Making History with VFL/AFL Final Scores

If the historical game data that I have is correct, we've gone very close to witnessing history this weekend, with the Hawthorn v Fremantle final score of 137-79 coming within a kick of finishing, instead, as a 131-79 or as a 138-79 win. Neither of these final scores have ever been recorded in the 14,373 game history of the VFL/AFL between 1897 and 2013.

Further analysis of this week's results reveals that Sydney's 134-71 win was also just a kick away from producing yet another never-before-seen final score, 133-71, and a scan of last week's results uncovers the startling truth that both the 139-91 result in the Hawthorn v Brisbane Lions game, and the 116-46 result in the Fremantle v Collingwood game were, in fact, first time ever outcomes.

Time for a chart.

View fullsize

Each tile on the chart relates to a specific final score, with the winning team's score depicted on the x-axis and the losing team's on the y-axis. The colour of the tile denotes the frequency with which that score has been recorded across all of history (excluding 2014), darker colouring denoting greater frequency.

The white spots designate score pairs that have never been witnessed and they are surprisingly prevalent. For example, if we restrict our attention to the 7,381 score pairs where the losing and winning teams scores are in the range (40,160), which includes about 86% of all the games ever played, 2,532 of those pairs, or 34% of them, have never been registered.

Restricting ourselves further still to the range (70,130), which now includes about 38% of game results, we find that 200 of the 1,891 combinations, or about 11% have, similarly, never been the final score in a game.

So, it's not all that surprising that we should be able to find a slew of recent results that are either unique or within a kick or so of uniqueness. If we take a final score and then add or subtract a single behind or a single goal to both teams' scores, changing only one of the team's scores at a time when we do so, we generate eight new results that are different by only a single kick. That gives us eight more chances, along with the original score, to make history.

It's fascinating to look at the frequency counts in the (70,130) range, which I've produced as another heatmap below.

View fullsize

Restricting the range of scores for the teams allows me the space to record the frequency count in each cell, which I think helps, among other things, to make the zeroes more prominent - for example, the tantalising strip of zeroes for winning scores of 123 and all losing scores in the range 114 to 119 jumps out.

Other quirks provide more evidence for the lumpiness of randomness: why, for example, have there been seven 79-all draws but no 80-all or 82-all draws, and just a single 81-all draw? And, why have there been only four final scores that have occurred on more than 10 occasions: 12 examples of near-draws in scorelines of 80-79 and 70-69, and 11 examples of 98-79 and 79-65 scorelines?

And, lastly, what exactly is the attraction of a 119-104 scoreline, which has been recorded nine times when other, nearby scores have struggled to notch up as many as four appearances?

Rhetorical questions all of them for the most part I know, but it's useful, I think, to occasionally be reminded how structured the results of essentially random processes can appear.