Xg Model
2025-06-17
Overview
Football is a sport where every year something new is introduced, so in the year 2012 a new metric X-g was introduced that changed the whole game and how we look at it. Let us first understand what X-g is & how it works
X-g is a statistic metric that is used in football to predict the probability of a shot being a goal. It assigns a value of 0-1 to each shot where if assigned 0.2, 2 out of 10 shots will be a goal meaning higher the value higher is the chance of being a goal.
I will be training a X-g Model that can predict the X-g value of a shot being a goal or not based on historical data of similar shots
Gathering & Cleaning Data
Loading the libraries & the Data set
library(jsonlite)
library(tidyverse)
library(ggsoccer)
library(caret)
library(pROC)The data set I will be using contains the Event Data of the matches played in the Bundesliga (German First Div) which i got from wyscout.
After downloading the zip file & extracting the json data, one can proceed with football data of all big European countries, Although I have also provided a zip file that contains just the event data of Germany in a Json format.
germany <- jsonlite::fromJSON("events_Germany.json")
germany <- as.data.frame(germany) #converting it to a data frame
head(germany)## eventId subEventName tags playerId positions matchId eventName teamId
## 1 8 Simple pass 1801 15231 50, 48, 50, 50 2516739 Pass 2446
## 2 8 Simple pass 1801 14786 48, 22, 50, 22 2516739 Pass 2446
## 3 8 Simple pass 1801 14803 22, 46, 22, 6 2516739 Pass 2446
## 4 8 Simple pass 1801 14768 46, 10, 6, 20 2516739 Pass 2446
## 5 8 Simple pass 1801 14803 10, 4, 20, 27 2516739 Pass 2446
## 6 8 Simple pass 1801 40657 4, 1, 27, 18 2516739 Pass 2446
## matchPeriod eventSec subEventId id
## 1 1H 2.409746 85 179896442
## 2 1H 2.506082 85 179896443
## 3 1H 6.946706 85 179896444
## 4 1H 10.786491 85 179896445
## 5 1H 12.684514 85 179896446
## 6 1H 15.530516 85 179896447We see that there is a lot of unwanted variables in this data so first need to clean it throughly & also extract the x,y co-ordinates of the players who shot the ball for calculating new metrics.
shots <- germany %>%
filter(subEventName == "Shot") %>% #filtering the rows with shot
mutate(goal = if_else(sapply(tags,function(x) any(x$id[1] == 101)),1,0)) %>% #Goal column with 1 , 0
mutate(X = sapply(positions,function(x) X = x$x[1])) %>% #x co-rd of shot
mutate(Y = sapply(positions,function(x) Y = x$y[1])) %>% #y co-rd of shot
select(goal,X,Y) we could have just used the normal x-y Co-ordinate of the players, but to step things up I will be using the convention used by FOT(friends of Tracking), who have made a similar project about X-g but in python.
So the two new metrics that i will be using are the Distance & Shot Angle metric as In Football, understanding the distance from the goal and the shooting angle against the goal post is crucial for maximizing scoring chances.
Distance Helper function
The distance metric is the straight-line distance from the player’s position to the center of the goal line. it is calculated by using the pythagoreon theorem
distance <- function(X,Y) {
x <- 95 # the width of the football field meters
y <- 75 # the height of the football field in meters
x_dist <- (100 - X)*x/100
y_dist <- abs(50 - Y)*y/100
distance <- sqrt(x_dist^2 + y_dist^2) #x-dist is the horizontal distance from the player to the goal line.
#(100%) along the x-axis "right edge
#y-dist is the vertical distance from the player to the center o
#of the goal.(50%) along the y-axis "middle"
}Shot Angle Helper function
The goal angle metric helps us to determine how much of the goal post is actually visible to the player while shooting meaning the bigger the goal angle better the chances of scoring.
goal_angle <- function(X,Y) {
x <- 95 # the width of the football field meters
y <- 75 # the height of the football field in meters
x_dist <- (100 - X)*x/100 # the horizontal distance from the shot taken to the right edge of the goal line(x-axis 100%)
y_dist <- abs(50 - Y)*y/100 # the vertical distance from the shot taken to the middle
angle <- atan((7.32*x_dist)/(x_dist^2 + y_dist^2 - (7.32/2)^2)) #the "7.32" is the width of the goal post
angle <- ifelse(angle < 0,angle + pi,angle)
}Now let’s use these function to calculate the new metrics
shots <- shots %>%
mutate(Distance = distance(X,Y)) %>%
mutate(Shot_angle = goal_angle(X,Y)) %>%
mutate(goal = as.factor(goal)) EDA - Analysis before training the model
plotting the shot taken along with the ones that were counted as a goal.
set.seed(123)
sampled_shots <- shots[sample(nrow(shots), 1000), ] #the data set is too big so sampling 1000 random rows
ggplot(sampled_shots) +
annotate_pitch(colour = "black",fill = "white") +
geom_point(aes(x = X,y = Y,color = goal),alpha = 0.7) + #used gg soccer to plot the pitch
coord_cartesian(xlim = c(45, 100))
with the visuals we can easily deduce how these two metric are very important for our X-g model:
Distance = we can see how most of the goals have been scored within or near the D-area meaning that the closer the player is higher is the chance of scoring the goal.
Shot Angle = the angel the shot was taken from can also be very important irrespective of the distance the ball was shot from , as we see the front of the goal line has a concentration of goal compared to the left and right side of the goal post indicating the shot angle matters alot
Model Training
Now coming to the main part of my X-G model project that is training
the model to predict the Expected goals, There are plethora of ML
algorithms that I can use
to train my model but since I have already done a project on Testing ML prediction
algorithms , I’ll be going with Random Forest that
has the most accuracy among all the prediction algorithm.
train_dat <- createDataPartition(shots$goal, p = 0.7,list = FALSE) #splitting into 70% train and rest as test
train_data <- shots[train_dat,]
test_data <- shots[-train_dat,]I will also be cross validating using k-fold CV 5 times and then use the model to predict the test data.
set.seed(101)
trcon <- trainControl(method = "cv",number = 5)
train_rf <- train(goal ~.,data = train_data,method = "rf",trControl = trcon,verbose = FALSE)Accuracy of the Model (Model Fit)
Firstly, let’s test how accurately the model fits on our testing data through a confusion matrix.
prediction <- predict(train_rf,test_data)
confusionMatrix(prediction,test_data$goal)## Confusion Matrix and Statistics
##
## Reference
## Prediction 0 1
## 0 1800 193
## 1 45 31
##
## Accuracy : 0.885
## 95% CI : (0.8704, 0.8984)
## No Information Rate : 0.8917
## P-Value [Acc > NIR] : 0.8475
##
## Kappa : 0.1606
##
## Mcnemar's Test P-Value : <2e-16
##
## Sensitivity : 0.9756
## Specificity : 0.1384
## Pos Pred Value : 0.9032
## Neg Pred Value : 0.4079
## Prevalence : 0.8917
## Detection Rate : 0.8700
## Detection Prevalence : 0.9633
## Balanced Accuracy : 0.5570
##
## 'Positive' Class : 0
## The Accuracy of our model is 88% which is really good but we see this model is heavily skewed towards predicting non-goal(0) which is due to class imbalance, meaning that the high accuracy of this model is misleading as it only predicts non-goals(0)
we can also see this in the Predictive values as well where it has a high PPV of 90% for non goals while its NPV is only 36% for goals meaning it fails to reliably predict actual goal scoring opportunities.
In sports analytics , this model would be nothing more than a model that predicts every shot as a non goal which can be fatal for tactical decision-making about scoring potential in a match.
ROC curve
A Receiver operating characteristic curve is one of the best ways to asses model fit for models that work on binary, which perfectly fits our test case. It works by plotting TPR(true positive rate) on y-axis & FPR(false positive rate) on x-axis at different threshold(eg changing what score counts as a positive prediction).
A perfect model would shoot up to the left top edge(100% correct prediction) whereas a diagonal line means a random guesser(like a coin flip) so anything between 0.6-0.9 would be a good model while 1 would be the perfect model.
pred_roc <- predict(train_rf,test_data,type = "prob")[,"1"] #only positive values
roc_data <- roc(test_data$goal ,pred_roc) #predicted goal## Setting levels: control = 0, case = 1## Setting direction: controls < casesggroc(roc_data,colour = "green",size = 2) 
Things we can improve
The model we just trained had a lot of flaws that could lead to a disaster if used in a real setting, so here are some of the things that we can improve on
Data = The main reason for our model to be this heavily skewed was the class imbalance of the data set where the the data for non-goal overpowered the data with goal, so opting for a data set with similar class balance would not have lead to this much of a accuracy paradox where it only predicts the majority class
Metric = The metrics that we used to train the model is the type of data that can easily be collected(X,Y co-rd of player shot) or can be calculated(Goal angle, Distance) , but metrics like no of defenders, position of the keeper, the body part used to shoot are the type of data hard to collect, so using complex metrics like these would have definitely improved our models predictive abilities.
conclusion
In this project we cleaned, explored the data while also creating new metrics that was used to train our model, after checking the accuracy of the model which was not up to the mark we also came up with ways that can improve our model’s predictive abilities.
In conclusion, as discussed earlier in the overview Football is a sport which keeps on evolving & so does the data collection of it so in the near future there will be a time where we can implement data in our X-G model that we now consider impossible to collect.
MIT License
Copyright (c) 2025 XgModel authors
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