Expected goals have become a prominent topic within the football blogging community since my last post. Although it can be hard to conduct expected goals analysis, due to the lack of availability of shot location data, there are some excellent sources available for people who do want to do some of their own research. Statisticians such as Michal Caley; Paul Riley; Ben Mayhew and 11tegen11 publish expected goals data, in a variety of forms, via Twitter or their own blogs. Ben Mayhew’s expected goals timeline visualisations, as shown below, provided particular inspiration for this blog post. These plots give the goals for each team, the expected goals of each team and the cumulative expected goals for each team plotted against time. Further details of these plots and the method for calculating expected goals is available at experimental361.com.

**Motivation**

From observing these plots for several matches, it appears that many of the timelines display similar game state behaviours to that shown in the above example. We can see that while the score is 0-0 Brighton’s cumulative expected goals increases more steeply than Nottingham Forest’s cumulative expected goals. However, once Brighton took a 1-0 lead around the 50th minute the cumulative expected goals of Nottingham Forest began to increase more steeply than the cumulative expected goals of Brighton. So what is the cause of this effect?

We know that in any given league game, the objective of each team is to maximise the number of points that the team gains from the match by maximising the number of goals that they score while minimising the number of goals that their opponent score. However, there is often a trade-off between these two objectives. A team that commits more players to attacking is more likely to concede goals at the other end and a team that is more defensive is less likely to score goals themselves. As the score changes within the game the relative importance of each of these objectives changes.

If we consider the example shown in the above timeline plot, we know that at 0-0 the importance of each objective is the same for each team. Scoring the first goal gains the team 2 points and conceding the first goal loses the team 1 point, if the game were to finish at that score line, meaning that both teams prioritise increasing their probability of scoring a goal over decreasing their probability of conceding a goal. When Brighton lead 1-0, conceding the next goal loses the team 2 points, if the game were to finish at that score line, whereas scoring the next goal merely increases the probability of them holding on to their current 3 points. Conversely, scoring the next goal gains Nottingham Forest 1 point, if the game were to finish at that score line, whereas conceding the next goal merely decreases the probability of them gaining any points. Therefore, when Brighton lead 1-0 the importance they associate with minimising the probability that their opponent scores the next goal increases and the importance they associate with maximising the probability that they score the next goal decreases. In contrast the importance Nottingham Forest associate with minimising the probability that their opponent scores the next goal decreases and the importance they associate with maximising the probability that they score the next goal increases. This may seem rudimentary but it is important to consider the main objectives of each team within the game. This leads to the question: how do changes in the importance each team associates with each objective effect the expected goals for and against each team within a match?

**Analysis**

Using Ben Mayhew’s cumulative expected goals timelines, we can compute the rate of increase in the cumulative expected goals for the home and the away team at each goal difference game state within each Championship game in the 2015/16 season. We will define each game state as each possible goal difference between the teams, i.e. we will define 0-0 and 1-1 as game state 0 and 1-2 and 2-3 as game state -1. We can then use it to find the expected goals per 90 minutes for the home and the away team at that game state. When we average the expected goals per 90 minutes for the home teams and the away teams at each game state we can construct the following bar graph.

The graph tells us that the average expected goals per 90 for a home team decreases as their lead increases within the game and increases as their deficit increases. Similarly, the average expected goals per 90 for an away team decreases as their lead increases within the game and increases as their deficit increases. This suggests that as the current state of the game becomes more favourable for a team then they become more defensive in order to maintain the current game state. This means that they prioritise reducing the number of chances their opponent has to score over increasing the number of chances they have to score and thus their expected goals per 90 decreases. On the other hand, as the current state of the game becomes less favourable for a team then they become more attacking in order to change the current game state and thus their expected goals per 90 increases.

We also know that the average expected goals per 90 for an away team at a given game state equals the average expected goals per 90 conceded by a home team at the opposite goal difference game state. I.e., the average expected goals per 90 for an away team with a -2 goal difference is the same as the average expected goals per 90 conceded by a home with a 2 goal difference. Therefore, the bar graph tells us than the average expected goals per 90 conceded by a home team increases as their lead increases and decreases as their deficit increases. Likewise, we see that the average expected goals per 90 conceded by an away team increases as their lead increases and decreases as their deficit increases. This appears to be caused by the greater attacking intent of the opposition when the current game state is out of the opponents favour and the reduced attacking intent of the opposition when the current game state is in the opponents favour.

We can then use this to calculate the average expected goal difference per 90 for a home team, as given in the below bar graph. It is also worth noting that the average expected goal difference per 90 for an away team at a given game state is the opposite of the average expected goal difference per 90 for a home team at the opposite game state.

We can see that as a team’s lead increases their expected goal difference per 90 decreases and as their deficit increases their expected goal difference per 90 increases, for both home and away teams. This suggests that as a team’s lead increases they become less likely to score the next goal and as their deficit increases they become more likely to score the next goal. We also can see that the bar graph is not symmetric about game state 0 which tells us that the average home team has a higher expected goal difference per 90 than the average away team at the same game state. This may be causes by home teams performing better at home than they do away but it may also be caused by a teams greater attacking intent at home than away. Many teams may feel that a draw away from home, especially against what they perceive to be a strong opponent, is a good result and thus the importance they associate with decreasing the probability of their opponent scoring the next goal is higher than it would be at home.

When computing the average expected goal difference per 90 at different game states it is important to consider the possibility of weaker teams spending more time losing and stronger teams spending more time winning, which may mean that our average expected goal difference per 90 doesn’t reflect the expected goal difference per 90 of an average team. From observing the data we find that some of the relegation favourites such as Rotherham, Bristol City and MK Dons appear to spend a slightly larger amount of time losing by 2 in the data set than other teams; but quantifying the strength of the teams which are losing or leading by 2 is difficult and will require further work. Now that we have analysed the average expected goal difference per 90 for home and away championship teams we can compare how different teams perform at different game states?

It is worth noting that the data used in this post is from the 2015/16 Championship season up to the 28/09/15 and thus each team has played at most 5 games, either home or away. This means that some teams have played very few minutes at each specific game state so we cannot analyse each team’s expected goal difference per 90 at each game state at this early point of the season. However, since every game starts at game state zero we can conduct some analysis of teams when the scores are level. We can begin by comparing team’s home expected goal difference per 90 at game state 0, as shown in the below bar graph.

We can see that Brighton, Bolton and Hull all appear in the top 5 expected goal difference per 90 at a 0 game state; the only teams who remain unbeaten at home in the Championship this season. Ipswich and several of the other teams who have been tipped for promotion such as Middlesbrough, Derby also appear to have high home expected goal differences per 90. Brentford have an extremely low expected goal difference per 90 at home at game state 0 so far this season but we should note that they have only played 116 minutes at home at game state 0. 45 of those minutes were against one of the promotion favourites Ipswich and 50 of which were against Sheffield Wednesday; who we will later see perform very well away from home at a 0 game state. Therefore, it is difficult to make any conclusions about their performance when the score is level at this early stage of the season. We can construct a similar bar graph representing each teams expected goal difference per 90 away from home, as shown below.

Again we see Middlesbrough, Brighton and Derby have an above average expected goal difference per 90 away from home; all of whom have been unbeaten away from home this season. We also find teams such as Bolton, Charlton and Blackburn who have not had an away win yet this season with some of the worst expected goal difference’s per 90 away from home in the league. Although Reading have the best expected goal difference per 90 away from home we should also note that they have only played 120 minutes at game state 0, as have Wolves, so these values may change as the sample size increases.

At this early stage of the season it is also important to consider the strength of the opponents that each team has played at each game state, either away or at home. As we mentioned previously, Brentford’s 116 minutes at game state 0 at home have included 112 minutes against Ipswich, Sheffield Wednesday or Reading; all of which appear in the top 10 in away expected goal difference per 90 at game state 0. Therefore, it may be more useful to calculate the adjusted expected goal difference per 90 for each team by computing the average strength of each team’s opponents at the same game state. The below bar graph gives the home adjusted expected goal difference per 90 for each Championship team.

After adjusting for the average away strength of each team’s opponents we do see the expected goal difference per 90 for Derby increase and the expected goal difference per 90 for Bolton, one of the relegation favourites, decrease when we adjust for their respective opponents away ability. We find that Brentford’s expected goal difference per 90 at game state 0 appears to be less of an outlier, although still the worst in the league. It may seem surprising to see Rotherham as the team with the highest expected goal difference per 90 at game state 0. When we examine the data closer we find that they have played a relatively large proportion of their minutes at game state 0 against Cardiff after they recieved a red card. Therefore, it is important to control for the effects of red cards in future analysis. We also see some other teams such as Blackburn and Sheffield Wednesday have very good expected goal differences per 90 at home at game state 0.

When we look at the away adjusted expected goal difference per 90 at game state 0 we see that Middlesbrough, Sheffield Wednesday and Brighton perform very well at home at game state 0. Reading still have one of the highest expected goal differences per 90 away at game state but, as we have stated previously, their sample size is relatively small. We see that Bolton, Brentford, Fulham and Bristol City all appear to have some of the lowest expected goal differences per 90 at game state 0 both at home and away; which may have contributed towards Marinus Dijkhuizen’s recent departure from Brentford.

**Summary**

Through analysing the cumulative expected goal timelines, constructed by Ben Mayhew, we have shown that teams have different expected goal difference per 90 at different goal difference game states within the game. This should be considered when ranking teams based on their expected goals per game and could be used to more accurately predict the results of games as the current game state changes. Our initial analysis of the current seasons games suggests that some teams perform better than others at different game states either at home or away, however we will require a larger sample size in order to accurately rank each teams expected goal difference per 90 and to compare their expected goal differences per 90 at different game states.

As the season progresses I aim to publish an updated post and conduct some more advanced statistical analysis of the expected goal difference per 90 of each team. Any comments about this analysis or any potential further work would be greatly appreciated.