Chelsea v West Ham. Not Quite A Typical 0-0.

In this blog, I've taken two slightly different approaches when looking at how game state alters the way teams balance their risk and reward approach to periods during a match. You can either primarily look at the best sides, which allows you to assume that a tied scoreline is almost always unsatisfactory for them and therefore scoreline can largely be used as a proxy for game state. Or more recently I've concentrated on games that remain scoreless and therefore, pregame odds can be used as a proxy for the overall game state experienced by each side.

On Wednesday night both of these approximations aligned as near top, Chelsea beat near bottom, West Ham 39-1 in shots, but only drew 0-0 on the scoreboard.

Chelsea were unsurprisingly strong pregame favourites, the hosts having about an 80% chance of winning and a 15% chance of drawing for an overall match success rate of 87.5%. So the longterm points expectancy for the title challengers from such a match was 2.55 league points, because they would win 80% of the games, gaining themselves 3 points and draw for a single point 15% of the time, leaving 5% left over for a shock away win.

The longer the game remained stalemate the further the expected reality on the night fell away from this hoped for average expectation. Goal expectation decays relatively slowly at first. As the clock ticked into the 40th minute, Chelsea could still expect to take around 2.3 points from West Ham, even though they had yet to make a breakthrough. Their points expectation after 40 minutes was still over 90% of what it had been at kick off. So there hadn't been particular cause to panic through the bulk of the first half.

 Above, I've plotted (in red) the rate and extent of Chelsea's declining pregame points expectation. 40 minutes in, as already mentioned, it had fallen to 90% of the original value at kickoff. But by the 90th minute, it had very nearly halved to 1.33 expected league points.

Superimposed on the graph I've included the goal expectation for Chelsea from each of their 39 goal attempts, based on the actual x,y location from where the attempt was taken. I've grouped the attempts into 10 minute slots.

Data from a single match is inevitably choppy, combined with sides perhaps playing in spurts of increased effort, rather than a smooth gradual cranking up of the pressure. However, the trend for Chelsea to become more intent on making a breakthrough appears to increase in tune with the decline of their game state. They produced enough individual goal attempts to find the net an average of nearly 3.3 times over the 90 minutes and they threaten more in general as the game wore on. Such was the extent that WHU became entrenched, that Chelsea's goal expectation from their actual shots taken in the second half approaches nearly three times their value from before the break.

The 39/1 shot ratio was exceptional. As noted here, superior sides, on average also have the lion's share of shots when a game ends 0-0. But typically, a side as superior as Chelsea are compared to WHU in terms of league placing should only claim around 72% of the total shots taken in the game.

Other splits, however were more typical, although they still indicate the excessively above normal rate at which Chelsea may have chased and WHU have hunkered down. Chelsea had 70% of the crosses compared to an expected 63%, and 74% of the total passes against an expected 62%.

Although the massive shot differential takes all the headlines and other attacking based ratios also indicate the severe imbalance between the mix of capability and intent on show from Chelsea and West Ham, the underdogs did have a minor "success" in the way clearances where divided on the night. Such large favourites might expected to only have to account for around 20% of the clearances made in the game, but WHU managed to force Chelsea into making over 30% of Wednesday's total.

Statistics for a single game are often determined as much by the in game situations each side is presented with, as by the relative gap in quality. Mourhino's side played a similarly limited side in Stoke on Sunday in the FA Cup. They didn't quite dominate The Potters in terms of shots, as they had done WHU, but they didn't need to, following Oscar's first half goal. After that it was just a case of keeping Stoke's relatively well disguised attempts at equalising at arms length and picking away with the regular opportunities that were available.

On Sunday, six goal attempts inflicted on WHU in injury time alone, simply wasn't called for against a Stoke side still playing possession football in their own half. A team produces a combination of what it can and what it needs to do and very occasionally, when the expected doesn't happen, one of those ratios goes off the scale.

A Use for 0-0's

Sooner or later anyone who regularly watches football will eventually be treated to a scoreless match. From a spectating point of view, especially for the neutral, 0-0's are often an unwelcome addition to their footballing experience, but from a statistical standpoint, stalemates may provide a valuable baseline into the complex, but increasingly relevant subject of game states.

It is quite natural that a side may change tactics based on their current needs and scoreline at a particular phase of a match. A cricket team having wickets aplenty in hand on the fifth day of a test match, with the winning scoreline tantalizingly in sight may take risks to reach the winning total. At least until falling wickets induce a more cautious, draw orientated approach. Such bursts of accelerated scoring, usually also involving increased numbers of falling wickets, are easy spotted in a sport, like cricket where every potentially scoring action is individually recorded.

In football this ebb and flow in the interactions between teams is less easy to define. Unlike many sports, such as cricket, American football, and baseball, were "goal" prevention and scoring occurs in defined periods of play, scoring and attempting to prevent being scored against occurs simultaneously in football. Retaining possession in football can be both an attacking or a defensive action.

Tactical adjustments based around game state, therefore are likely to be as real in football as in other sports, but even overt changes to a more possession based/risk averse approach when leading may be difficult to spot across a match, especially if the opposition quickly changes their own game state by rapidly equalising a go ahead score.

Stoke and Cardiff Prepare to Serve Up a Statistically Interesting 0-0.

Game state is being increasingly used in football analytics and inevitably the phrase may have different interpretations across different sites. In this blog I have described game state principally as the interaction between the team quality of each side taking part in the match, the current scoreline, the time remaining and any dismissals that may have transpired due to red cards. As a consequence, accurately calculating the game state over even a single match, requires constant re-calculation. Some of the inputs may remain relatively constant, but time elapsed is always moving forwards towards full time.

Thus, goalless games, especially where we have more detailed statistical breakdowns of on field actions, provide the easiest doorway to how sides react in certain game states. A side, especially a talented one often only shows us part of what they are capable of, tempered by what they needed to do, especially if they recorded a fairly comfortable win. For example, anecdotally, 2-0 victories increased in international football when the cast and spread of team quality increased in the 1990's as good teams adopted risk averse strategies in the face of relatively unknown, but probably inferior opponents.

If we stick with 0-0 games, with no red cards, played between teams of known quality, the only major contributor to changing game state that remains is time elapsed. In short, there are no major peaks or falls in game state across the 90+minutes caused by reckless tackles or deflected 30 yarders. Therefore, how game state progresses for such contests is almost entirely a function of the quality differential between the sides at kick off.

The plot above shows how dominant teams were in terms of collecting their share of the total attacking touches of the ball made in the penalty area, during 0-0 matches from 2011/12. The pregame success rate defines how balanced the match was expected to be prior to kick off and red card matches have been omitted. To anchor an example in reality, Spurs would currently have about an expected 0.8 success rate prior to kicking off at home to Stoke.

The trend is well defined, superior pre game sides had the lion's share of attacking touches inside the penalty box recorded across the 90 minutes. For example, the line of best fit gives a side with a pre game predicted success rate of 0.8 an average of 75% of the game's attacking penalty box touches. The longer the game remains stalemated, the more the game state turns against the pre-match favourite, merely through the ticking of the clock, sustaining their efforts to deliver passes and touches in the dangerous area of the penalty box.

The trend in 0-0's spills over into other statistical categories. Superior teams on matchday, on average, enjoyed majority shares of shots, chances created, dribbles, crosses, final 3rd touches and blocked efforts, allied to reduced levels of clearances compared to their inferior opponents.

In short, these historical rates indicate what level of on field actions a typical EPL side is likely to record in a 0-0 match, where the talent gap between the teams is readily known, without intervention from other major game state changing factors, such as goals or dismissals.

If we now wish to see the direction these shared proportions take as factors other than simply time elapsed combine to change the overall game state experienced by each side, we can look at the next lowest match result. Namely, games decided by a single goal.

A single goal victory will improve the average game state of the superior side compared to an identical match that remains scoreless. And similarly, data from single goal defeats should be characteristic of how matchups perform under poorer game states than those experienced in 0-0 games.

How Proportion of Penalty Box Touches Changes by Result & Match-up.

Pre Game Expcted Strike Rate.	Game Result 0-0	1-0 Win. (Better Game State)	1-0 Loss. (Poorer GS)
0.8	75%	67%	76%
0.75	71%	63%	72%
0.7	66%	60%	69%
0.65	62%	56%	65%
0.6	58%	53%	62%

Above, I've charted the proportion of penalty box touches derived from the line of best fit from plotting graphs for matches that ended in single goal wins and defeats, as well as goalless draws.

In games where the favoured team won by a single goal, their proportion of touches in the area declined compared to the baseline figures derived from a 0-0 result, whether through their opponents becoming more adventurous or themselves more cautious. Where the team lost 1-0, they were good enough and needy enough force an increase in their share of such touches compared to the baseline numbers.

As an example, the best fit for a team with a pre-game expected success rate of 0.7, sees their share of touches in the box falls to a low of around 60% when they win 1-0 and scoring becomes less of a priority for part of the match, reaches a high of 69% when they are chasing a one score deficit and is anchored at 60% when neither side finds the net.

There's nothing new in these conclusions. It has been established that a side that performs poorly by their usual standards over a season, tends to accumulate more products of the attacking football they must undertake to rectify matters than they do in better times. Corners are a prime example. But the use of the 0-0 match as a handy baseline may restore a bit of (statistical) love to a usually underwhelming extravaganza.

Scoring Efficiency and Game State.

An old post from a year ago that is available on the OptaPro site, but I forgot to ever link it here.

It uses Opta data to relate game state, expressed as a percentage of a side's initial points expectation to shooting type, efficiency and outcomes. It ties in well with some of the recent posts here based around shots, blocks and goals.

It can be found here.

http://www.optasportspro.com/en/about/optapro-blog/posts/2012/guest-blog-scoring-efficiency-and-current-score-by-mark-taylor.aspx

Game States And Team Quality.

In my previous post I looked at how Arsenal's attacking and shooting tendency was tailored towards the particular game and scoreline states in which they found themselves over the 2010/11 season. Arsenal were the pregame favoured team in virtually all of their 38 Premiership matches in that season and it was only in the four matches where they traveled to Liverpool, Chelsea and the two Manchester sides that they went into the contest as underdogs. Consequently, the scoreline state and game states mirrored each other fairly well. A lead was obviously a good game state, a draw could almost always be improved upon compared to pregame expectations and when trailing, the Gunners had both the incentive and almost always the potential ability to turn the scoreboard around.

However, in the case of more mediocre sides, these correlations aren't always as clear cut, especially when the game is stalemated.

The final 2010/11 table was a fairly typical example of the recent Premiership. Manchester United were comfortably crowned champions, Chelsea, Arsenal and Manchester City followed them home in a tight group of three and then came those aspiring to qualify for the Europa league. The mediocre EPL sides then begin to appear and going into the final round of matches just seven points separated 9th place from 19th. Therefore, Aston Villa, 13th after 37 games and 9th a game later could reasonable be chosen as a typically, run of the mill side.

Villa were the favoured side in just 17 of their 38 games and unlike Arsenal, there would likely have been many more games where a draw would have been an acceptable result for the team from the West Midlands. So where Arsenal's approach would be consistently to tend towards pushing for a go ahead goal, the connection between Villa's scoreline state and game state is likely to be more ambiguous. A current point away to Fulham was most probably acceptable, (although they may harbour thoughts of capturing all three), but one at home to ultimately relegated Blackpool would be much less acceptable. In short, the scoreline states don't coincide as neatly with a side's perceived game state in the case of Villa compared to Arsenal.

Similarly when Villa trailed, their ability to match the desire to improve the scoreline with their capability of achieving that aim is also unlikely to tally with that of Arsenal. Villa trailed at some stage on 19 occasions, against teams who were as determined to hang onto their three points as Villa were to retrieve something from the match. So the change in scoring effort from Villa is likely to be a function of these shifting priorities shown by each side. When the same thing happened on 14 occasions to Arsenal, the Gunners had a more potent attacking force to call on for a more concerted retrieval approach than did the Villans in their various contests.

As with the previous Arsenal analysis, I've used the x, y data of the shot to determine a goal expectation, which in turn leads to an expected long term scoring rate in different scoreline states. At worst, this type of analysis can give an enhanced picture of how Villa tried to play during different phases of matches in that season and we may also be begin to see the interaction between teams without painstakingly plotting minute by minute changes in game state.

Aston Villa's Goal Expectancy From Chances Created in Various Scoreline States.2010/11.

Scoreline State.	Ahead.	Level.	Behind.
Goal Expectation From Chances Created.	A Goal Every 72 Minutes.	A Goal Every 52 Minutes.	A Goal Every 58 Minutes.

We see a similar trend to that exhibited by Arsenal. Chance creation and long term scoring rates decline when Villa led, compared to other scorelines. Shots were less frequent and marginally of the lowest quality on average. Interestingly, potential scoring rates are actually highest when games were level, Villa were creating best and most frequent chances in this scoreline state. Numerically, creation rates only fell away very slightly when they trailed, but quality was noticeably poorer.

All Hands On Defence As Villa Protect A Lead.

These changing rates coupled with those produced by Arsenal in the same season, hint at the changing dynamics of a football game, where desire and capability are pitched against opponent ability and intent. The game state at level scorelines is likely to be less clear cut in the case of Villa compared to Arsenal. In the former, both sides may be still be actively seeking a win, whereas the opponents facing Arsenal are likely to be more uniformly engaged in defending their point. In short, when drawing Villa are more likely facing teams who are also willing to take a chance.

Once Villa trail the eventual priorities are more clear, but as Villa lack the attacking expertise of the top sides, exemplified by Arsenal, their ability to create valuable chances may now be less than they were capable of achieving in a more open situation where both sides may still have been trying to break a stalemate.

Overall the Villa figures show a similar general trend as Arsenal in 2010/11. Both sides were at their least dangerous in goal scoring terms when already ahead. The differing potency of both Arsenal and Villa at level or trailing scoreline states may merely be simply an artifact of sample size or it may represent a genuine difference between the very best in such situations and the mediocre.

Often in football analysis, such as the relevance of possession, the characteristics of the very best overwhelm the tendencies of the less gifted majority, in turn hiding a more complex reality and this may be the case in determining game states for different teams under the same scoreline, especially stalemates.

Ultimately, game states will have to be defined by the non trivial interplay of relative team quality, current scoreline and time remaining.

Cranking Up The Goal Expectation When Doing Badly.

A football match is a contest that is constantly and subtly changing in many ways. Goals are the obvious major events that alter the balance by which teams either seek to consolidate an advantageous position or retrieve a potentially losing one. Goals come about through a combination of skill, random chance and no little effort and the varying degrees to which teams choose to attempt to impose this factors on an opponent determines how successful they will be. In this post  I looked at how trailing teams are more likely to score than they had been previously when they concede the lead.The amount of time remaining is also a contributing factor, but sooner rather than later every team will launch a concerted effort to retrieve a losing position. They don't automatically become the most likely team to claim the next goal, if there is one, but they do, on average become more dangerous in attack than had previously been the case.

The extra potency shown by such teams could previously only be quantified if their efforts produce a goal and over large enough samples their scoring rate when trailing can be shown to increase by upwards of 10%. However, by using models that predict goal expectations for individual goal attempts based on the x,y co ordinates from where they were made, we can demonstrate how sides, on average attempt to up their attacking game in certain match situations. Either until their opponents succumb, they themselves are caught on the counter attack or the game merely excitingly runs it's full course.

Arsenal, being a consistently successful side are less prone to ambiguous, stalemated game states, where doubt lies as to whether or not they are reasonably happy to be on level terms. Original game winning probabilities of around 25% or smaller are the break even point, whereby a side is theoretically content with a point and the vast majority of Arsenal's matches will see them quoted at greater probabilities than this to win at the outset. Therefore, Arsenal are almost certain to push for a winner at some point in almost every tied game unless they are visiting either Manchester club or Stamford Bridge.

Arsenal's Goal Expectancy from Chances Created in Various Scoreline States. 2010/11.

Scoreline State.	Ahead.	Level.	Behind.
Goal Expectation from Chances Created.	A Goal every 55 minutes.	A Goal every 45 minutes.	A Goal every 45 minutes.

The overall level of Arsenal's ability in 2010/11 was on par with a side expected to score, on average a goal every 51 minutes. The goal expectancy based on the quality and quantity of the chances they created when they led suggests that then they played like a team capable of scoring only once every 55 minutes. So, as a team which had the lead they moved into a move defensive mode to the detriment of their attacking expectations.

The Gunners' urge to improve during level and trailing scoreline states is reflected in their quantity and quality of goal attempts being the equivalent of a long term average scoring rate of a goal every 45 minutes. In 2010/11 they upped the rate of chance creation and partly maintained the quality in a level scoreboard state and upped creation even more, but at the cost of chance quality when behind.

In the absence of goals, we can still show the efforts, sometimes fruitless, made by Arsenal in losing or frustratingly stalemated situations. During the 79 minutes they trailed to Villa in their final home game of the season, Arsenal fired in enough goal attempts of varying quality to have scored at a long term rate of a goal every 30 minutes and their game long potential goal expectancy over the full 90 minutes was an equally urgent goal every 35 minutes. But the randomness of conversion rates saw them merely register a 89th minute consolation, despite their numerous efforts. They lost on the day, but through random variation rather than lack of trying.

Above I've plotted the overall, theoretical scoring rate suggested by all the chances created by Arsenal in each 2010/11 match against the average of the game state they encountered on the day. In matches where they were consistently chasing their hoped for outcome, they were able to up their attacking output, producing chances that would yield almost a goal every 20 minutes in their home loss to WBA and these bouts of increased effort often remain in the overall game figures. But, as with the Villa game, short term randomness again beat them.

At the opposite end of the plot, they were unable or unwilling to continue to take the fight to United and Chelsea when beating both. Defence was probably more of a priority once the lead had been secured. An early goal from the game's best chance against Wolves, allowed Arsenal to dictate much of the game at Molineux. More goals would have been welcome, but weren't essential and a second goal only arrived in injury time as Wolves pressed forward.

It appears that all sides eventually tailor their attacking intent to suit the current score, their own pre game expectations, the quality of the opposition and time remaining and if random distribution of your innate talent is kind enough to gift you a three goal lead at home to Chelsea, there is little need to try to run up the score at the risk of opening up the game. Scoring further goals no longer remains a high priority.

Single game scoring efficiency is a heady mix of match day randomness that infrequently yields significant, talent driven events and the relative abilities of the contestants. High quality chances often fail to result in a goal, whereas poorer quality ones sometimes do, and these partly random outcomes often help to frame how the remainder of the match is played out.

For more interesting work on this essential context driven subject check out Paul's recent post at differentgame.