Since the time of his post, some slight modifications have been made to the model. Karun incorporated pass completion rates so the first expression shown above is now also multiplied by the probability that a pass is completed from zone (x,y) to zone (z,w). Including this helps us factor in pass difficulty, which was previously not accounted for. He also changed the dimensions of the zones, so field is broken up into a 12x8 grid with 96 zones rather than the original 192.

As Karun mentions later in his post, this final metric requires a bit more work because, as noted above, the calculation for the xT value of a zone requires previously knowing xT values for all of the other zones. He solved this problem by first setting the initial xT = 0 for all of the zones and then evaluating the formula iteratively until convergence.

Using the work Karun did to create the xT map with values for all of the zones, I first focused on finding the value of a player carrying the ball. During a possession, I attributed the change in the xT value of when a player receives the ball to when he releases the ball as the value of the ball carry for the player. Since no one else touches the ball during that time, the change in xT can only be attributed to the player with the ball at his feet, thus denoting the value of the carry.

There are only two ways in which a player can ‘receive’ the ball. Either he has received a pass from one of his teammates, or he has won the ball back from the other team with a successful defensive action (interception or tackle won).

When the shooter’s team already has the ball and the player is simply receiving a pass from one of his teammates before shooting, the calculation is simple. Using the ending coordinates of the pass from a player’s teammate, we are able to assign an xT value at the time the player receives the ball. Then, by subtracting that value from the xT at the time of the shot, we’re able to assign a shotcreating.xT value to each and every attempt by a player.

The second scenario, where a player wins the ball back from the opposition and, without passing it off to one of his teammates, goes on to take a shot, is far less common – but with the increased pressing in the modern game, defenders have become more prone to trying difficult passes in dangerous areas, often surrendering possession in and around their own box.