Bayesian Bradley-Terry

Bayesian Bradley-Terry

bbt_run(
  formula,
  data,
  r = numeric(0),
  rd = numeric(0),
  init_r = 25,
  init_rd = 25/3,
  lambda = NULL,
  share = NULL,
  weight = NULL,
  kappa = 0.5
)

Arguments

formula

formula which specifies the model. RHS Allows only player rating parameter and it should be specified in following manner:

rank | id ~ player(name).

• rank player position in event.

• id event identifier in which pairwise comparison is assessed.

• player(name) name of the contestant. In this case player(name) helps algorithm point name of the column where player names are stored.

Users can also specify formula in in different way:

rank | id ~ player(name|team). Which means that players are playing in teams, and results are observed for teams not for players. For more see vignette.

data

data.frame which contains columns specified in formula, and optional columns defined by lambda, weight.

r

named vector of initial players ratings estimates. If not specified then r will be created automatically for parameters specified in formula with initial value init_r.

rd

rd named vector of initial rating deviation estimates. If not specified then rd will be created automatically for parameters specified in formula with initial value init_rd.

init_r

initial values for r if not provided. Default (glicko = 1500, glicko2 = 1500, bbt = 25, dbl = 0)

init_rd

initial values for rd if not provided. Default (glicko = 350, glicko2 = 350, bbt = 25/3, dbl = 1)

lambda

name of the column in data containing lambda values or one constant value (eg. lambda = colname or lambda = 0.5). Lambda impact prior variance, and uncertainty of the matchup result. The higher lambda, the higher prior variance and more uncertain result of the matchup. Higher lambda flattens chances of winning.

share

name of the column in data containing player share in team efforts. It's used to first calculate combined rating of the team and then redistribute ratings update back to players level. Warning - it should be used only if formula is specified with players nested within teams (player(player|team)).

weight

name of the column in data containing weights values or one constant (eg. weight = colname or weight = 0.5). Weights increasing (weight > 1) or decreasing (weight < 1) update change. Higher weight increasing impact of event result on rating estimate.

kappa

controls rd shrinkage not to be greater than rd*(1 - kappa). kappa=1 means that rd will not be decreased.

Value

A "rating" object is returned:

• final_r named vector containing players ratings.

• final_rd named vector containing players ratings deviations.

• r data.frame with evolution of the ratings and ratings deviations estimated at each event.

• pairs pairwise combinations of players in analysed events with prior probability and result of a challenge.

• class of the object.

• method type of algorithm used.

• settings arguments specified in function call.

Examples

# the simplest example
data <- data.frame(
  id = c(1, 1, 1, 1),
  team = c("A", "A", "B", "B"),
  player = c("a", "b", "c", "d"),
  rank_team = c(1, 1, 2, 2),
  rank_player = c(3, 4, 1, 2)
)

bbt <- bbt_run(
  data = data,
  formula = rank_player | id ~ player(player),
  r = setNames(c(25, 23.3, 25.83, 28.33), c("a", "b", "c", "d")),
  rd = setNames(c(4.76, 0.71, 2.38, 7.14), c("a", "b", "c", "d"))
)

# nested matchup
bbt <- bbt_run(
  data = data,
  formula = rank_team | id ~ player(player | team)
)