```
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
```