Movatterモバイル変換

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 onhttp://www.tennis-data.co.uk/notes.txt

Usage

data(atp_2019)

Format

An object of class"data.frame".

Source

Tennis archive fromhttp://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 thresholdsr andq, 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 playeri for allthe 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 playeri wins the matcht against playerjandq_{i,j}(t) is its implied probability obtained as the reciprical of the Bet365 odds. The impliedprobabilityq_{i,j}(t) is assumed to be greater thanq. Ifq=0, all the players are considered. Ifq increases,heavy longshot players are excluded.In general, higher thresholdsr andq 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

Value

A matrix including the number of bets placed, the Return-on-Investiment (ROI), expressed in percentage, and its boostrap confidence interval,calculated usingR 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 thewelofit function.

Usage

clean(x, MNM = 10, MRANK = 500)

Arguments

Details

The cleaning operations are:

1. Remove all the uncompleted matches;

2. Remove all the NAs from B365 odds;

3. Remove all the NAs from the variable "ranking";

4. Remove all the NAs from the variable "games";

5. Remove all the NAs from the variable "sets";

6. Remove all the matches where the B365 odds are equal;

7. Define playersi andj and their outcomes (Y_i andY_j);

8. Remove all the matches of players who played less than MNM matches;

9. Remove all the matches of players with rank greater than MRANK;

10. 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 playersi andj randomly chosen, among all the matches selected bythe following strategy:by default, the amount of $1 is placed on the best odds (that is, the highest odds available) for playeri for allthe 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 playeri wins the matcht against playerjandq_{i,j}(t) is its implied probability obtained as the reciprical of the Bet365 odds. The impliedprobabilityq_{i,j}(t) is assumed to be greater thanq. Ifq=0, all the players are considered. Ifq increases,heavy longshot players are excluded.Once got the number of matches satisfying the previously described strategy, each player (i andj) on whichplace a bet is randomly selected. Then the Return-on-Investiment (ROI) of this strategy is stored. Finally, the mean of the ROIobtained from repeating this operationB times is reported.

Usage

random_betting(  x,  r,  q,  model,  bets = "Best_odds",  B = 10000,  start_oos = NULL,  end_oos = NULL)

Arguments

Value

A matrix reporting the number of bets and the mean of the ROI (in percentage) across theB values for everythreshold 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

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

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 playeri wins over playerj for match at timet+1 using the WElo or Elo rates at timet. Formally:

\hat{p}_{i,j}(t+1) = \frac{1}{1+10^{\left(E_j(t)-E_i(t)\right)/400}},

whereE_{i}(t) andE_j(t) are the WElo or Elo rates at timet.

Usage

tennis_prob(i, j)

Arguments

Value

Probability that playeri wins the match against playerj

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

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 systemdefines the rates (for playeri) as:

E_{i}(t+1) = E_{i}(t) + K_i(t) \left[W_{i}(t)- \hat{p}_{i,j}(t) \right],

whereE_{i}(t) is the Elo rate at timet,W_{i}(t) is the outcome (1 or 0) for playeri in the match at timet,K_i(t) is a scale factor, and\hat{p}_{i,j}(t) is the probability of winning for match at timet, calculated usingtennis_prob.The scale factorK_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},

whereN_i(t) is the number of matches disputed by playeri up to timet. Alternately,K_i(t) can be multiplied by 1.1 ifthe match at timet 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)),

whereE_{i}^\ast(t+1) denotes the WElo rate for playeri,\hat{p}_{i,j}^\ast(t) the probability of winning usingtennis_prob andthe WElo rates, andf(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.

whereNG_i(t) andNG_j(t) represent the number of games won by playeri and playerj in matcht, 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.

whereNS_i(t) andNS_j(t) represent the number of sets won by playeri and playerj in matcht, respectively.The scale factorK_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

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 andafter the matcht, for playersi andj,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 datadb_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 onhttp://www.tennis-data.co.uk/notes.txt

Usage

data(wta_2019)

Format

An object of class"data.frame".

Source

Tennis archive fromhttp://www.tennis-data.co.uk/

Examples

head(wta_2019)str(wta_2019)