# Hypotheticals under Arguably Better Systems

The Australian Football League (AFL) finals series (or playoffs in the US/Canadian lingo) kicks off this weekend, with betting markets indicating that the field of eight is more open than in most recent years. At the business end of the season, it is always worth considering how things would be different under alternative systems used to rank teams at the conclusion of the home-and-away (regular) season.

One possibility here is if the AFL used a ‘bonus points’ system analogous to that used in some Rugby (Union) competitions (see an earlier post). Niven Winchester (MIT) and I estimated a theoretical bonus point system, ‘optimal’ in the sense of being able to reveal the truly best teams. As opposed to the current system of four points for a win, two each for a draw (infrequent) and zero for a loss; our results indicated a preferred allocation of four league points for a win, three points for a draw, two points for winning by 27 or more and two points for losing by 26 or less (however, the partition could instead be altered to let’s say 24 points (four goals) to make it more interpretable to fans).

The 2012 ladder under a bonus point system does produce a few notable differences – Collingwood would have finished 7^{th} instead of 4^{th}, giving them an elimination final against North Melbourne, and handing Geelong the double-chance and a sumptuous qualifying (non-elimination) final against minor premiers Hawthorn. West Coast and North Melbourne are also ranked above Collingwood under the alternative system due to these teams picking up a large number of bonus points, even though they won fewer games than Collingwood. Additionally, a bonus point system point system would have resulted in the ‘dream’ Western-derby elimination final in Perth between West Coast and Fremantle. Outside the final eight, Richmond would have been the only significant mover, climbing from 12th to 9th, forcing each of the three teams above them down a spot.

It’s not all bad for Collingwood fans, however. In the original paper (published in *Economic Papers* in 2010), when we used our alternative system to backtrack over our original 12-year sample, we found Collingwood would actually have fared best overall with the bonus points system, finishing significantly better in five seasons, while finishing significantly worse only on one other occasion. For the other teams, it made a significant difference either way in only two seasons on average. Niven, along with Ray Stefani (California State, Long Beach) have since used similar methodology to estimate a bonus points system for the NFL (this paper is now forthcoming in *Applied Economics*). Perhaps the NRL (Rugby League) should be next on the research agenda.

The other hypothetical I typically like to consider is the application of a correction accounting for the strength of schedule problem – I tackled this one for AFL data in *Economic Modelling* last year. If the ladder was based on adjusted wins, Collingwood would actually leap from 4^{th} to 2^{nd}, forcing both Adelaide and Sydney down a spot, and giving both themselves and Hawthorn easier fixtures in Melbourne against interstate visiting sides. All other rankings were unchanged here, and standard within-season competitive balance measures would have been higher (indicative of a truly less-balanced competition than realised; this owing to most of the top teams playing each other twice, *mutatis mutandis* for most of the bottom teams).

If nothing else, these counterfactuals help reinforce how sensitive standings can be to alterations in the criteria used to rank teams, holding fixed the results of all matches in the season. What the implications are, however, is another matter – ask 10 Sports Economists this question and you may get 10 completely different answers.

Comments are closed.

These are interesting scenarios, but I wonder how much behavior of teams would change. Certainly there would be some adjustment from teams, however I am inclined to believe that the “best” team is not invariant to the rules of winning a league.

Makes the BCS look simple…

Hi Robert, this behavioural aspect is not so much of concern for strength ‘adjustment’ – it is merely that. However, it is definitely relevant to bonus points. The way I think of it is as follows [with a calssical statistical analogy in square parenthese]: any tornament ranking system is just an ‘estimate’ of the true (unobservable) ordering of teams [underlying data generating process], and we believe that this system [a new test] produces better [more powerful] estimates.

…and so, I would infer that under bonus points, the “best” team is more likely to finish top than uder the current system.

The 4 points for a win, 2 for a draw and zero for a loss never made sense … that’s pointage inflation! How is that different from 2 points for a win, 1 for a draw and zero for a loss? Soccer awards 3 for a win and 1 for a draw to incentivize wins.

I do prefer your system. It would also change incentives within the game to have loosing teams continue to work hard into the 4th quarter to get within the magical bonus 4 goal points marker (like avoiding the follow on in cricket). It means that less games become uninteresting “blow-outs” (or at least become uninteresting later in the match).