| Title: | Weighted and Standard Elo Rates |
| Version: | 0.1.4 |
| Description: | Estimates the standard and weighted Elo (WElo, Angelini et al., 2022 <doi:10.1016/j.ejor.2021.04.011>) rates. The current version provides Elo and WElo rates for tennis, according to different systems of weights (games or sets) and scale factors (constant, proportional to the number of matches, with more weight on Grand Slam matches or matches played on a specific surface). Moreover, the package gives the possibility of estimating the (bootstrap) standard errors for the rates. Finally, the package includes betting functions that automatically select the matches on which place a bet. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.2.3 |
| RdMacros: | Rdpack |
| Depends: | R (≥ 4.1.0), |
| Imports: | xts (≥ 0.12.0), Rdpack (≥ 1.0.0), boot (≥ 1.3), rio (≥ 0.5.29), ggplot2 (≥ 3.3.5), reshape2 (≥ 1.4.4) |
| Suggests: | knitr |
| NeedsCompilation: | no |
| Packaged: | 2024-03-19 08:20:37 UTC; candi |
| Author: | Vincenzo Candila [aut, cre] |
| Maintainer: | Vincenzo Candila <vcandila@unisa.it> |
| Repository: | CRAN |
| Date/Publication: | 2024-03-19 13:50:02 UTC |
Accuracy
Description
Calculates the accuracy rate score.
Usage
ACC(y, y_hat, quant)
Value
Percentage of matches correctly predicted.
Brier score
Description
Calculates the Brier score.
Usage
BS(y, y_hat)
Value
Vector of the errors.
Log-loss score
Description
Calculates the Log-loss score.
Usage
LL(y, y_hat)
Value
Vector of the errors.
ATP matches in 2019
Description
Tennis data for male matches played in 2019. Details can be found on http://www.tennis-data.co.uk/notes.txt
Usage
data(atp_2019)
Format
An object of class "data.frame".
Source
Tennis archive from http://www.tennis-data.co.uk/
Examples
head(atp_2019)
str(atp_2019)
Betting function
Description
Places bets using the WElo and Elo probabilities, on the basis of two thresholds r and q, according to Angelini et al. (2022).
By default, the amount of $1 is placed on the best odds (that is, the highest odds available) for player i for all
the matches where it holds that
\frac{\hat{p}_{i,j}(t)}{q_{i,j}(t)} > r,
where \hat{p}_{i,j}(t) is the estimated probability (coming from the WElo or Elo model) that player i wins the match t against player j
and q_{i,j}(t) is its implied probability obtained as the reciprical of the Bet365 odds. The implied
probability q_{i,j}(t) is assumed to be greater than q. If q=0, all the players are considered. If q increases,
heavy longshot players are excluded.
In general, higher thresholds r and q imply less betting opportunities.
Usage
betting(
x,
r,
q,
model,
bets = "Best_odds",
R = 2000,
alpha = 0.1,
start_oos = NULL,
end_oos = NULL
)
Arguments
x |
an object of class 'welo', obtained from the |
r |
Vector or scalar identifying the threshold of the ratio between the estimated and the implied probability (see above) |
q |
Scalar parameter used to exclude the heavy underdogs signalled by Bet365 bookmaker.
No bets will be placed on those matches where players have implied probabilities smaller than |
model |
Valid choices are: "WELO" and "ELO" |
bets |
optional Parameter identifying on which type of odds the bet is placed. Default to "Best_odds". Valid choices are: "Best_odds", "Avg_odds" and "B365_odds". "Best_odds" are the highest odds available. "Avg_odds" are the average odds for that match and "B365_odds" are the Bet365 odds |
R |
optional Number of bootstrap replicates to calculate the confidence intervals. Default to 2000 |
alpha |
optional Significance level for the boostrap confidence intervals. Default to 0.1 |
start_oos |
optional Character parameter denoting the starting year for the bets. If included (default to NULL), then the bets will be placed on matches starting in that year. It has to be formatted as "YYYY" |
end_oos |
optional Character parameter denoting the ending year for the bets. If included (default to NULL), then the bets will be placed on matches included in the period "start_oos/end_oos". It has to be formatted as "YYYY" |
Value
A matrix including the number of bets placed, the Return-on-Investiment (ROI), expressed in percentage, and its boostrap confidence interval,
calculated using R replicates and the significance level \alpha.
Examples
data(atp_2019)
db_clean<-clean(atp_2019)
db_est<-welofit(db_clean)
bets<-betting(db_est,r=c(1.1,1.2,1.3),q=0.3,model="WELO")
bets
Cleaning function
Description
Cleans the dataset in order to create a suitable data.frame ready to be used in the welofit function.
Usage
clean(x, MNM = 10, MRANK = 500)
Arguments
x |
Data to be cleaned. It must be a data.frame coming from http://www.tennis-data.co.uk/. |
MNM |
optional Minimum number of matches played by each player to include in the cleaned dataset. Default to 10. This means that each player has to play at least 10 matches |
MRANK |
optional Maximum rank of the players to consider. Default to 500. This means that all the matches with players with ranks greater than 500 are dropped |
Details
The cleaning operations are:
Remove all the uncompleted matches;
Remove all the NAs from B365 odds;
Remove all the NAs from the variable "ranking";
Remove all the NAs from the variable "games";
Remove all the NAs from the variable "sets";
Remove all the matches where the B365 odds are equal;
Define players
iandjand their outcomes (Y_iandY_j);Remove all the matches of players who played less than MNM matches;
Remove all the matches of players with rank greater than MRANK;
Sort the matches by date.
Value
Data.frame cleaned
Examples
data(atp_2019)
db_clean<-clean(atp_2019)
str(db_clean)
Random betting function
Description
Places bets on players i and j randomly chosen, among all the matches selected by
the following strategy:
by default, the amount of $1 is placed on the best odds (that is, the highest odds available) for player i for all
the matches where it holds that
\frac{\hat{p}_{i,j}(t)}{q_{i,j}(t)} > r,
where \hat{p}_{i,j}(t) is the estimated probability (coming from the WElo or Elo model) that player i wins the match t against player j
and q_{i,j}(t) is its implied probability obtained as the reciprical of the Bet365 odds. The implied
probability q_{i,j}(t) is assumed to be greater than q. If q=0, all the players are considered. If q increases,
heavy longshot players are excluded.
Once got the number of matches satisfying the previously described strategy, each player (i and j) on which
place a bet is randomly selected. Then the Return-on-Investiment (ROI) of this strategy is stored. Finally, the mean of the ROI
obtained from repeating this operation B times is reported.
Usage
random_betting(
x,
r,
q,
model,
bets = "Best_odds",
B = 10000,
start_oos = NULL,
end_oos = NULL
)
Arguments
x |
an object of class 'welo', obtained from the |
r |
Vector or scalar identifying the threshold of the ratio between the estimated and the implied probability (see above) |
q |
Scalar parameter used to exclude the heavy underdogs signalled by B365 bookmaker.
No bets will be placed on those matches where players have odds smaller than |
model |
Valid choices are: "WELO" and "ELO" |
bets |
optional Parameter identifying on which type of odds the bet is placed. Default to "Best_odds". Valid choices are: "Best_odds", "Avg_odds" and "B365_odds". "Best_odds" are the highest odds available. "Avg_odds" are the average odds and "B365_odds" are the Bet365 odds |
B |
optional Number of replicates to calculate the overall mean ROI. Default to 10000 |
start_oos |
optional Character parameter denoting the starting year for the bets. If included (default to NULL), then the bets will be placed on matches starting in that year. It has to be formatted as "YYYY" |
end_oos |
optional Character parameter denoting the ending year for the bets. If included (default to NULL), then the bets will be placed on matches included in the period "start_oos/end_oos". It has to be formatted as "YYYY" |
Value
A matrix reporting the number of bets and the mean of the ROI (in percentage) across the B values for every
threshold r used
Examples
data(atp_2019)
db_clean<-clean(atp_2019)
db_est<-welofit(db_clean)
rand_bets<-random_betting(db_est,r=c(1.1,1.2,1.3),q=0.3,model="WELO",B=1000)
rand_bets
Plot for official (ATP or WTA) rates
Description
Plots the official (ATP or WTA) rates.
Usage
rank_plot(x, players, line_width = 1.5, nbreaks = 1)
Arguments
x |
An object of class 'welo', obtained after running the |
players |
A character vector including the players whose rates will be plotted. The indication of the player has to be: 'Surname N.'. For instance, 'Roger Federer' will be included in the 'players' vector as 'Federer R.' |
line_width |
optional Line width, by default it is 1.5 |
nbreaks |
optional Number of breaks for y-axis, by default it is 1 |
Value
A ggplot2 plot
Examples
db<-tennis_data("2022","ATP")
db_clean<-clean(db,MNM=5)
res_welo<-welofit(db_clean)
players<-c("Nadal R.","Djokovic N.","Berrettini M.","Sinner J.")
rank_plot(res_welo,players,line_width=1.5)
Download data from http://www.tennis-data.co.uk/
Description
Imports ATP or WTA data from the site http://www.tennis-data.co.uk/
Usage
tennis_data(YEAR, Circuit)
Arguments
YEAR |
Year to consider, in "YYYY" format. Only years from 2013 onwards are allowed |
Circuit |
Valid choices for Circuit are: "ATP" or "WTA" |
Value
Data.frame for the YEAR and Circuit specified
Examples
db<-tennis_data("2022","ATP")
head(db)
Probability of winning
Description
Calculates the probability that player i wins over player j for match at time t+1 using the WElo or Elo rates at time t. Formally:
\hat{p}_{i,j}(t+1) = \frac{1}{1+10^{\left(E_j(t)-E_i(t)\right)/400}},
where E_{i}(t) and E_j(t) are the WElo or Elo rates at time t.
Usage
tennis_prob(i, j)
Arguments
i |
WElo or Elo rates for player |
j |
WElo or Elo rates for player |
Value
Probability that player i wins the match against player j
Examples
tennis_prob(2000,2000)
tennis_prob(2500,2000)
Plot for WElo and Elo rates
Description
Plots WElo and Elo rates.
Usage
welo_plot(x, players, rates = "WElo", SP = 1500, line_width = 1.5)
Arguments
x |
An object of class 'welo', obtained after running the |
players |
A character vector including the players whose rates will be plotted. The indication of the player has to be: 'Surname N.'. For instance, 'Roger Federer' will be included in the 'players' vector as 'Federer R.' |
rates |
optional Rates to be plotted. Valid choices are 'WElo' (by default) and 'Elo' |
SP |
optional Starting points from which the rates originate. By default, SP is 1500 |
line_width |
optional Line width, by default it is 1.5 |
Value
A ggplot2 plot
Examples
db<-tennis_data("2022","ATP")
db_clean<-clean(db,MNM=5)
res_welo<-welofit(db_clean)
players<-c("Nadal R.","Djokovic N.","Berrettini M.","Sinner J.")
welo_plot(res_welo,players,rates="WElo",SP=1500,line_width=1.5)
Calculates the WElo and Elo rates
Description
Calculates the WElo and Elo rates according to Angelini et al. (2022). In particular, the Elo updating system
defines the rates (for player i) as:
E_{i}(t+1) = E_{i}(t) + K_i(t) \left[W_{i}(t)- \hat{p}_{i,j}(t) \right],
where E_{i}(t) is the Elo rate at time t, W_{i}(t) is the outcome (1 or 0) for player i in the match at time t,
K_i(t) is a scale factor, and \hat{p}_{i,j}(t) is the probability of winning for match at time t, calculated using tennis_prob.
The scale factor K_i(t) determines how much the rates change over time. By default, according to Kovalchik (2016), it is defined as
K_i(t)=250/\left(N_i(t)+5\right)^{0.4},
where N_i(t) is the number of matches disputed by player i up to time t. Alternately, K_i(t) can be multiplied by 1.1 if
the match at time t is a Grand Slam match or is played on a given surface. Finally, it can be fixed to a constant value.
The WElo rating system is defined as:
E_{i}^\ast(t+1) = E_{i}^\ast(t) + K_i(t) \left[W_{i}(t)- \hat{p}_{i,j}^\ast(t) \right] f(W_{i,j}(t)),
where E_{i}^\ast(t+1) denotes the WElo rate for player i, \hat{p}_{i,j}^\ast(t) the probability of winning using tennis_prob and
the WElo rates, and f(W_{i,j}(t)) represents a function whose values depend on the games (by default) or sets won in the previous match.
In particular, when parameter 'W' is set to "GAMES", f(W_{i,j}(t)) is defined as:
f(W_{i,j}(t)) \equiv f(G_{i,j}(t))=
\left\{
\begin{array}{ll}
\frac{NG_i(t)}{NG_i(t)+NG_j(t)} \quad if~player~i~has~won~match~t;\\
\frac{NG_j(t)}{NG_i(t)+NG_j(t)} \quad if~player~i~has~lost~match~t,
\end{array}
\right.
where NG_i(t) and NG_j(t) represent the number of games won by player i and player j in match t, respectively.
When parameter 'W' is set to "SET", f(W_{i,j}(t)) is:
f(W_{i,j}(t)) \equiv f(S_{i,j}(t))=
\left\{
\begin{array}{ll}
\frac{NS_i(t)}{NS_i(t)+NS_j(t)} \quad if~player~i~has~won~match~t;\\
\frac{NS_j(t)}{NS_i(t)+NS_j(t)} \quad if~player~i~has~lost~match~t,
\end{array}
\right.
where NS_i(t) and NS_j(t) represent the number of sets won by player i and player j in match t, respectively.
The scale factor K_i(t) is the same as the Elo model.
Usage
welofit(
x,
W = "GAMES",
SP = 1500,
K = "Kovalchik",
CI = FALSE,
alpha = 0.05,
B = 1000,
new_data = NULL
)
Arguments
x |
Data cleaned through the function |
W |
optional Weights to use for the WElo rating system. Valid choices are: "GAMES" (by default) and "SETS" |
SP |
optional Starting points for calculating the rates. 1500 by default |
K |
optional Scale factor determining how much the WElo and Elo rates change over time. Valid choices are:
"Kovalchik" (by default), "Grand_Slam", "Surface_Hard", "Surface_Grass", "Surface_Clay" and, finally, a constant value |
CI |
optional Confidence intervals for the WElo and Elo rates. Default to FALSE. If 'CI' is set to "TRUE", then the confidence intervals are calculated, according to the procedure explained by Angelini et al. (2022) |
alpha |
optional Significance level of the confidence interval. Default to 0.05 |
B |
optional Number of bootstrap samples used to calculate the confidence intervals. Default to 1000 |
new_data |
optional New data, cleaned through the function |
Value
welofit returns an object of class 'welo', which is a list containing the following components:
results: The data.frame including a variety of variables, among which there are the estimated WElo and Elo rates, before and after the match
t, for playersiandj, the lower and upper confidence intervals (if CI=TRUE) for the WElo and Elo rates, labelled as '_lb' and '_ub', respectively, and the probability of winning the match for playeri(labelled as 'WElo_pi_hat' and 'Elo_pi_hat', respectively, for the WElo and Elo models).matches: The number of matches analyzed.
period: The sample period considered.
loss: The Brier score (Brier 1950) and log-loss (used by Kovalchik (2016), among others) averages, calculated considering the distance with respect to the outcome of the match.
highest_welo: The player with the highest WElo rate and the relative date.
highest_elo: The player with the highest Elo rate and the relative date.
dataset: The dataset used for the estimation of the WElo and Elo rates.
References
Angelini G, Candila V, De Angelis L (2022).
“Weighted Elo rating for tennis match predictions.”
European Journal of Operational Research, 297(1), 120–132.
Brier GW (1950).
“Verification of forecasts expressed in terms of probability.”
Monthly weather review, 78(1), 1–3.
Kovalchik SA (2016).
“Searching for the GOAT of tennis win prediction.”
Journal of Quantitative Analysis in Sports, 12(3), 127–138.
Examples
data(atp_2019)
db_clean<-clean(atp_2019)
res<-welofit(db_clean)
# append new data
db_clean_1<-db_clean[1:500,]
db_clean_2<-db_clean[501:1200,]
res_1<-welofit(db_clean_1)
res_2<-welofit(res_1,new_data=db_clean_2)
WTA matches in 2019
Description
Tennis data for female matches played in 2019. Details can be found on http://www.tennis-data.co.uk/notes.txt
Usage
data(wta_2019)
Format
An object of class "data.frame".
Source
Tennis archive from http://www.tennis-data.co.uk/
Examples
head(wta_2019)
str(wta_2019)