Calculate ELO ratings — ELO • mELO

This function implements the ELO rating system for performing pairwise comparisons.

ELO(
  match_data,
  init_data = NULL,
  init_rating = 2200,
  eta = 27,
  p1_advantage = 0,
  save_history = TRUE,
  sort = TRUE
)

Arguments

match_data	A data frame containing four columns: (1) a numeric vector denoting the time period in which the game took place (2) a numeric or character identifier for player one (3) a numeric or character identifier for player two and (4) the result of the game expressed as a number, typically equal to one for a player one win, zero for a player two win and one half for a draw.
init_data	Initialise a rating model with ratings component of the returned list of the output from a previous `ELO()` call or a data.frame with columns Player and Rating.
init_rating	The initial rating for players not appearing in `init_data`.
eta	The learning rate.
p1_advantage	Player 1 advtange parameter. Either a single value or a vector equal to the number of rows in `match_data`.
save_history	If `TRUE` return the rating history for each player.
sort	If `TRUE`, sort the output ratings from highest to lowest.

Value

A list object of class "mELO_rating" with the following components:

ratings

A data frame of the results at the end of the final time period. The variables are self explanatory except for Lag, which represents the number of time periods since the player last played a game. This is equal to zero for players who played in the latest time period, and is also zero for players who have not yet played any games.

history

An array containing the ratings history for all players.

p1_advantage

A single value or a vector values for the advantage Player 1 had.

eta

The learning rate.

type

The type of model. In this case, "ELO".

preds

The player 1 success probabilities predicted prior to adjusting to the outcome of the match.

outcomes

The outcome for player 1 for each match.

preds_logloss

The mean logloss error for all predictions.

References

Elo, Arpad (1978) The Rating of Chessplayers, Past and Present. Arco. ISBN 0-668-04721-6.

Examples

# AFL data
head(afl_df)
#> # A tibble: 6 x 7
#>   match_index home_team     away_team   outcome date       home_score away_score
#>         <int> <chr>         <chr>         <dbl> <date>          <int>      <int>
#> 1           1 Richmond      Melbourne         1 2000-03-08         94         92
#> 2           2 Essendon      Port Adela~       1 2000-03-09        156         62
#> 3           3 North Melbou~ West Coast        0 2000-03-10        111        154
#> 4           4 Adelaide      Footscray         0 2000-03-11        108        131
#> 5           5 Fremantle     Geelong           0 2000-03-11        107        129
#> 6           6 St Kilda      Sydney            0 2000-03-12        100        134
afl_ELO_ratings <- ELO(afl_df[1:4], eta = 20, p1_advantage = 70)
afl_ELO_ratings
#> 
#> ELO Ratings For 18 Players Playing 3887 Games
#> 
#>             Player Rating Games Win Draw Loss Lag
#> 1         Richmond 2392.3   454 215    5  234   0
#> 2       West Coast 2340.3   468 254    4  210   4
#> 3          Geelong 2329.6   475 309    5  161   2
#> 4      Collingwood 2294.9   472 266    3  203   1
#> 5              GWS 2285.7   187  82    3  102   0
#> 6         Hawthorn 2282.1   471 276    2  193  12
#> 7           Sydney 2235.3   477 280    5  192  16
#> 8         Adelaide 2232.5   464 259    1  204  11
#> 9    Port Adelaide 2217.1   462 240    3  219   9
#> 10       Footscray 2207.2   458 213    4  241   6
#> 11        Essendon 2204.7   457 222    5  230   8
#> 12 North Melbourne 2184.2   457 227    3  227  15
#> 13  Brisbane Lions 2146.5   459 209    4  246   3
#> 14       Melbourne 2124.1   452 172    3  277  15
#> 15       Fremantle 2116.1   455 212    1  242   9
#> 16        St Kilda 2089.0   457 207    8  242  16
#> 17         Carlton 2001.0   451 165    4  282  14
#> 18      Gold Coast 1917.4   198  47    1  150  13
#>