The AFL draw remains imbalanced, with teams meeting only five of their 17 potential opponents twice, and meeting the other 12 teams only once. In constructing the draw, the League can respond to the imbalance by either:

1. seeking to minimise the impact of the imbalance on the competition prospects of the 18 teams, or
2. taking the opportunity to reduce the impact of difference in underlying team strengths by instead  seeking to equalise the average quality of the opponents faced by each team

These objectives are mutually incompatible. The pure logic of the situation is that stronger teams should face easier draws because, absent an ability to play themselves, the average quality of the available opponents must be lower for them than for weaker teams. Any attempt to equalise the quality of opponents faced by all teams - unless all teams are of similar quality - must skew the outcome that would otherwise be achieved by adopting an all-plays-all home and away draw or by making a random sample from such a draw. 

Very clearly the League has chosen to pursue the second of these objectives while simultaneously accommodating a variety of historical and financial constraints. Doubtless this makes for a better competition from a spectator's viewpoint, but a complete discussion of the fairness or otherwise of the draw should encompass both differences in teams' "schedule strength" (ie the average quality of their opponents) as well as the extent to which the draw alters each team's finals prospects relative to what they'd be under an all-plays-all home and away schedule. 

TEAM RATINGS AND HOME GROUND ADVANTAGE

To assess each team's schedule strength we need to quantify the average quality of the opponents it faces, adjusting for the effects, if any, of Home Ground Advantage (HGA) and Interstate travel.

A team's base quality is reflected in its ChiPS Rating, an ELO-style team rating system defined such that the difference between two teams' Ratings is an estimate of the margin of victory that would be expected if they met in a contest on a neutral ground. For today's blog I've started with the ChiPS Ratings as they stood at the end of the 2014 season and then adjusted them in the traditional manner by taking, for each team, 61% of its final Rating and adding 390 Rating Points (RPs) to the result. This adjustment serves to drag the Ratings of all teams closer to the all-team average of 1,000. The 61% figure is based on an optimisation calculation that was performed at the time ChiPS was devised, and the 390 figure preserves the 1,000 all-team Rating average.

ChiPS has it that the Hawks are the strongest team in the competition, about 4 points better than the Swans and almost 7 goals better than the Saints. It Rates ten teams as above-average and eight as below-average, with Ratings at the top slightly more compressed than those at the bottom: the ten above-average teams span only a 17 RP range, while the eight below-average teams span almost a 20 RP range.

For many teams, playing them at home represents a different challenge to playing them away, so any complete assessment of a team's schedule requires that we account for any HGA. To estimate the HGA that teams enjoy at the ground - or, in some cases, grounds - where they play the majority of their home games I calculated the average under- or over-performance of every team when playing at a home ground, relative to the quality of the opposition it was facing at the time. So, for example, if the Hawks, Rated 1,020 faced the Cats, Rated 1,015 and won by 8 points, that would be a 3 point over-achievement by the Hawks since the difference in Ratings alone would suggest a 5-point victory was to be expected.

I looked at all games played since 2010 and rounded my estimates of HGA to the nearest half goal, setting HGA to zero whenever the actual average came out negative. Five teams are assessed as enjoying no significant HGA at any of their most-common home grounds: Carlton, Collingwood, GWS, Melbourne, and the Western Bulldogs. Every other team enjoys at least a half-goal advantage at one of their home grounds. Port Adelaide has the largest HGA of 4 goals when playing at the Adelaide Oval though that estimate carries a large standard error as it's based on relatively few games. Geelong's 3.5-goal HGA at Kardinia Park is the largest advantage for any team at a venue with a longer history. Most teams have HGAs in the 0.5- to 2-goal range.

Empirical evidence suggests that teams enjoy an additional fillip when they face a team that has had to travel interstate to meet them when they have not. I estimated the value of this to be about 6 points, and this advantage is in addition to the HGA.

To assess the quality of a team's opponents in a particular game then, we take the opponent's base Rating and adjust it for any HGA or Interstate advantage that the opponent might enjoy by virtue of the venue at which the game is to be played. So if Sydney were to face Hawthorn at the SCG, Sydney's base Rating of 1,015.2 would be boosted by 18 points, 12 for the HGA and 6 for the Interstate Advantage.

By performing calculations of this sort for every game in the 2015 Draw we can arrive at a strength of schedule figure for every team.

STRENGTH OF SCHEDULE

Based on the average adjusted quality of the teams they face, Sydney has the toughest draw in 2015. Their average opponent carries an adjusted Rating of 1,007.3, which is half a point higher than the average faced by any other team. The Swans' away draw looks particularly challenging as they meet Fremantle, Port Adelaide, Geelong, West Coast, Hawthorn and the Roos away and interstate, which translates into five games against opponents Rated about 1,020 or more on the day. 

Fremantle faces an away schedule of a similarly daunting nature as the Swans, though they don't, of course meet themselves and they also meet the Eagles without the need to bring cabin luggage. They do, however, face a 1,016 Rated Adelaide at the Adelaide Oval.

Richmond have the third-toughest schedule overall and the toughest schedule of all teams away from home. Melbourne have the third-easiest home draw and the third-easiest away draw which, combined, makes for the easiest overall draw Rated some 1.5 RPs lower than any other team.

As it turns out, the teams with the six least-difficult schedules are are all Victoria-based, but this has little to do with the relative levels of Interstate Advantage enjoyed and endured by them.

Amongst the five teams, St Kilda and Collingwood both endure twice more often than they enjoy, the Roos endure once more often than they enjoy, and the Blues enjoy and endure in equal measures. Only Melbourne can point to a nett surplus, enjoying the Advantage five times and enduring it only twice.

The assessed difficulty of the draw for most other teams is similarly unrelated to the extent of their travel. Gold Coast, for example, enjoy the Interstate Advantage in 11 games and face opponents enjoying it only 7 times, for a net surplus of 4 games, higher than the surplus for any other team, Their draw, however is Rated only the tenth-easiest.

Also, Sydney, the team with the toughest draw enjoy and endure the Interstate Advantage on the same number of occasions, 10 each, which places them in the middle of the pack in terms of the nett effect of this Advantage across the season.

(Note that the figures in the "Endure" column do not necessarily reflect the amount of interstate travel required of a team in the 2015 draw since games necessitating travel by BOTH teams - such as for games in NT, the ACT or NZ - are not counted there. This is because neither team is assumed to enjoy the Interstate Advantage in these games.)

The table below provides the adjusted Ratings of the opponents faced by every team in the 2015 draw. You can also use the table to identify, for each team, the five opponents they face twice and the 12 opponents they face only once.

Melbourne aside, there's only about a 3.5-points per game difference between the average opponent Rating of the team with the toughest draw (the Swans) and the average opponent Rating of the team with the next-to-easiest draw (the Saints). On this measure then I think you'd have to say that the draw does a reasonable job of minimising the differences in schedule strengths across the teams. 

Another, simpler method of assessing the draw's balance is to look at the average 2014 home-and-away season ladder finish of a team's opponents. This approach ignores any HGA or Interstate Advantage and, in a sense, assesses playing the Hawks as being 18 times "harder" than playing the Saints, but it should still highlight any major imperfections in the draw.

On this metric, Port Adelaide have the toughest draw as they face opponents whose average ladder finish was just under 9th. The Dogs have the easiest draw, their opponents averaging a whole ladder spot lower at just over 10th. 

This data too suggests that the schedule strengths of the teams are fairly well balanced.

LADDER IMPLICATIONS OF THE IMBALANCED DRAW

As I mentioned earlier, balancing team schedule strength of necessity alters the finals chances of teams relative to what they'd be in an all-play-all twice schedule. To assess the size of these effects we estimate the difference between each team's ladder prospects under the 2015 schedule as proposed and compare this to a similar assessment performed assuming an all-play-all, home and away season.

For this purpose I've run two sets of 100,000 simulations of the 2015 season, the first using the schedule as published and the second supplementing the schedule by also simulating the "missing" 108 games required for such an all-play-all twice schedule.

In both sets of simulations the result of every game is assumed to follow a Normal distribution with a mean equal to the adjusted Ratings difference of the two teams and a standard deviation of 36 points. The venue for all missing games was set as the ground with the highest HGA for the home team. Essendon, for example, get to play all of their missing games at the MCG rather than Docklands, because their HGA is higher at the G than at Docklands; Richmond are assumed to do the opposite because their HGA is higher at Docklands.

THE RESULTS

Across the 100,000 simulations of season 2015 as it is scheduled, most teams finish in every ladder position at least once. The exceptions are Port Adelaide, who never finish last, and Melbourne, who never finish first.

These simulation results rank the teams' chances similarly to their prices on the TAB AFL Futures market for the 2015 Premiership. The major differences in the rankings are that:

• Port Adelaide is ranked 2nd in the simulations but 3rd in the TAB market
• Richmond and Essendon are both ranked above West Coast and Adelaide by the TAB
• Carlton is ranked below Collingwood and the Gold Coast on the TAB

Port Adelaide's elevated position is probably due at least in part to the generous 4-goal HGA I've assessed for them when playing at the Adelaide Oval. In a future blog I'll estimate the sensitivity of the teams' simulated rankings to this and other assumptions I've made about HGAs. 

Some other features of these simulations are that:

• Only three teams - Hawthorn, Port Adelaide and Sydney - are assessed as better than even-money chances for a Top 4 finish
• Eight teams - Hawthorn, Port Adelaide, Sydney, Fremantle, Geelong, the Kangaroos, West Coast and Adelaide - are rated better than even-money chances for a Top 8 finish. The first six of these teams are finalists from 2014, while the Eagles and Crows have taken the Dons' and Tigers' 2014 spots.
• St Kilda are slightly more likely than the Dees to take the Spoon.

Before we review the results of the simulations in which the missing 108 games have been reinstated, it's useful to review the overall impact of including these games on the average strength of each team's opponents.

Whilst the teams that Geelong play in the actual 2015 schedule represent only the 4th-toughest assemblage of opponents, the inability to play every team twice hurts them more than any other team. Adding the missing 12 contests to the Cats' schedule reduces the average Rating of their opponents by over 2.5 RPs.

Sydney are next-most affected, their average opponent Rating being almost 2 RPs higher for the as-published schedule than it would be under a full 306 game season. Fremantle, Hawthorn, Richmond and Port Adelaide are the only other teams whose average opponent strength declines in moving to the full season.

Melbourne benefits most from the abridged season, facing an average opponent almost 4 RPs weaker than it otherwise would. St Kilda and GWS also enjoy relatively large average opponent discounts under the AFL's scheduling.

The results of the simulations very much reflect the insights in this table.

• Hawthorn is 8% points less likely to win the Minor Premiership, 8% points less likely to finish in the Top 4, and 2% points less likely to finish in the Top 8 under the 2015 draw than they would be under an all-play-all twice schedule
• For Geelong the equivalent figures are 1%, 11% and 12%, and for Sydney they're 1%, 8% and 5%.
• There are also impacts on Port Adelaide, Fremantle and Richmond, though not in terms of winning the Minor Premiership. Richmond in particular sees its Top 8 chances significantly diminished under the actual 2015 draw compared to what they'd be in a full 306 game season: they plummet from 61% to 47%, the largest decline of any team. Whilst, in an absolute adjusted opponent-Rating sense, the impact of missing games is only fifth-harshest for them, their likely ladder situation is such that the inequities they face take on a much larger significance in terms of Finals prospects.

At the other end of the table, Melbourne's Wooden Spoon prospects are significantly altered by the draw. Under the schedule as it stands they're assessed as a 24% chance for the Spoon; in a full 306 game season they'd be 34% chances instead.

For completeness, here are the charts for the 100,000 simulations of the full 306 game season.

CONCLUSION

The various analyses suggest that the League has done an admirable job in equalising teams' Strength of Schedule but that, inevitably, in pursuing that goal, they've differentially affected teams' ladder prospects.

Sydney, Fremantle, Richmond, Geelong,  Brisbane Lions, Port Adelaide and Adelaide have the worst of the draw in terms of Strength of Schedule, while Melbourne has the best of it, but from the viewpoint of September involvement, Richmond, Geelong, Fremantle and Sydney are most entitled to feel aggrieved, while West Coast, Collingwood, Carlton and the Gold Coast have most to celebrate.