News
Stochastic modelling and the AFL
Stochastic modelling forms a significant part of the actuarial work we perform for clients. Some examples of stochastic work we have conducted for clients include simulations of future asset returns, demographic modelling and insurance claims. Recently, a stochastic model was designed to compete in our internal football tipping competition. This news article summarises the stochastic model and its findings for the 2008 AFL Home & Away season.
Basis of model
The model works by assuming that a team's performance for any particular match will follow a Normal distribution, with the distribution of "Home" performances differing from "Away" performances. The basis for differentiating between home and away performance is quite intuitive and borne out in practice with most teams exhibiting stronger performances at home venues:
Chart 1: Home (top of bar) vs Away (bottom of bar) performance by team in 2008. Geelong and Port Adelaide have actually performed better in their away games
Click on the image to view a larger version.
More specifically, it assumes that the winning / losing margin of any particular match is based on the difference of each team's performance distribution and is also Normally distributed. This is also borne out in practice in VFL/AFL match statistics since 1897. An interesting and logical by-product of this is that the most common winning margin in VFL/AFL history has been by a single point!
Chart 2: Frequency of winning margins since 1897.
Click on the image to view a larger version.
Model calibration
The model is calibrated by solving for the parameters of the distributions that have the greatest likelihood of explaining past winning margins. This has advantages over fitting distributions independently for each team as it rewards close performances against strong teams. Using 2008 match statistics up to and include Round 18 yields the following parameters (with a minimum standard deviation to ensure variability):
| Team | Home | Away | ||
| Average | St.Dev | Average | St.Dev | |
| Adelaide | 111.87 | 9.40 | 90.32 | 31.38 |
| Brisbane Lions | 99.04 | 15.31 | 73.40 | 5.00 |
| Carlton | 83.35 | 25.30 | 113.75 | 5.00 |
| Collingwood | 99.96 | 24.14 | 122.75 | 5.00 |
| Essendon | 82.32 | 34.71 | 74.01 | 46.83 |
| Fremantle | 104.33 | 5.00 | 87.27 | 5.00 |
| Geelong | 132.90 | 32.55 | 131.99 | 45.12 |
| Hawthorn | 111.24 | 27.36 | 106.83 | 15.51 |
| Kangaroos | 102.82 | 5.00 | 65.22 | 16.18 |
| Melbourne | 60.43 | 21.94 | 53.35 | 5.00 |
| Port Adelaide | 86.61 | 21.46 | 88.68 | 32.68 |
| Richmond | 81.48 | 13.07 | 109.60 | 61.83 |
| St Kilda | 100.45 | 5.00 | 67.52 | 5.00 |
| Sydney | 98.73 | 5.00 | 97.59 | 5.00 |
| West Coast | 84.49 | 6.04 | 39.59 | 4.75 |
| Western Bulldogs | 112.02 | 20.03 | 111.37 | 5.00 |
Table 1: Fitted team parameters based on 2008 results up to and including Round 18
Model predictions
The model can then be used to simulate the remaining 4 rounds and predict the final ladder configuration. After 10,000 simulations the following results were obtained:
| # | GEE | WB | HAW | SYD | NM | ADE | STK | COL | BRI | RIC | CAR | ESS | FRE | PA | WC | MEL |
| 1 | 100% | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 2 | - | 38% | 62% | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 3 | - | 62% | 38% | - | - | - | - | - | - | - | - | - | - | - | - | - |
| 4 | - | - | - | 60% | 8% | 11% | 7% | 14% | - | - | - | - | - | - | - | - |
| 5 | - | - | - | 26% | 24% | 18% | 14% | 17% | - | 1% | - | - | - | - | - | - |
| 6 | - | - | - | 11% | 30% | 18% | 14% | 25% | - | 2% | - | - | - | - | - | - |
| 7 | - | - | - | 2% | 21% | 22% | 22% | 24% | - | 6% | 1% | 1% | - | - | - | - |
| 8 | - | - | - | 1% | 12% | 19% | 31% | 17% | 2% | 12% | 5% | 2% | - | - | - | - |
| 9 | - | - | - | - | 3% | 9% | 9% | 3% | 15% | 34% | 20% | 8% | - | - | - | - |
| 10 | - | - | - | - | 1% | 3% | 3% | - | 30% | 24% | 24% | 14% | - | - | - | - |
| 11 | - | - | - | - | - | 1% | 1% | - | 35% | 14% | 29% | 19% | - | 1% | - | - |
| 12 | - | - | - | - | - | - | - | - | 18% | 7% | 19% | 52% | 1% | 5% | - | - |
| 13 | - | - | - | - | - | - | - | - | - | - | 2% | 4% | 60% | 34% | - | - |
| 14 | - | - | - | - | - | - | - | - | - | - | - | - | 39% | 61% | - | - |
| 15 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | 71% | 29% |
| 16 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | 29% | 71% |
| Average | 1.0 | 2.6 | 2.4 | 4.6 | 6.2 | 6.6 | 7 | 6.2 | 10.5 | 9.4 | 10.4 | 11.2 | 13.4 | 13.5 | 15.3 | 15.7 |
| % of ▲ | - | - | 62% | - | 8% | 29% | 34% | 81% | 2% | 55% | 50% | 44% | 1% | 39% | - | 29% |
| % of ▼ | - | 62% | - | 40% | 67% | 53% | 43% | 3% | 83% | 21% | 21% | 4% | 39% | - | 29% | - |
| % in Top-8 | 100% | 100% | 100% | 100% | 95% | 88% | 87% | 97% | 2% | 21% | 6% | 3% | - | - | - | - |
| % in Top-4 | 100% | 100% | 100% | 60% | 8% | 11% | 7% | 14% | - | - | - | - | - | - | - | - |
Table 2: Predicted probabilistic ladder configuration for 2008
Current positions are shown on the highlighted diagonal.
Conclusions
- Hawthorn are almost twice as likely than Western Bulldogs to finish second. This is because Hawthorn's last 4 games are all against bottom 8 teams whereas the Western Bulldogs are playing stronger opponents
- Sydney are highly likely to finish in 4th place, but 5th through 8th are still hotly contested
- Though Richmond is currently placed 10th, they have a surprisingly good chance (21%) of making the finals. This is probably due to them playing Fremantle and Melbourne in the last 2 rounds
- Collingwood have a substantial chance of climbing the ladder and even getting into the top-4
- Though not shown in the tables above, there is a 28.5% chance of at least one more draw occurring this season
Disclaimer
The information displayed or given on this website is of a general nature and does not take into account any person's objectives, financial situation or needs. Cumpston Sarjeant makes this material available on the understanding that users exercise their own skill and care with respect to its use. Before relying on the material, users should carefully evaluate the source, accuracy, currency, completeness and relevance for their purposes and should obtain appropriate professional advice relevant to their particular circumstances.