The Offense-Defense Team Rating System

We're not short of a Rating System here on MAFL, but none of the three that we have separately rates the offensive and defensive abilities of each team. That's what's different about the Offense-Defense Model (ODM), which I'll be reviewing and applying to AFL in this blog.

If you're curious about the technical details of ODM, please see the end of this blog, but an intuitive explanation will suffice for now and it is that the method produces a measure of each team's offensive and defensive capability by forming a weighted sum of the offensive and defensive ratings of the teams that it has played, where the weights are the points that the team scored in those games (to come up with its offensive rating) or the points that it conceded (to come up with its defensive rating). So, scoring highly against a team with a strong (ie highly rated) defence is weighted highly in the assessment of a team's offensive capability, and conceding few points to a team with a strong offence is weighted highly in the assessment of a team's defensive capability.

A team's aggregate strength is defined as the ratio of its offensive and defensive ratings.

Applying the ODM approach to the AFL season so far yields the following.

Team rankings based on the ODM approach appear as the first 3 columns of the table. So, for example, ODM rates Adelaide as having the 3rd best offence and the 8th best defence, which combined make it the 4th best team in the competition.

The comparative ratings of Colley, Massey and MARS appear in the righmost columns, along with the average overall ranking of the four systems (using, for ODM, only its Aggregate ranking).

Ranks shown in green are four spots or more higher than the all-System Average and those shown in red are four spots or more lower.

Hawthorn's big scores, especially those against Collingwood, St Kilda and Adelaide, have impressed ODM enough to have it ranking the Hawks as the best team offensively, ahead of Essendon who've broken 100 in every game bar one, albeit against generally lesser opponents.

Melbourne, the Gold Coast and GWS share the bottom three rankings for offensive capability, an assessment with which it's hard to argue.

Defensively, Sydney is rated number 1 by ODM. It's yet to concede 100 points to any team this season despite having faced three of the four highest-ranked teams offensively. Hawthorn's ranked at 2 as a defensive unit, having conceded 100 points or more only twice, on both occasions to teams (Collingwood and Sydney) ranked in the top half offensively. It's also conceded relatively few points to the teams ranked 3rd (Adelaide) and 5th (Fremantle) offensively.

The same three teams that share the lowest rungs of the offensive ladder also share these rungs on the defensive ladder. Again, it's hard to argue with that assessment.

Combining these assessments, the ODM ranks Hawthorn 1st, Sydney 2nd and Essendon 3rd amongst the teams.

You can make your own assessment about the common sense of these and other of ODM's team offensive and defensive rankings by reviewing the table below, which summarises the scores for every game so far this season.

Generally, ODM's overall team rankings are very consistent with the all-System average. The only exceptions are Geelong and West Coast, both of which it ranks some 3 places lower than the all-System average.

Comparing ODM's ranking with each of the three other rating systems individually yields the following matrix of pairwise correlations:

The lowest level of agreement is between ODM's team Defence rankings and the overall team rankings of MARS, while the highest level of agreement is between ODM's Aggregate team rankings and the overall team rankings of Massey.

In general, ODM's Aggregate team rankings are highly correlated with all three Systems' rankings.

Technical Details

This ranking system works as follows:

• Define a square matrix A such that A[ij] is the number of points given up by team i when playing team j. If teams i and j have not met then A[ij] = 0
• Require that team j's offensive ability, o[j], satisfy the equation:
  • o[j] = a[1j] * (1/d[1]) + a[2j] * (1/d[2]) + ... + a[nj] * (1/d[j])
• Require that team i's defensive ability, d[i], satisfy the equation:
  • d[i] = a[i1] * (1/o[1]) + a[i2] * (1/o[2]) + ... + a[in] * (1/o[n])

We achieve this by setting d[1] = e, a vector of 1s, and then repeatedly using the following equations (where t is the iteration number):

• o[t] = A'*(1/d[t-1])
• d[t] = A*(1/o[t-1])

(note that 1/d is defined as (1/d[1], 1/d[2], ..., 1/d[n]. A similar definition pertains to 1/o)

In practice, if we use the A matrix in the equations above we can't be guaranteed of convergence so we use instead P = A+eps*e*e', which adds a tiny amount eps to each entry in A. Larger values of eps increase the time for the algorithm to converge.

Note that a team with a strong defence will have a low value of d, and a team with a strong offence will have a high value of o. A team's aggregate strength can then be defined by the ratio of its offensive and defensive strength ratings (ie o[j] / d[j]).

Where teams have played one another more than once it has been proposed that either the sum or the average of the points from the multiple games be used to form the relevant entries in the matrix A.

Possible Variations

A number of variations to ODM that might improve its application to AFL, suggest themselves:

• In the standard ODM no adjustment is made for Home Ground Advantage. This could be incorporated, for example, by discounting the points scored by the Home team and/or inflating the points scored by the Away team. Alternatively, separate ratings could be created for each team depending on whether it was playing at home or away.
• Blowout results could disproportionately alter team ratings. Accordingly, a cap might be placed on the scores used in the A matrix, or a maximum winning margin imposed.
• No adjustment is made to reflect the age of game results. To cater for this, some decay function might be applied that progressively reduces the impact of older games.
• Overall team strength is defined as offensive rating divided by defensive rating. Alternative functional forms taking these two ratings as inputs could be defined so as to maximise some objective function, such as ability to predict game margin.
• Ratings based on other game metrics could be constructed, for example using Inside 50s, Tackles, Marks, Kicks, Handballs, and so on. These might then be combined to come up with a more complete measure of team ability.