The 17-D-4 AFL Fixture

A full 17-match Round Robin. A guaranteed return Derby match in Round 18. Then four matches to complete the schedule, carefully chosen to achieve a proper handicap. What’s not to like?

What Does 17-D-4 Do Better than the Alternatives?

Alternative 17-D-4
Current Fixture
Return matches based on last year’s ladder Return matches based on this year’s ladder (actual strength)
Clubs grouped by six, #7 gets much easier draw than #6 Toughness of draw scales with the strength of the team, no arbitrary blocks
Everyone gets a bye the week before the finals to discourage resting of star players Everyone gets a bye in the last five weeks before finals; the best teams get it later
Prime timeslots late in the season contain mismatches Schedule them when you know who is actually good
Proposed 6-6-6
Top six after 17 weeks guaranteed a home final Every position open until the last match
Local rivalries not played twice All rivalries played in the special Derby Round
The last five rounds have to be fixtured in a hurry There is an extra week during Derby Round, so you can take a couple of days to get it right
Home-Away balance not achievable unless all blocks have exactly three teams who have played 9 Home / 8 Away Every team gets 9 Home / 9 Away in the first 18, then 2 Home / 2 Away selected from unplayed return legs

And What Won’t it Solve?

Tanking
For that, use a more targeted points-based draft system
Some matches being more important than others
Any finals system is vulnerable to this. In the AFL, there are sharp divisions between 8 & 9, and between 4 & 5 that have huge rewards.
Some teams being crap
Mismatches will happen. There will be fewer under 17-D-4 because teams play their return matches against teams of similar strength

2016 Example

Let’s pretend that each team has played a single round-robin. In Round 18 (or Round 19 with the current counting for the early bye), each team plays its local rival. If they don’t have one, we’ll make them up for now. Clubs would have some say in this.

We assume that a good estimate of a team’s strength is the number of games it has won out of those 17. Looking at 2016’s ladder after 17 matches:

Team Won Points Target
Hawthorn 14 56 203
GWS 12 48 191
Sydney 12 48 191
Geelong 12 48 191
WC Eagles 12 48 191
Adelaide 12 48 191
W Bulldogs 12 48 191
North Melb 11 44 185
St Kilda 9 36 173
Port Adel 8 32 167
Melbourne 7 28 161
Collingwood 7 28 161
Richmond 7 28 161
Carlton 6 24 155
Gold Coast 6 24 155
Fremantle 3 12 137
Bris Lions 2 8 131
Essendon 1 4 125

That Target is the combined number of points that we want the team’s last five opponents to sum to — including their Derby rival. The average team has scored 34 points, so the average five-week schedule comes to 170 points. I’ve used a scaling factor of 1.5 to give stronger teams stronger opponents, but that number is malleable. Note: a perfectly fair draw would give the bottom teams a higher Target than the top teams, to account for self-reference. That would be a scaling factor of -1.0.

I’ve written a tree search program that finds close fits to the target totals, choosing matches from the return legs that have not yet been played. In the fixture below, every team is within 13 points of the target opponent strength (or an average of 2.6 per opponent, less than one win). For instance, Hawthorn’s opponents would be Geelong (already fixtured, 48) + West Coast (48) + Sydney (48) + Carlton (24) + St Kilda (36) for a total of 204, compared with a target of 203.

Team Target Actual Rival Other Opponents
Haw 203 204 Geel WCE, Syd, Carl, St.K
GWS 191 192 Syd Ess, N.M., W.B., WCE
Syd 191 204 GWS Geel, G.C., Melb, Haw
Geel 191 192 Haw B.L., P.A., Syd, Adel
WCE 191 192 Freo W.B., GWS, Rich, Haw
Adel 191 180 P.A. Geel, Rich, Coll, N.M.
W.B. 191 188 St.K P.A., GWS, G.C., WCE
N.M. 185 188 Melb Adel, Coll, St.K, GWS
St.K 173 164 W.B. Haw, N.M., Freo, Ess
P.A. 167 164 Adel B.L., Freo, Geel, W.B.
Melb 161 168 N.M. Carl, Syd, G.C., Rich
Coll 161 156 Carl Adel, Rich, Freo, N.M.
Rich 161 156 Ess Melb, WCE, Coll, Adel
Carl 155 144 Coll Haw, G.C., B.L., Melb
G.C. 155 156 B.L. Melb, W.B., Carl, Syd
Freo 137 148 WCE Coll, St.K, P.A., Ess
B.L. 131 132 G.C. Carl, Ess, P.A., Geel
Ess 125 132 Rich Freo, St.K, GWS, B.L.

We can then shuffle these 36 matches across five weeks, giving the top four a bye in the last round, and the next four a bye in the second-last round.

  1. Syd v Geel, WCE v GWS, G.C. v W.B., Carl v Haw, N.M. v Adel, P.A. v B.L., Freo v St.K, Rich v Melb (Ess, Coll byes)
  2. GWS v N.M., WCE v W.B., Haw v Syd, Geel v P.A., Adel v Rich, Ess v St.K, Freo v Coll (B.L., G.C., Carl, Melb byes)
  3. W.B. v GWS, Haw v WCE, Syd v G.C., B.L. v Ess, Adel v Geel, N.M. v Coll, Melb v Carl (Freo, P.A., St.K, Rich byes)
  4. St.K v Haw, Coll v Rich, GWS v Ess, Melb v Syd, Carl v G.C., P.A. v Freo, Geel v B.L. (Adel, WCE, W.B., N.M. byes)
  5. Rich v WCE, W.B. v P.A., Coll v Adel, St.K v N.M., G.C. v Melb, B.L. v Carl, Ess v Freo (Haw, GWS, Geel, Syd byes)

I noticed after I’d done this that I’d forgotten to enforce the constraint of Fremantle and West Coast not both playing at home in the same week, so I’ll leave that as an exercise for the reader.

Feedback welcome here and on Twitter.

A Simulation by Athletes

From the outside, Sport can be reasonably treated as a mathematical model, A Simulation By Athletes. But it cannot be taught this way. Expert knowledge from coaches and players is not built up from atoms of data, but top-down and augmented by experience.

At Ranking Software, we are looking to bridge the gap between the two approaches: assist coaches and experts with smarter ways of dealing with numerical information. We have to be aware that a sports result is a measurement that contains both skill and luck effects, and the latter is routinely underestimated.