AN ANALYSIS OF THE FINALS SYSTEMS
USED BY THE AFL AND THE NRL
1.0. Abstract
The "Final 8" systems used by the Australian Football League (AFL) and the National Rugby League (NRL) are explained and compared. The NRL finals system, also known as the McIntyre Final 8 System, is shown to be flawed.
1.1. The Analysis of Both Systems
The analysis is purely mathematical in that each finals game is considered a 50/50 contest. The history of a competing team is not considered, nor is the history of their opponent, nor are any other factors which may effect the outcome of a game.
A summary of the analysis is contained in the following table which shows the percentage chance of winning the premiership for each team in each week of the finals. The team which wins the Grand Final wins the premiership.
Percentage chance of winning the premiership
Team Ranking | Week 1 (NRL)
Four Qualifying Finals | Week 1 (AFL)
Two Qualifying and two Elimination Finals | Week 2
Two "Semi" Finals | Week 3
Two Preliminary Finals | Week 4
One Grand Final |
1 | 18.75 | 18.75 | (bye) 25 | 25 | 50 |
2 | 18.75 | 18.75 | (bye) 25 | 25 | 50 |
3 | 15.625 | 18.75 | 12.5 | 25 |
|
4 | 12.5 | 18.75 | 12.5 | 25 |
|
5 | 12.5 | 6.25 | 12.5 |
|
|
6 | 9.375 | 6.25 | 12.5 |
|
|
7 | 6.25 | 6.25 |
|
|
|
8 | 6.25 | 6.25 |
|
|
|
The two systems are different in week 1 of the finals. They are identical in weeks 2, 3 and 4, where all the games are elimination finals, that is, the winner proceeds and the loser is eliminated.
A team's ranking in each week of the finals depends on their initial ladder position and, thereafter, whether they win or lose.
When explaining the finals systems it is easier to start at the end.
Week 4 of the finals has one game, the Grand Final, where the two teams each have a 50% chance of winning the premiership. [ 50% is 100% ÷ 2 ]
Week 3 of the finals has two games, the Preliminary Finals, where the four teams each have a 25% chance of winning the premiership. [ 25% is 50% ÷ 2 ]
Week 2 of the finals is more complicated. There are six teams still "alive" with the two top ranked teams having a bye. There are two games, the "Semi" Finals, where the other four teams each have a 12.5% chance of winning the premiership. [ 12.5% is 25% ÷ 2 ]
Week 1 of the AFL finals has four games. There are two Elimination Finals (5 v 8, 6 v 7) where the four bottom ranked teams each have a 6.25% chance of winning the premiership. [ 6.25% is 12.5% ÷ 2 ]
There are two Qualifying Finals (1 v 4, 2 v 3) where the four top ranked teams each have a "double chance", that is, the loser plays next week and the winner has a bye. Therefore the four teams each have an 18.75% chance of winning the premiership. [ 18.75% is 6.25% (12.5% ÷ 2) plus 12.5% (25% ÷ 2) ]
Week 1 of the NRL finals has four Qualifying Finals (1 v 8, 2 v 7, 3 v 6, 4 v 5). The two top ranked teams are in the same situation as the teams in the AFL Qualifying Finals and thus have an 18.75% chance of winning the premiership. The two bottom ranked teams are in the same situation as the teams in the AFL Elimination Finals and thus have a 6.25% chance of winning the premiership.
The four other teams (ranked 3, 4, 5 and 6) have a percentage chance of winning the premiership which depends on the results of the other games. There are sixteen possible combinations of results in week 1, which, when averaged out, give the numbers shown in the shaded area of the table.
1.2. The Flaw in the McIntyre Final 8 System
In the years when the three top ranked teams all win in week 1 of the finals they retain the same ranking in week 2.
In that situation the teams ranked 3, 4, 5 and 6 have effectively played "dead rubbers".
Even worse, the mathematical flaw is then exposed.
The third ranked team finds that their chances of winning the premiership have decreased from 15.625% to 12.5% even though they won. Conversely, or perversely, the sixth ranked team's chances of winning the premiership have increased from 9.375% to 12.5% even though they lost.
The AFL used the McIntyre Final 8 System from 1994 to 1999. The flaw can be demonstrated by examining the 1999 Qualifying Final (3 v 6) where the Brisbane Lions 20.18 (138) defeated Carlton 8.17 (65).
Carlton's "penalty" for losing was an increase in their chances of winning the premiership, which they took advantage of to reach the Grand Final that year. Question... Did the AFL abandon the McIntyre Final 8 System because of this?
1.3. Conclusion
The NRL must abandon the McIntyre Final 8 System, just like the AFL did on 22 December 1999.
