In an earlier blog we found that the score of the Home team carried more information about the final game margin than did the score of the Away team. One way of interpreting this fact is that, given the choice between improving your prediction of the Home team score or your prediction of the Away team score, you should opt for the former if your goal is to predict the final game margin.
While that's true, it turns out that it's less true now than it once was.
To investigate this issue, today I thought I'd delve more deeply into the relationship between the scores of the two teams in each game and the extent to which they contain information about three different game outcome metrics: game margin, total score and game result.
I'll start by using linear correlation as my measure of information content.
(As is now customary, images can be clicked to access larger versions.)
Predicting Game Margins
The first block of data provides information about the correlation between team score and game margin. So, for example, the +0.77 represents the average - averaged for each of the 115 seasons taken separately - of the correlation between the Home team scores and the game margins within a season. In a typical season then, about 50% of the variability in game margin can be explained by variability in Home team scores. The next 6 figures on that same row provide the same average but for different groups of seasons. From those you can see that the correlation between Home team scores and game margins has been fairly consistent across time. Put another way, the information content of the Home team score in terms of predicting the final game margin has been similar across the entire history of the VFL/AFL.
That's also been broadly true of the Away team score, though there's been signs in more recent periods of an increased (negative) correlation. The columns at the far right of the table provide the relevant correlations for the 6 most recent completed seasons, and you can see there the relatively large correlations between Away team scores and game margin for the past 4 seasons in particular.
In the third row of this block you can find the proportion of seasons for which the Home team scores have been more highly correlated with game margins than have Away team scores. For the season groups up to and before 1980, about 80-90% of seasons have had this characteristic. In the last two season groups, however, this proportion has been diminishing - in the 2001-2011 block it's been true for only 6 of the 11 seasons.
The only reasonable conclusion is that the information content of Away team scores in terms of predicting game margins, has been increasing and is now roughly at the same level as that of Home team scores.
Predicting the Total Score
We find a similar story in the second block of data, which relates to the information content of team scores in predicting the aggregate points scored in each game.
Here the correlations are smaller, both for Home team scores and for Away team scores, but again we find that the information content of the Away team scores has been increasing to roughly match that of Home team scores. Last year was something of an exception in this regard.
Predicting the Game Result
Perhaps instead you're more interested in predicting the game winner. Here - treating the game result as a variable that takes on the value 1 if the Home team wins, 0 if the Away team wins, and 0.5 if the game finishes as a draw - we find lower correlations still. But we also find that, for the periods 1980-2000 and 2001-2011, including for each of the past 4 seasons, Away team scores have contained more information about game results than have Home team scores. So, if your interest is in tipping winners you should be more focussed on improving your Away team predictions than your Home team predictions.
Correlations Between the Home and Away team Scores
Across VFL/AFL history there's been a small negative correlation between Home team and Away team scores. In other words, in games where the Home team has scored more points than the average Home team, the Away team in that same game has tended to score fewer points than the average Away team. You can see from the table that this correlation has been increasing (in absolute terms) in recent times, especially in the past 4 seasons, reflecting an increasing propensity for blowout victories, about which I've written previously.
Team Score Standard Deviations
One of the reasons that Away team scores have become more highly correlated with game outcome measures is because the variability of their scores has started to match that of Home team scores, as reflected in the final row of the table above.
Mutual Information Measures
For today's blog I've used a normalised measure of mutual information, a number of which have been recommended by different people at different times and for different purposes. The variant I've used here normalises by dividing the measured mutual information between two variables by the minimum of the entropies of each of them. This produces a measure that is (0,1) bounded and that is recommended, for example, in this journal article.
Here's what we get using this normalised measure:
The numbers here all tell much the same story about the relative information content of Home scores versus Away scores:
- The information content of Away team scores is moving closer to (and in some seasons exceeding) the information content of Home team scores in relation to predicting game margins and total scores
- The information content of Away teams scores is now generally greater than that of Home team scores in predicting game results
Regardless of whether your interest is in predicting game margins, game score aggregates, or game results, producing accurate estimates of Away team scores is more important now that it's ever been. So much so in the case of predicting game results in fact, that the accuracy of Away team predictions is now more important than the accuracy of Home team predictions.
One of the reasons for this is likely to be the diminishing importance of home ground advantage, precipitated by shared home grounds and, more recently, weaker interstate teams.