The 2012 Draw: Winners and Losers

It's February, and the Test and T20 cricket seasons are over, so it must be about time for our annual look at the footy draw for the upcoming season.

We've 23 home-and-away rounds again this season. In twenty of them all 18 teams take part while in the other three rounds - the 11th, 12th and 13th - just 12 teams compete, with the six remaining teams all having byes. The season starts on the 24th of March with Greater Western Sydney, the competition's new team, taking on Sydney at Stadium Australia. Then there's a 5-day gap until the remainder of the first round is played out over the 29th, 30th, 31st of March, and the 1st of April. The final game of the home-and-away season, the 198th, will be played on the 2nd of September. 

Viewed from a home-and-away and venue location standpoint, this year's draw looks like this:

You'll notice that there are a lot of blanks in this matrix. These represent games that would have taken place had we had an all-plays-all home-and-away draw but which are not scheduled because of the truncated nature of the draw.

This year, with teams playing just 22 games out of a possible 34 and just 198 games of a possible 306, that truncation is even more pronounced than usual. Roughly 35% of possible home-and-away pairings won't take place this season. 

The AFL makes no secret of the fact that the draw is not randomly determined, and an analysis of the draw based on teams' 2011 ladder position finish hints at some of the biases that have been introduced, perhaps by design.

Most importantly, the teams that finished in the top 4 last season are paired up on 11 occasions, just one short of the maximum possible (the only missing pairing is Geelong playing West Coast at home). The teams from ladder positions 5th through 8th also pair up at a rate greater than chance would dictate - 75% of all possible pairings occur at sometime during the season compared to the overall rate of about 65%. The only other pairings that occur at a greater than average level are matchups between teams from positions 13th to 18th (I've assigned GWS position 18 for this purpose). For these teams we'll see 22 of the 30 possible pairings. Great.

The pairings that, relatively speaking, are underrepresented in the draw are those that are potential mismatches, to the extent that last year's ladder finish is a reliable indicator of this year's performance. For example there are only 14 games in which teams from 1st to 4th play teams from 13th to 18th, which is just 58% of the number of possible such pairings.

Such biases affect the prospects of teams differentially, which is why the kind of draw we have in the AFL is sometimes referred to as being "imbalanced". The question is, which teams benefit most and which lose out, and how might we quantify those rewards and those punishments?

One way of quantifying them is to project the season on the basis of the actual draw, then project the results of the "missing" games and compare each team's fate in the projected actual season with its fate in the full, extended season.

For this purpose we need to assess the relative strengths of each team, and a way to convert these relative strengths, along with information about the venue at which each game will be played, into victory probabilities. It was for this purpose that I created the statistical model described over on the Statistical Analyses blog. 

This model requires MARS Ratings as inputs. For the analysis here I've used two sets of these:

• Set A - the MARS Ratings that we'll be using for Round 1 of this season, which are for each team 47% of their final season 2011 MARS Rating plus 530. For the new team, GWS, I used a Rating of 950.
• Set B - the final season 2011 MARS Ratings. Again I used a Rating of 950 for GWS.

Lastly, we need to make an assumption about the venues for the "missing" games. I've assumed they were all played at the Home team's usual home ground.

As a first metric of the effects let's consider each team's projected winning percentage in the actual and in the extended seasons:

(NB All results in this blog are based on 10,000 simulations of the season, which means that the worst-case 95% confidence intervals are about plus or minus 1%.)

Using the Set A Ratings, the differences in projected winning percentages span the range from +2.4% for Adelaide to -2.8% for Collingwood. Using Set B Ratings instead, the differences range from +3.7% for Adelaide to -3.6% for Collingwood. The wider range for Set B is a consequence of the larger Ratings differences between consecutive teams in Set B compared to those in Set A, coupled with the nature of the bias in the draw.

When a season is imbalanced to reduce the number of potential mismatches, stronger teams will be relatively more disadvantaged because they are more likely to win the games they don't get to play; the opposite is true for weaker teams. Under these conditions, the more highly Rated a team is, the greater this effect will be, and the larger will be the estimated impact of a curtailed season.

The following chart highlights the team by team impacts on winning percentage:

Still, even with the Set B Ratings, the estimated impact of the imbalanced draw on each team's winning percentage is smaller than 4% points. Can that make much difference to anything that matters? 

Well one thing that matters a lot to teams is their final ladder position. In this next table I've recorded the probabilities for each team finishing in the Top 8 or the Top 4 in the actual versus the all-play-all, extended season.

Let's first consider the middle columns, which relate to teams' chances of playing in the finals. Here we can see that those fairly small effects on winning percentages can translate into quite significant effects on the likelihood of playing in the finals.

For Adelaide for example, the truncated season boosts its chances of running around in September relative to an all-plays-all season by either 7 or 11 percentage points, depending on the set of Ratings you choose. Put more dramatically, it more than quarters their odds (from about 45/1 to about 21/2) using Set B Ratings, and almost halves them (from about 15/2 to 4/1) using Set A Ratings. 

The other teams to benefit significantly are Melbourne, the Roos, Fremantle and Richmond, and those that suffer most are Carlton, West Coast, Sydney, St Kilda, Hawthorn and the Dogs, as the following chart of the first two "Diff" columns above shows:

We can also look at the impact on the chances of each team finishing in the Top 4. These numbers are shown in the righthand columns of the table above, the two "Diff" columns from which is charted here:

What this chart depicts, perhaps best of all the charts so far, is how the imbalance in the draw functions to transfer opportunity from strong teams to weaker ones - not so much to the weakest teams of all, but instead to those teams likely to be on the fringes of the finals. The seven topmost teams in the chart above are the teams ranked 8th to 14th on MARS Ratings at the end of season 2011; the four bottommost are the teams ranked 1st to 4th.

You might have noticed extra columns in the earlier tables, labelled "Actual - True Home". The data in these columns is there to address the question: how are each team's projected results estimated to change if all home games were played at teams' usual home ground, rather than some of them being moved to other locations?

For Hawthorn, for example, that would mean shifting the four games it's scheduled to play at Aurora Stadium this year back to the MCG. Since three of these games pit the Hawks against a non-Victorian team, such a shift would materially alter the Hawks' modelled victory probability - and its actual victory probability too if you believe in statistical modelling.

The following chart shows that, overall, the nomadic behaviour of Hawthorn, GWS, Melbourne, Richmond and the Dogs has the largest detrimental effect on the finals aspirations of Hawthorn, the Roos, Carlton and Richmond, and the greatest beneficial effect on those of Sydney, Port Adelaide and the Gold Coast. (Note that differences of about 1% or less might be purely due to sampling variation, so I'd not read too much into them.)

The effects on Hawthorn and Richmond are easiest to explain. Hawthorn suffers from shifting three games for which it would otherwise enjoy the Interstate team probability uplift, and Richmond suffers from moving one of its home games to the home state of its opponent, in so doing not just losing but transferring the Interstate uplift. How much, I wonder, would the Richmond Board price an additional 1% chance of making the Finals. Implicitly they think it's less than whatever they're getting financially from moving the Gold Coast game to Cazaly's, or they don't think my 1% estimate is correct.

Carlton's and the Roos' finals chances are also hurt, relatively speaking, by the current draw though only indirectly in that the teams with which they are vying for spots in the finals are teams that are favoured by the scheduling of some home games at alternative grounds. The teams that so benefit are:

• Teams playing GWS at Manuka: the Dogs, Gold Coast and Melbourne
• Teams playing Hawthorn at Aurora: Sydney, Fremantle, the Roos and Port Adelaide
• Teams playing Richmond at Cazaly's: Gold Coast
• Teams playing Melbourne at Mararra: Port Adelaide

Note that Port Adelaide and the Gold Coast appear twice in that list, which explains the overall positive estimated effect of the draw on their finals chances. Sydney appears once, which also explains a part of the positive effect on its chances.

I'll end by noting the broad similarities of the analysis here to that of Rohan Connolly. The largest differences between his analysis and mine are that he assesses the draw as being more favourable to GWS than I do, and as being less favourable to Collingwood, Geelong and Carlton than I do. That's because, I think, his analysis is more absolute and mine more relative. In what I've done here, the implicit assumption is that if a team's very likely or very unlikely to make the finals there's little effective damage or assistance that the draw can render; in Rohan's analysis, a legup is a legup regardless of whether it might help lift you from 16th to 15th or from 9th to 8th. Both approaches are entirely valid.