Measures of Game Competitiveness

All this analysis of victory margins, and a query from Dan about a recent blog post, has had me wondering about victory margin as a measure of the competitiveness of games.

Within a given era - say 10 years or so - during which the average points scored per game doesn't vary by too much, victory margin seems to be a reasonable proxy for competitiveness, but if you want to consider a broader swathe of AFL history, it strikes me as being deficient.

The average number of points scored in a game of footy has more than doubled since the competition's inception and, last year, was up by almost one-third on the average for season 1960, the low point around that era.

An alternative metric, which adjusts for the fact that scoring levels have tended to increase over time, is the Winners' Average Percentage of Scoring, which is calculated for each game by taking the winning team's score and dividing it by the sum of the winning and losing teams' scores. To arrive at an average for the season these game-by-game percentages are averaged. (This ensures that each game has an equal weighting. A practice of pooling all winning teams' points scored and dividing this by the sum of all points scored during the season would increase the weighting of high-scoring contests and decrease the weighting of low-scoring contests.)

The chart below shows this metric for every season.

The correlation between Average Victory Margin and Average Winners' Percentage of Scoring is quite high (about +0.84) if we look only at the last 40 seasons, but the growth in total points scored relative to the preceding periods virtually eliminates the correlation (it's +0.04) if the entirety of the history of AFL/VFL is included.

Another alternative measure of game competitiveness that can also legitimately be used across the span of AFL/VFL history is the percentage of games in a season in which the winning team scored less than 55% of the points. Last season, where the average game saw about 186 points scored, this would equate to a score-line of about 102-84 or closer.

Here's that metric charted across history (it's the line in blue).

This new metric is highly correlated with the previous metric, even if the entirety of the time period charted is included (it's -0.84).

So what does this all mean if the topic for discussion is whether the competition is becoming less competitive?

Well, both the two newly proposed metrics - as well as the original Average Victory Margin metric - spiked last year, the Average Winners' Percentage of Scoring reaching over 60% for the first time since 1996 and only the second time since 1971, and the other metric, the proportion of games in which the winner secured less than 55% of the total points scored, falling to just 28.6%, the lowest it's been since 2004. 

These are, doubtless, troubling movements in these metrics and do point to a reduction in game competitiveness, at least relative to more recent times. But, adopting a longer historical time frame, they perhaps suggest a less serious reduction than might be implied by looking at changes in Average Victory Margins alone. The Average Victory Margin for season 2011 was the 6th highest ever, whilst the Average Winners' Percentage of Scoring measure was only the 26th highest, and the proportion of games in which the winner secured less than 55% measure (a measure crying out for an abbreviation if ever there was one) was ranked only 33rd.

The point is, I suppose, that the rate at which teams score points these days means that large victory margins don't necessarily mean that games are uncompetitive, or a foregone conclusion long before they ended. These other metrics, arguably, provide a better measure of game competitiveness, and they paint a bad but not catastrophic picture.

Still, it'd be nice to have another season like 2002, when over 38% of the contests finished with the winning team securing less than 55% of the points, the average winning team secured just 58.5% of the points, and the average victory margin was only 31.7 points per game. With GWS entering the competition this season, that might just be a bit much to wish for.