Tuesday, 9 April 2013

Game State and Goalless Games.

It goes without saying that a goal scored changes the balance and dynamics of a football game. In the widest, most general terms, the average opening goal scored by an average home side against similarly mundane opponents adds about eight tenths of a league point to that teams long term points expectation. So scoring first is always good for the team taking the lead.

What is less obvious is the overall effect the concession of the opening goal has on their opponents. The relative ability of opponents can readily be expressed in terms of goal expectancy, the value of which is reduced as time elapses. It is reasonable to assume that once a goal has been scored, the remainder of the game proceeds in accordance with the present values of these decayed goal expectancy values.

However, this isn't quite what happens. Either through a re balance of tactical approaches or a burst of more intense effort from the trailing side, the side which conceded the opening goal becomes slightly more likely to score next goal, if there is one, than if the game had remained scoreless. In short, goal expectancy is a product of relative team talent, but it is also tweaked by the current state of the game.

Some great work is currently being done in this area and I'll link the best at the end of this post. But for now I'd like to flesh out some previous posts of mine to try to understand the subtle changes that occur over a season and also within a single match.

2010/11 was a reasonably successful season for Arsenal. They were in contention for the title well into March, but ultimately fell away to finish 4th. A series of scoreless home draws meant that even a narrow late season win at home to ultimate champions, Manchester United offered more hope to pursuers such as Chelsea than it did to the Gunners themselves.

Their season had peaks and troughs and they spent just over 43% of the time stalemated, led for around 40% of the playing time and trailed for 16% of the time. So in terms of game state as measured purely by current score, the Gunners provided a reasonably sized sample in terms of winning, drawing and trailing.

Goal attempts are a decent measure of a side's attacking intent, particularly if shot location is incorporated to provide the likely chance of success for each effort. In previous posts, I've charted the increased rate at which Arsenal peppered the opposition goal as they moved from a position of supremacy on the score board to a losing position. Those numbers are worth repeating and with the addition of an average goal expectancy, based on x, y data we can see how a team's frequency and potency of attempt might change with the current scoreline.

                Arsenal's Shooting Frequency and Efficiency By Game State. 2010/11.

Game State by Score. Time Between Shots. Goal Expectation/Shot Average Time To Score.
Leading. 5 min 40 secs. 0.106 53 mins 19 secs.
Drawing. 5 min 03 secs. 0.108 46 mins 34 secs.
Losing. 4 min 43 secs. 0.105 44 mins 47 secs.

The table above paints a broad picture of Arsenal's attacking response to certain scorelines averaged over a wide variety of opponents. However, much of the detail and nuances of individual games is lost. Overall, the most ambiguous game state occurs when sides are level and in the case of Arsenal in 2010/11 this was their most common state in which the team found itself.

Game states change dramatically if a goal is scored, but they are also shaped by the relentless passing of time and the quality of the opposition. Arsenal are a top side, so a draw, especially at home is below their pregame expectation. However, even against the poorest teams in the Premiership a stalemate after just 10 minutes of play isn't totally unexpected or even cause for much concern. This isn't the case if the same game is still goalless in the 80th minute. The game is still scoreless, but the game state from an Arsenal perspective is massively different from the one they were experiencing 70 playing minutes earlier.

To demonstrate how game state can change, even if the scoreline doesn't, I've plotted Arsenal's disappointing 0-0 draw at home to Blackburn from 2010/11. At the start of the match, the Gunners would have expected to average just under 2.4 points from such a miss match. As time elapsed back in April 2011 and Arsenal's initial burst failed to produce an opening goal, their current points expectation slowly declined from the optimistic initial total. By halftime their current average expected number of league points stood about 15% below the total at kickoff and is denoted by the red column.

The situation at the interval wasn't satisfactory, but it wasn't dire for Arsenal and after creating a barrage of chances in the first half hour, they had drawn breath slightly. The cumulative goal expectancy of all their goal attempts in the first ten minutes would have averaged a third of a goal, long term. In the reality of this particular trial, the shots had proved fruitless. Their long term goal expectation during each ten minute period is denoted by the green columns.

As the game remained goalless, Arsenal's likely points haul retreated further from their hoped for pregame average. Aside from a barren ten minute spell after the hour (possibly indicative of an inability of even the fittest of sides to maintain maximum effort across an entire 90 minutes) Arsenal's goal expectation from their increasing goal efforts rose in step with their declining likely final reckoning. The final 10 minutes plus stoppage time alone saw four goal attempts and in a goalless game Arsenal played the final 20 minutes as though they were losing on the scoreboard.

Small effects are often magnified and become more noticeable in extreme match ups. Arsenal's experience and reaction to their failure to break the deadlock in a game which they expected to win is mirrored in varying amounts in every game. A draw at any stage of a match will rarely be equally satisfying to both sides. The ticking clock, as well as goals can subtly alter a side's approach to a match.

For more on game states, check out Ben Pugsley and 11tegen11

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