind is more likely to follow another Rushed Home Behind.
An Away Goal, however, is more likely to follow an Away Rushed Behind, an Away Behind more likely to follow the Start of the Quarter, and an Away Rushed Behind is more likely to follow another Away Rushed Behind.
Comparisons with 2014 data alone are again instructive. Back-to-back Home Goals have been more common in 1st Quarters (7.2% vs 6.8%) and 3rd Quarters (7.4% vs 6.6%) in 2014, yet less common in 2nd Quarters (5.9% vs 6.5%) and 4th Quarters (6.1% vs 6.9%).
Back-to-Back Away Goals have been rarer in 2014 more generally, but especially in 3rd and 4th Quarters where their prevalence has been down by 10-15% compared to the entire period. In 3rd Quarters in 2014 only 5.4% of Event Pairs have been successive Away Goals compared to an all-season average of 6.0%; in 4th Quarters the equivalent figures are 5.2% and 6.0%.
The increase in the prevalence of Rushed Behinds has been particularly prominent in 2nd and 3rd Quarters. They've accounted for more than 10% of all 2nd and 3rd Quarter Events, which represent increases over the all-season averages of about 10% and 17% respectively.
Finally, a look at Event Incidences conditioned on the previous Event.
Only in 3rd Quarters this season has a Home Goal been more likely than an Away Goal to be the first Scoring Event of a Quarter. In Final Terms, Away Goals have been the first Scoring Event almost 20% more often than Home Goals.
Goals, by either side, have been more commonly the first Scoring Event of most Quarters this season compared to the all-season average. In 1st Quarters the first Scoring Event has been a Goal 59.6% of the time (compared to the all-season 52.9% average), in 2nd Quarters 54.6% (vs 52.2%), and in 4th Quarters 56.6% (vs 53.1%). Only 3rd Quarters have produced the opposite outcome with just 49% of first Scoring Events being Goals in 2014 compared to a 50.8% all-season average.
Clearly there are broadly stable patterns in Event Pair frequencies across Seasons and between Quarters. Goals are most often followed by more Goals, Goals are more common than Behinds, and Behinds more common than Rushed Behinds, Scoring by one team tends to mildly depress Scoring by the other, at least in terms of the immediately subsequent Scoring Event.
There are though some differences in the Quarter-to-Quarter profiles and these can change from one season to the next. Season 2014, for example, differs from the 2008 to 2014 period in aggregate in terms of the relative likelihood of specific Event Pairs and in terms of the base frequency of particular Scoring Types. Home Goal / Home Goal Event Pairs have, for example, been more common in some Quarters and less common in others, and Rushed Behinds have been more prevalent in 2014 generally.
As we've seen before, football statistics are a combination of medium-term stability and shorter-term relative chaos. Once more I'm reminded of the difference between climate and weather ...