Using xPG variants to assess risk-and-reward of the game
We introduced Expected Possession Goals (xPG) in two recent articles. xPG groups and rates the outcome of a possession and began from an idea that every action in the possession connects to create a shot. Here, we’re introducing new xPG variants, extensions to the original xPG definition to assess the risks and rewards inherent in a soccer possession.
xPG rates a group of uninterrupted events - or when an interruption lasts fewer than two seconds - based on where the ball travels. It assumes the purpose of the possession is to move the ball within shooting distance.
For xPG, we use a non-shot xG (NSxG) model that divides a pitch into 162 zones (zNSxG). Each zone is assigned a value based upon the mean xG of MLS shots taken within that zone since the start of the ASA era. This forms the Positive NSxG map. Additionally, we invert the map, negate all non-zero values and create the Negative NSxG map. Each action in a game (e.g. passes, dribbles, shots) is assigned a Positive and Negative NSxG value based upon the zone where the action started. These two maps allow us to assign weighted values to all actions for the team possessing the ball- not just shots for each team in the game. Put another way, the Positive non-shot xG is the value of the action to the offensive team, and the negative non-shot xG is the potential cost of the action if the ball was turned over to the defensive team.
We developed Positive xPG and Negative xPG because a possession generally serves two key purposes:
- when the possessing team advances the ball, its probability to score – or its Positive xPG – increases.
- at the same time, as the possessing team moves the ball away from its own goal, the risk of a turnover to immediately result in a shot for the other team decreases. This is expressed in Negative xPG.
Let’s take a look at an example possession.
The diagram above shows the same possession on both Positive NSxG (scoring probability) and Negative NSxG (risk) maps beginning with a goal kick (successful pass) out to the right back (1), a successful pass to the defensive midfielder (2), a successful dribble by the DM past a defender (3) and then an unsuccessful pass to the right midfielder (4). Actions (1), (2), and (3) add up to 0.009 Positive xPG and -0.197 Negative xPG for the team. Action (4) gets no value since it was unsuccessful.
In this case, the possession did not result in any shot, and Expected Goals (xG) would not assign the possession any value. The same goes for Expected Goal Chain (xGChain) and Expected Buildup (xB), which are also derived from xG. In contrast, our xPG model will give the possession the same value whether it results in the shot or not. xPG measures how likely the possession can create a shot and the risk if the ball was turned over during the possession while xG measures how likely a shot can become a goal.
Next, we define possessions that end in a shot as Successful xPG. Successful xPG differs from xG in that value for the entire possession (Positive xG) is assigned to every involved player, which includes, but is not limited to, the xG of the shot. The sequence above was not Successful xPG because it did not result in a shot, but if it had, the value of each of the actions in the sequence would have been assigned to each involved player. As such, Successful xPG resembles xGChain, but it is different since xGChain gives only the shot xG value to all the players in the chain, whereas Successful xPG gives the NSxG values of all actions in the chain to each player involved.
Let’s take a look at a Successful xPG example:
The diagram above shows a series of four consecutive successful actions, beginning with a ball-winning defensive action (1) by the left midfielder and ending with a shot (4) in the yellow zone by the striker. The first three actions: defensive action, successful dribble, and successful pass, total 0.052 Positive xPG. Again, we are using the value from the zone where each action took place to calculate xPG. Any possession sequence which ends in a shot will also receive the possession value in Successful xPG in addition to Positive xPG. The shot uses ASA’s coordinate xG model (rather than xPG’s zonal model) so the actual value may vary from the 0.111 seen here just outside the six-yard box (the yellow shaded box). For simplicity, let’s say the shot’s xG was 0.100. If we add the values of the tackle (0.008), the dribble (0.016) and the pass (0.028), the total value is 0.152 for both Positive xPG and Successful xPG. 0.152 will be added to each player who performed at least one of the four actions. In this example, actions (1), (2), and (3) were all performed by the same player, the left midfielder, who would get all 0.052 of those actions plus the 0.100 shot xG. The same values would also be given to the Positive xPG and Successful xPG of the striker who took the shot.
Finally, we quantify the materialized risk of a possession that ends with a failed pass or dribble as Mistake xPG. Mistake xPG is determined by the total Positive xPG of the following opponent possession. While the other xPG values (Positive, Negative, and Successful) are shared by all players involved in a possession, Mistake xPG is assigned only to the player that lost possession. This allows us to measure identify players who make the most damaging errors.
Let’s look at a Mistake xPG example:
Let’s revisit our earlier Positive xPG example. The possession on the Positive NSxG map ends with an unsuccessful pass from the defensive midfielder (the red arrow in the image on the left). For Mistake xPG, the opponent’s ensuing possession’s xPG values, overlaid on the Negative NSxG map, are assigned to the player who made the “mistake.” The origin of the defensive action (1) has no Negative xPG value (0.000), but it is followed by actions (2), (3), and (4) which each are successful for a total of -0.027 xPG. The possession is ended by an unsuccessful cross, so the Mistake xPG stops accruing. The defensive midfielder is assigned the Mistake xPG of -0.027. During this possession, the opponent is accruing their own Positive xPG and Negative xPG (not shown).
We now have four xPG variants that each provide us different information about possessions:
- Positive xPG is the sum of the action values when overlaid on the Positive NSxG map for a particular sequence regardless if the possession ends in a shot or not.
- Successful xPG is the same as Positive xPG, but it is only used for possession sequences which end in a shot.
- Negative xPG is the sum of the action values when overlaid on the Negative NSxG map for a particular sequence regardless if the possession ends in a shot or not.
- Mistake xPG is the Positive xPG of the opponent’s ensuing possession when a player turns the ball over.
Here are a couple game clips to help further explain the concepts of the four xPG variants (get out your earbuds for the audio):
First, one on Positive xPG and Negative xPG with the Columbus Crew
Successful xPG and Mistake xPG with the New York Red Bulls:
Now, let's take a look at how each MLS team breaks down in each of the four categories. Values in green show the top 20% and Values in red show the bottom 20%. Remember that high negative xPG is not undesirable unless accompanied by a high Mistake xPG, so the higher values here are expressed with green rather than with red.
MLS 2018 xPG Leaders and Laggards
|Games||Avg Successful xPG||Avg Positive xPG||Avg Negative xPG||Avg Mistake xPG|