From the Archives: Score Effects and Game Paths

Score effects in the 14/15 Championship

Originally published 12/03/2015

One of the most useful and widespread tools in football ‘fanalytics’ is the shot ratio. Both Total Shots Ratio (TSR) and Shots on Target Ratio (SoTR) derive their utility from their high repeatability and predictability; though they by no means tell the full story,we are more likely to be correct in predicting a team’s future performance within a season by looking at their TSR than by simply looking at their points or goal difference.

Shots ratios are also useful as they allow us to quantify how much a team dominates the shots tally. Again, despite not telling the full picture (just look at Derby County this season), we know intuitively that teams that can take more shots than their opponents will generally score more points than those that concede a greater share of the shots.

However, as the old cliché goes, goals change games. In fact, the change that takes place on the scoreboard can be seen no the shots chart, too. As Ben Pugsley, puts it in his primer for score effects in the Premier League: “The team that takes the lead in any given fixture is likely to sit a little deeper and take fewer shots. The team that is trailing will attack more and take more shots – especially as time begins to tick down.”

So do we see the same effect in the Championship?

Using 2014/15 data, we can look at the shots ratios by each game state, where game state is simply the relative score (i.e. a team winning by one goal is at a game state of +1, while a team losing by four goals would be at -4). N.B. The vast majority of playing time and shots occur at the ‘close’ game states (-1,0, and +1), so due to the reduced sample sizes of more extreme scores, it is best to focus most of our attention on trends within close states.

Total Shots Ratio

TSR GS

Mirroring Ben Pugsley’s Premier League findings, we see that teams at +1 tend to be slightly outshot. The effect is not huge; their shot share is reduced from 50% to a little over 48% which is not a huge drop. This can seem like a strange behaviour. If teams are winning by one goal, why not push for more to extent their lead to a more comfortable 2-0, especially when they’ve proven that they can score?

The most popular explanation offered, when teams take the lead, it can be advantageous to sit back and create a defensive shell. By sitting deeper and sacrificing some of your attack in favour of defence you protect your lead. Furthermore, as the opponent struggles to break down the leading team, taking more shots from poorer situations, you can open up opportunities for the counter. Teams at +1 can therefore afford to take fewer risks and be more selective with their shots, taking fewer shots but from situations from which they are more likely to score.

So does the defensive shell hypothesis match the data? Well, we can test this by looking at expected goals by game state.

Expected Goals Ratio / Expected Goals per Shot

In short, expected goals (or xG for short) models are an attempt to weight different shots according to their likelihood of being scored. For instance, a  shot from 40 yards is generally not as valuable as one from the centre of the penalty box, and will therefore have a lower expected goals value.

xG game state

We can see here that despite taking 48.4% of the shots, teams at +1 have an xG share of 54.4%, fitting nicely with our defensive shell explanation and the bump in shot quality that teams at +1 and higher have can be seen even more clearly by looking at the average xG per shot (a measure of shot quality) and conversion by game state:

Rplot02 Rplot05

An alternative explanation

There is, of course, a competing explanation for these trends that I haven’t yet confronted. The sample of teams at +1 is likely to be biased; good teams with good players are more likely to spend time in a winning game state as opposed to bad teams and it would be unsurprising for these teams with better players to be taking better shots and converting at higher rates.

If this were the case, we would expect the trend in xG share to disappear when teams of similar quality played each other.

To test this, I split the league into 4 groups of six teams, ranked by their total xG ratio, and looked at the trends for score effects only in games in which teams of the same groups played each other. This resulted in the following plot:

Rplot06

  • Green (Top 6 xG): Bournemouth, Middlesbrough, Derby, Norwich City, Ipswich Town, Brighton-and-Hove Albion
  • Red: Watford, Nottingham Forest, Blackburn Rovers, Brentford, Reading, Sheffield Wednesday
  • Blue: Wolves, Cardiff City, Wigan Athletic, Millwall,  Huddersfield Town, Rotherham United
  • Black (Bottom 6 xG): Bolton Wanderers, Birmingham City, Fulham, Charlton Athletic, Leeds United and Blackpool.

As we can see, despite the teams being grouped by model ranking, the effect remains. This evidence is more suggestive of the defensive shell effect; however, I would expect that the alternative explanation of sample bias also plays an effect, though perhaps a smaller one.

Closing point

With all this in mind, it is incredibly important to get the first goal in the Championship. If we look at this chart of goal share by game state, we can see just how hard it is for teams to clamber out of a losing position:

Rplot07

Teams at -1 (losing by one goal) get back level just 12% of the time. Perhaps this is part of what makes the Championship such a volatile and exciting league. Even the best teams can be flipped onto their backs by a goal against and have difficulty coming back.

EDIT: Having shared this, Ronnie (@NotAllGlsEqual) shared an image of score effects in different time bands for the Premier League. This then inspired me to do something similar to show how score effects changed over the course of a Championship match:

mins75

Approximating game paths and the defensive shell hypothesis.

Originally published 02/03/2015

Recently, I looked at game states in the Championship; however, by taking some of the ideas presented by Dan Altman, namely the idea that score can be interpreted as path-dependent rather than a state variable, we can shed more light on the effect that goals have on shot ratios. In short, being path-dependent simply means that how a game state is reached is significant. In my previous post, I treated all the time spent at +1 as equivalent. However, a team can reach the +1 game state either by scoring a goal at +0, or by conceding from +2. A path oriented approach treats both of these instances as separate rather than lumping them together. By taking into account which team scored the previous goal (i.e. is Game State decreasing or increasing, we can further investigate how goals change games.

Total Shot Share

Rplot37

Expected Goals Ratio

Rplot36

This would appear to suggest, along with the effect of time on score effects (see Garry Gelade’s excellent piece and this gif), that defensive shelling occurs when the leading team is under more pressure; it suggests that having just scored, teams are more likely to be outshot especially towards the end of matches. The position of the blue line (teams having just scored) relative to the pink in these two plots agrees with the defensive shell rationalisation, as touched upon in the previous post on game states. Having just scored, teams take fewer shots (blue lower than pink on total shots); however, those shots that they do take tend to be of better quality (blue higher than/similar to pink on xG).

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