rate_colley(cr_data)
rank_colley(cr_data, keep_rating = FALSE, ties = c("average", "first",
"last", "random", "max", "min"), round_digits = 7)| cr_data | Competition results in format ready for as_longcr(). |
|---|---|
| keep_rating | Whether to keep rating column in ranking output. |
| ties | Value for |
| round_digits | Value for |
rate_colley() returns a tibble with columns
player (player identifier) and rating_colley (Colley
rating). The mean rating should be 0.5. Bigger value
indicates better player performance.
rank_colley() returns a tibble with columns player, rating_colley (if
keep_rating = TRUE) and ranking_colley (Colley ranking
computed with round_rank()).
This rating method was initially designed for games between two
players. There will be an error if in cr_data there is a game not between
two players. Convert input competition results manually or with
to_pairgames() from comperes package.
It is assumed that score is numeric and higher values are better for the player.
Computation is done based only on the games between players of interest (see
Players). Note that it isn't necessary for all players of interest to be
present in cr_data but it might be a good idea in order to obtain plausible
outcome rating.
The outline of the Colley method is as follows:
Compute Colley matrix: diagonal elements are equal to number of games played by certain player plus 2, off-diagonal are equal to minus number of common games played. This matrix will be the matrix of system of linear equations (SLE).
Compute right-hand side of SLE as 1 + 0.5*("number of player's wins" - "number of player's losses").
Solve the SLE. The solution is the Colley rating.
comperank offers a possibility to handle certain set of players. It is done
by having player column (in longcr format) as factor
with levels specifying all players of interest. In case of factor the result
is returned only for players from its levels. Otherwise - for all present
players.
Wesley N. Colley (2002) Colley’s Bias Free College Football Ranking Method: The Colley Matrix Explained. Available online at http://www.colleyrankings.com
rate_colley(ncaa2005)#> # A tibble: 5 x 2
#> player rating_colley
#> <chr> <dbl>
#> 1 Duke 0.214
#> 2 Miami 0.786
#> 3 UNC 0.5
#> 4 UVA 0.357
#> 5 VT 0.643
rank_colley(ncaa2005)#> # A tibble: 5 x 2
#> player ranking_colley
#> <chr> <dbl>
#> 1 Duke 5
#> 2 Miami 1
#> 3 UNC 3
#> 4 UVA 4
#> 5 VT 2
rank_colley(ncaa2005, keep_rating = TRUE)#> # A tibble: 5 x 3
#> player rating_colley ranking_colley
#> <chr> <dbl> <dbl>
#> 1 Duke 0.214 5
#> 2 Miami 0.786 1
#> 3 UNC 0.5 3
#> 4 UVA 0.357 4
#> 5 VT 0.643 2