Who's Best To Play At Home?

The 2015 AFL Schedule is imbalanced, as have been all AFL schedules since 1987 when the competition expanded to 14 teams,  by which I mean that not every team plays every other team at home and away during the regular season. As many have written, this is not an ideal situation since it distorts the relative opportunities of teams' playing in Finals. 

As we'll see in this blog, teams will have distinct preferences for how that imbalance is reflected in their draw. Specifically, what we'll find is that, given a choice in relation to two teams that the imbalanced schedule will mean they'll meet only once, teams will almost always have clear preferences about which they'd rather meet at home and which they'd rather meet away.

For this analysis we'll be assuming that final game margins are distributed as Normal random variables with a mean equal to some fixed amount reflecting a combination of the relative underlying abilities of the participating teams and an allowance for Home Ground Advantage (HGA). Further, we'll assume that the standard deviation of this Normal distribution is 37, although the argument doesn't hinge on this.

THE ANALYSIS

Let's consider a range of plausible scenarios, each involving two teams, one of which is stronger than our team and the other of which is weaker. Across the scenarios we'll vary the size of the relative underlying superiorities in ability, and of our own and our opponents' HGA. Within a given scenario we'll assume that both the weaker and the stronger opponents have the same HGA as we don't want this to be the source of any preference for playing one at home and the other away. The sole source of that preference will, instead, be down to a combination of relative abilities and relative HGAs.

We'll determine the preference for one draw over another based on the sum of the probabilities of our team's victory across the two contests with these teams under the two possible configurations.

The table below provides the results for 31 different scenarios.

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The first block models the situation where our team is 5 points stronger than the weaker team, Team 1, and 5 points weaker than the stronger team, Team 2. The first row of this block assumes that our own HGA is 5 points and that of both our opponents' 10 points. 

In this scenario we're faced with two possibilities:

1. playing Team 1 at home with a net 10 point positive superiority (the 5 points of underlying superiority plus 5 more for the HGA) and Team 2 with a net 15 point deficit
2. playing Team 1 away with a net 5 point deficit and Team 2 at home with no deficit at all

When we crank the numbers through the relevant Normal CDF we find that we would, very narrowly, prefer to play the weaker team, Team 1, at home, and the stronger team, Team 2, away. In doing this we're 0.3% of a game better off than we'd be were we to play the two teams with the venues switched.

Other rows in this same block consider other values for the respective HGAs and, in some cases, see us preferring to play the stronger team at home, and sometimes away.

In that first block, the differences are all very small - less than 1% - but we do find some larger ones in, for example the second row of the third block where the difference is over 4%. To give that some context, a 4% increase in probability is equivalent to about 4 points in an otherwise even-money contest.

I've tried but been unable to devise any heuristic by which to succinctly describe the situations where it's preferable to meet the stronger team at home and when to meet the weaker team at home. At the moment, it seems as if the only way to determine a preference is to calculate the numbers, but I will keep striving to find a simple summary.

SUMMARY AND CONCLUSION

It's true that the differences we see in the table above are relatively small, even at their largest in absolute terms, but bear in mind that this calculation is for only a single pair of teams. Since every team in the current competition faces 12 teams only once, there will be 66 (ie 12 x 11 / 2) such calculations to make for every team. Those 1 and 2 percents could well amount to something more significant if enough of those 66 are in the same direction.

To me, the most interesting aspect of this analysis is that it raises the possibility of performing a much larger analysis, assessing the draw for each team to see how many of the two-teams-met-once matchups have been favourably scheduled from their viewpoint and how many have been unfavourably scheduled.

But that's for another day.