vignettes/elo-ratings-example.Rmd
elo-ratings-example.RmdA 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.
First we need to grab a few packages. If you don’t have any of these, you’ll need to install them.
Our first job is to now get the relevant data. For the most basic of
ELO models, we need to have the results of past matches that includes
the home and away team and the score of the match. To do our
predictions, we also need upcoming matches. We can get both of those
things using fitzRoy.
For this example we will use results data from AFL Tables and
fixture data from Footywire. While this is generally
fine, it can cause issues with teams, dates, venues or various other
data to be inconsistent. This example will try to show some ways to take
that into account.
# Get data
results <- fitzRoy::fetch_results_afltables(1897:2019)
fixture <- fitzRoy::fetch_fixture_footywire(2019)We can make sure our results are from before the fixture we are trying to predict for.
results <- results %>% filter(Date < "2019-01-01")
tail(results)
#> # A tibble: 6 × 16
#> Game Date Round Home.Team Home.Goals Home.Behinds Home.Points Away.Team
#> <dbl> <date> <chr> <chr> <int> <int> <int> <chr>
#> 1 15402 2018-09-08 QF West Coa… 12 14 86 Collingw…
#> 2 15403 2018-09-14 SF Hawthorn 10 11 71 Melbourne
#> 3 15404 2018-09-15 SF Collingw… 9 15 69 GWS
#> 4 15405 2018-09-21 PF Richmond 8 10 58 Collingw…
#> 5 15406 2018-09-22 PF West Coa… 18 13 121 Melbourne
#> 6 15407 2018-09-29 GF West Coa… 11 13 79 Collingw…
#> # ℹ 8 more variables: Away.Goals <int>, Away.Behinds <int>, Away.Points <int>,
#> # Venue <chr>, Margin <int>, Season <dbl>, Round.Type <chr>,
#> # Round.Number <int>
fixture <- fixture %>% filter(Date > "2019-01-01")
head(fixture)
#> # A tibble: 6 × 7
#> Date Season Season.Game Round Home.Team Away.Team Venue
#> <dttm> <dbl> <int> <dbl> <chr> <chr> <chr>
#> 1 2019-03-21 19:25:00 2019 1 1 Carlton Richmond M.C.…
#> 2 2019-03-22 19:50:00 2019 2 1 Collingwood Geelong M.C.…
#> 3 2019-03-23 13:45:00 2019 3 1 Melbourne Port Adelai… M.C.…
#> 4 2019-03-23 16:05:00 2019 4 1 Adelaide Hawthorn Adel…
#> 5 2019-03-23 19:20:00 2019 5 1 Brisbane Lions West Coast Gabba
#> 6 2019-03-23 19:25:00 2019 6 1 Footscray Sydney Dock…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.
Since our fixture data and results data are
coming from different sources, we need to fix a few things up. This is a
good time to point out that using similar sources is great when
possible!
fixture <- fixture %>%
filter(Date > max(results$Date)) %>%
mutate(Date = ymd(format(Date, "%Y-%m-%d"))) %>%
rename(Round.Number = `Round`)
head(fixture)
#> # A tibble: 6 × 7
#> Date Season Season.Game Round.Number Home.Team Away.Team Venue
#> <date> <dbl> <int> <dbl> <chr> <chr> <chr>
#> 1 2019-03-21 2019 1 1 Carlton Richmond M.C.G.
#> 2 2019-03-22 2019 2 1 Collingwood Geelong M.C.G.
#> 3 2019-03-23 2019 3 1 Melbourne Port Adelaide M.C.G.
#> 4 2019-03-23 2019 4 1 Adelaide Hawthorn Adela…
#> 5 2019-03-23 2019 5 1 Brisbane Lions West Coast Gabba
#> 6 2019-03-23 2019 6 1 Footscray Sydney Dockl…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 for a great explainer on the types of parameters that could be included.
# Set parameters
HGA <- 30 # home ground advantage
carryOver <- 0.5 # season carry over
k_val <- 20 # update weighting factorThe 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.
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.
# Run ELO
elo.data <- elo.run(
map_margin_to_outcome(Home.Points - Away.Points) ~
adjust(Home.Team, HGA) +
Away.Team +
regress(Season, 1500, carryOver) +
group(seas_rnd),
k = k_val,
data = results
)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.
as.data.frame(elo.data) %>% tail()
#> team.A team.B p.A wins.A update.A update.B elo.A
#> 15402 West Coast Collingwood 0.5515137 0.60000 0.9697255 -0.9697255 1539.107
#> 15403 Hawthorn Melbourne 0.5113012 0.29375 -4.3510249 4.3510249 1523.735
#> 15404 Collingwood GWS 0.5392561 0.56250 0.4648788 -0.4648788 1531.709
#> 15405 Richmond Collingwood 0.5895225 0.25625 -6.6654499 6.6654499 1557.928
#> 15406 West Coast Melbourne 0.5208901 0.91250 7.8321977 -7.8321977 1546.939
#> 15407 West Coast Collingwood 0.5552715 0.53125 -0.4804305 0.4804305 1546.459
#> elo.B
#> 15402 1531.244
#> 15403 1554.582
#> 15404 1533.445
#> 15405 1538.375
#> 15406 1546.750
#> 15407 1538.855We 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 Footscray
#> [2776,] 1518.969 1460.671 1407.966 1532.832 1506.459 1500 1459.628
#> [2777,] 1526.679 1458.724 1400.256 1532.214 1510.554 1500 1462.985
#> [2778,] 1526.679 1458.724 1400.256 1531.244 1510.554 1500 1462.985
#> [2779,] 1526.679 1458.724 1400.256 1531.709 1510.554 1500 1462.985
#> [2780,] 1526.679 1458.724 1400.256 1538.375 1510.554 1500 1462.985
#> [2781,] 1526.679 1458.724 1400.256 1538.855 1510.554 1500 1462.985
#> Fremantle Geelong Gold Coast GWS Hawthorn Melbourne
#> [2776,] 1441.642 1545.611 1407.340 1531.149 1527.969 1542.932
#> [2777,] 1442.260 1551.114 1401.837 1526.721 1530.186 1547.360
#> [2778,] 1442.260 1548.243 1401.837 1533.910 1528.086 1550.231
#> [2779,] 1442.260 1548.243 1401.837 1533.445 1523.735 1554.582
#> [2780,] 1442.260 1548.243 1401.837 1533.445 1523.735 1546.750
#> [2781,] 1442.260 1548.243 1401.837 1533.445 1523.735 1546.750
#> North Melbourne Port Adelaide Richmond St Kilda Sydney University
#> [2776,] 1501.208 1523.464 1565.850 1454.058 1536.062 1500
#> [2777,] 1503.590 1519.369 1562.493 1451.676 1533.845 1500
#> [2778,] 1503.590 1519.369 1564.594 1451.676 1526.655 1500
#> [2779,] 1503.590 1519.369 1564.594 1451.676 1526.655 1500
#> [2780,] 1503.590 1519.369 1557.928 1451.676 1526.655 1500
#> [2781,] 1503.590 1519.369 1557.928 1451.676 1526.655 1500
#> West Coast
#> [2776,] 1536.190
#> [2777,] 1538.137
#> [2778,] 1539.107
#> [2779,] 1539.107
#> [2780,] 1546.939
#> [2781,] 1546.459Lastly, 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).
final.elos(elo.data)
#> Adelaide Brisbane Lions Carlton Collingwood Essendon
#> 1526.679 1458.724 1400.256 1538.855 1510.554
#> Fitzroy Footscray Fremantle Geelong Gold Coast
#> 1345.451 1462.985 1442.260 1548.243 1401.837
#> GWS Hawthorn Melbourne North Melbourne Port Adelaide
#> 1533.445 1523.735 1546.750 1503.590 1519.369
#> Richmond St Kilda Sydney University West Coast
#> 1557.928 1451.676 1526.655 1386.787 1546.459We 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.
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.
fixture <- fixture %>%
mutate(Prob = predict(elo.data, newdata = fixture))
head(fixture)
#> # A tibble: 6 × 8
#> Date Season Season.Game Round.Number Home.Team Away.Team Venue Prob
#> <date> <dbl> <int> <dbl> <chr> <chr> <chr> <dbl>
#> 1 2019-03-21 2019 1 1 Carlton Richmond M.C.… 0.324
#> 2 2019-03-22 2019 2 1 Collingwood Geelong M.C.… 0.530
#> 3 2019-03-23 2019 3 1 Melbourne Port Ade… M.C.… 0.582
#> 4 2019-03-23 2019 4 1 Adelaide Hawthorn Adel… 0.547
#> 5 2019-03-23 2019 5 1 Brisbane Lio… West Coa… Gabba 0.418
#> 6 2019-03-23 2019 6 1 Footscray Sydney Dock… 0.452From here - you could turn these probabilities back into a margin through another mapping function. Again - I’ll leave that for the reader to decide.