A common example of how one might use fitzRoy is for creating a simple ELO rating system. These models are common for tippers that are part of The Squiggle and also becoming common in other team sports. This vignette shows a minimum working example to get you started on creating an ELO model from scratch, using fitzRoy to get data and the elo package to do the modelling.

Prepare data

Before we create our model, some data preparation. In the ELO package we are using, we need a way to identify each round as a separate match, so we’ll combine season and Round.Number into a string as a unique identifier when combined with the team name. We also need a way to tell it when a new season is starting, so we’ll create a logical field that indicates if the game is the first game for a team that season.

For the fixture data, we need to ensure the dates are in the same format as results (note - this should probably be done internally in fitzRoy - see #58). For now, we can do it manually.

fixture <- fixture %>%
  filter(Date > max(results$Date)) %>%
  mutate(Date = ymd(format(Date, "%Y-%m-%d"))) %>%
  rename(Round.Number = Round)

Set ELO parameters

There are a range of parameters that we can tweak and include in ELO model. Here we set some basic parameters - you can read a bit more on the PlusSixOne blog, which uses a similar method. For further reading, I strongly recommend checking out Matter of Stats or The Arc for great explainers on the types of parameters that could be included.

Map margin function

The original ELO models in chess use values of 0 for a loss, 1 for a win and 0.5 for a draw. Since we are adapting these for AFL and we want to use the margin rather than a binary outcome, we need to map our margin to a score between 0 and 1. You can do this in many varied and complex ways, but for now, I just normalise everything based on a margin of -80 to 80. Anything outside of this goes to the margins of 0 or 1.

We create that as a function and then use that function in our elo model.

Calculate ELO results

Now we are ready to create our ELO ratings! We can use the elo.run function from the elo package for this. I won’t explain everything about what is going on here - you can read all about it at the package vignette - but in general, we provide a function that indicates what is included in our model, as well as some model parameters.

Now that is run, we can view our results. The elo package provides various ways to do this.

Firstly, using as.data.frame we can view the predicted and actual result of each game. Also in this table is the change in ELO rating for the home and away side. See below for the last few games of 2018.

We can specifically focus on how each team’s rating changes over time using as.matrix. Again - viewing the end of 2018 also shows teams that didn’t make the finals have the same ELO as the rounds go on since they aren’t playing finals.

as.matrix(elo.data) %>% tail()
#>         Adelaide Brisbane Lions  Carlton Collingwood Essendon Fitzroy
#> [2778,] 1507.172       1483.508 1416.965    1534.198 1514.869    1500
#> [2779,] 1507.172       1483.508 1416.965    1534.100 1514.869    1500
#> [2780,] 1507.172       1483.508 1416.965    1538.643 1514.869    1500
#> [2781,] 1507.172       1483.508 1416.965    1538.991 1514.869    1500
#> [2782,] 1499.878       1500.522 1499.671    1500.139 1495.989    1500
#> [2783,] 1504.051       1503.485 1498.703    1506.431 1495.810    1500
#>         Footscray Fremantle  Geelong Gold Coast      GWS Hawthorn
#> [2778,]  1466.641  1460.093 1537.625   1420.941 1517.090 1524.854
#> [2779,]  1466.641  1460.093 1537.625   1420.941 1517.187 1522.293
#> [2780,]  1466.641  1460.093 1537.625   1420.941 1517.187 1522.293
#> [2781,]  1466.641  1460.093 1537.625   1420.941 1517.187 1522.293
#> [2782,]  1499.953  1508.989 1500.161   1499.879 1504.136 1500.237
#> [2783,]  1503.217  1504.850 1509.218   1499.583 1496.364 1496.878
#>         Melbourne North Melbourne Port Adelaide Richmond St Kilda   Sydney
#> [2778,]  1549.640        1511.378      1506.200 1552.536 1452.330 1509.285
#> [2779,]  1552.201        1511.378      1506.200 1552.536 1452.330 1509.285
#> [2780,]  1544.309        1511.378      1506.200 1547.993 1452.330 1509.285
#> [2781,]  1544.309        1511.378      1506.200 1547.993 1452.330 1509.285
#> [2782,]  1500.105        1490.900      1500.093 1500.193 1499.626 1499.953
#> [2783,]  1490.914        1492.226      1501.179 1493.734 1501.997 1495.864
#>         University West Coast
#> [2778,]       1500   1534.675
#> [2779,]       1500   1534.675
#> [2780,]       1500   1542.566
#> [2781,]       1500   1542.218
#> [2782,]       1500   1499.579
#> [2783,]       1500   1505.493

Lastly, we can check the final ELO ratings of each team at the end of our data using final.elos (here - up to end of 2018).

We could keep tweaking our parameters until we are happy. Ideally we’d have a training and test set and be using some kind of cost function to optimise these values on like a log likelihood, mean absolute margin or something similar. I’ll leave that as beyond the scope of this vignette though and assume we are happy with these parameters.

Do predictions

Now we’ve got our ELO model and are happy with our parameters, we can do some predictions! For this, we just need to use our fixture and the prediction function with our ELO model as an input. The elo package takes care of the result.

From here - you could turn these probabilities back into a margin through another mapping function. Again - I’ll leave that for the reader to decide.

Looking forward to seeing all the new models utilising the power of fitzRoy.