Tuesday 31 December 2013

The Christmas Number One.

Sir Alex Ferguson often made the point that the race to win the Premiership title only really starts around the turn of the year, when about half of the 38 games have been completed and the true front runners have begun to put some distance between themselves the very best of the rest. A couple of media sources took a much more dogmatic reading of the post Christmas table, by pointing out that the last four table toppers on Christmas Day also occupied top spot in May.

This year's Christmas number one was Liverpool, whom clung on to the prized top spot by the finest of margins following Arsenal's dour 0-0 pre-Christmas Monday night draw with Chelsea. Only goal difference separated the top two, affluent Manchester City lay a point further back in third and just another single point further back found both Chelsea and Everton. So the simplistic predictive power of the Christmas number one, alluded to in the Daily Mail is apparently going to be sorely tested this season.

Being top of the league at any time outside of the very early weeks of the season is of course no mean feat. Liverpool are performing consistently at a higher level than they have managed in recent seasons, but the close proximity of a raft of talented challengers, allied to the upcoming transfer window and the ever present threat of injury and suspension, makes their potential crowning in May far from certain.

The flaws present in a naive statistic, such as the ultimate fate of Christmas table toppers is easily demonstrated. 17 matches can see front runners over perform and chasing sides fail to reap their just rewards. League position also tells you nothing about how dominant the leaders are in relation to their challengers and a trend that is quoted over just a four year timescale almost certainly failed to "predict" the league champions reliably in seasons previous to 2009-10.

Inevitably, if we ignore the chosen selective cutoff point and look back one more season to 2008-09, the leaders on Christmas Day that year, coincidentally, also Liverpool, only finished 2nd in May. Arsenal slipped to 3rd in 2007-08 and there then followed a run of three season where the leaders held on to completion. From  2003-04 to the inception of the 20 team Premiership, eight sides failed to maintain top spot, with only Manchester United in 2000-01 honouring this implied trend during the early years of the EPL.

Overall less than half of the sides that are top at Christmas (8/18) are also to in May. Four sides that were placed 2nd went on to lift the title, a similar number of 3rd placed teams and a single 4th placed side coupled with a single team placed 5th or lower before ultimately rising to the top completes the Christmas record.

So despite the inevitable temptation to create certainty and cast iron cause and effect through selectively chosen outcomes, there does appear to be some benefit from enjoying Christmas from the top of the tree, but this needs to be couched in terms of probability and expectation, rather than small sample certainty.

One way to add some context to league positions is to convert the rate at which sides have accumulated points into standard scores, essentially measuring how far from the league average a side's achievements have strayed.

Team. Year. Position at Christmas. Points per Game as a Standard Score. Final Position.
Liverpool. 2013-14 1 1.45 2
Manchester United. 2012-13 1 2.12 1
Manchester City. 2011-12 1 2.08 1
Manchester United. 2010-11 1 2.17 1
Chelsea. 2009-10 1 1.94 1
Liverpool. 2008-09 1 1.96 2
Arsenal 2007-08 1 1.78 3
Manchester United. 2006-07 1 2.24 1
Chelsea. 2005-06 1 2.30 1
Chelsea. 2004-05 1 2.08 1
Manchester United. 2003-04 1 2.12 3
Arsenal. 2002-03 1 1.75 2
Newcastle United. 2001-02 1 1.79 4
Manchester United. 2000-01 1 2.15 1
Leeds United. 1999-00 1 1.67 3
Aston Villa. 1998-99 1 1.77 6
Manchester United. 1997-98 1 2.10 2
Liverpool. 1996-97 1 1.53 4
Newcastle United. 1995-96 1 2.18 2

The larger the standard score, the more dominant a side has been when measured against the league as a whole. And while an impressive score doesn't guarantee that they will have also left most of their championship challengers well behind, it does make a raft of close pursuers less likely.

Liverpool's 2013-14 figure is the least impressive recorded in the history of a 20 team Premiership and visually from the table shown above, the lower the Christmas standard score achieved by the leaders, the less likely they appear to be able to carry their pre Christmas success into May. Liverpool last topped the mid season table with a similarly poor standard score back in 1996-97, when four teams, all with games in hand lay within six points of them and they ultimately fell back to finish fourth.

A more formal relationship between the standard score of the Christmas leaders and their final finishing position gave Liverpool around a 16% chance of lifting the title based solely on the historical precedents of previous EPL seasons. Well in line with the odds of 6.0 being quoted about them on Christmas Sir Alex says and the bookmakers also recognise "the 2013-14 race starts now".

Wednesday 11 December 2013

The Power Of Goals.

It is perhaps an indication of the rarity of goals that of the 100's of photographs I've taken at EPL games, I've only managed to record one goal (a penalty) and one disallowed effort. In comparison I've snapped countless pictures of final third passes, shots at goal and the ubiquitous touches.

Locally, where junior football goal counts climb steadily as the skill differential between sides also increases, I've been more successful at capturing some of the defining moments of a match. Uttoxeter's Oldfields Ground may fall well down in the pecking order of sporting venues, although the turn of the (second last) century pavilion did once host over three rain curtailed days, the 1909 touring Australian cricket team. Nowadays, when it stages local junior football, it is the place for goals and when sides are regularly playing matches will lots of goals, that important measure quickly reaches useful sample sizes.

Goal number six in a nine goal shootout.
As the title of this blog implies, goals and the ability of a side to cumulatively score the lion's share in their matches over a prolonged period of time is a good indicator of how successful a team will be. In addition, goal difference doggedly tracks points accumulated, so the proportion of total goals scored by a side would appear to be the ideal way to express different levels of team talent and likely league success.

However, the relative scarcity of goals in the highest ranks of the professional game, compared to its more lowly cousin, park football, has understandably led to a search for a more numerous match action to act as an improved proxy for this comparatively rare event.

In the opening 10 matches of 2011/12 for example, relegation bound Bolton, scored 10 times by their own efforts with generous opponents chipping in with a further three strikes, took 122 shots, including blocked efforts, completed 737 final third passes and made 1190 final third touches. By comparison, their opponents had scored 27 goals in reply, shot 188 times, completed 970 final third passes and touched the ball 1475 times in that area by the time game totals had reached double figures.

None of the figures gave cause to suppose that the 19th place Bolton occupied after 10 matches was anything but a fair reflection of the abilities they had shown in the opening matches. But did more clues to their future performance lie with their 27% goal share (32% in you included gifts from the opposition) or their 39% share of a tenfold numerically inflated shot count.

100+ shots attempted and around 200 shots conceded is immediately appealing because of the inflated sample size. However, shots and every other secondary statistic often come with unwanted baggage. In particular, as this post shows, such figures are prone to inflated or reduced levels due to the course a game takes. In short, shots, passes in certain pitch areas and touches are highly situational.

The path a team takes when attempting to impose their superiority over an opponent may depend on the order in which the goals arrive in a single game. Following an opening goal, the balance of offensive and defensive actions may shift, as illustrated by the large minority of matches where a winning team may find itself out-shot by a defeated opponent, especially if the winners sprinted to an early lead.

If a side wants to win a match, the only option is to outscore their opponent, but fluctuating scorelines on route to that win may allow a side greater flexibility in how they chose to try to guarantee that win.

So even though shots attempted greatly out number goals as match events, the degree to which a team dominates the other in this secondary statistical category may be highly dependent upon the course the game took. We cannot guarantee that matches for individual sides will follow similar patterns in the future. Therefore, shots, especially over smallish sample sizes may prove to be poorer indicators of future performance than that much rarer prize, the goal, over the same time scale.

To test this, I repeated the auto-correlation post here, but charted the correlation as measured by the r^2 values between the cumulative, proportional share of such game events as shots, touches and goals over the first 10 games of a season and each individual side's points total or goal difference over the subsequent 28 matches.

R^2 for Proportion of Game Events Recorded by Teams in First 10 Games and Points/GD in Subsequent Games. 2011/12.

Proportion of  Game Events For Team in
First 10 Games.
r^2 Between Event and Points over
Final 28 Games.
r^2 Between Event and Goal Difference over Final 28 Games.
Shots. 0.229 0.339
Shots+Blocked Shots. 0.272 0.374
Touches in Final 3rd. 0.287 0.396
Total Touches. 0.348 0.435
Goals. 0.531 0.546

When the individual proportions of match events accrued by teams from 2011/12 are used to try to predict subsequent performance for those same individual teams, shots languish in the table. Only 23% of the variance in team points over the subsequent 28 matches is explained by the variance in team shots over the first 10 games. Adding blocked efforts improves matters, in 2011/12 at least, as does moving to final 3rd touches and total touches all over the pitch in the first 10 games. However, the proportion of total match goals scored by each individual team, despite their rarity, prove far and away the best predictor of future individual team performance over the remainder of the 2011/12 season.

And the same plot, but this time using the proportion of total match goals scored by each side from the 2011/12 Premiership.

The strong tie between the proportion of shots that a side accrued and the unique situations that transpired within those first 10 matches during 2011/12 appears to seriously weaken their use as a predictive tool.

R^2 for Proportion of Total Goals Scored by Teams in First 10 Games and Points/GD in Subsequent Games. 2012/13 to 2004/05.

r^2 Between Goals & Points Accrued Over Final 28 Games.
r^2 Between Goals & GD Over Final 28 Games.
2012/13 0.499 0.432
2011/12 0.531 0.546
2010/11 0.400 0.390
2009/10 0.669 0.687
2008/09 0.572 0.579
2007/08 0.557 0.466
2006/07 0.420 0.401
2004/05 0.591 0.505

To see if the power of goals in 2011/12 was a fluke, I have also looked at the strength of the relationship between the proportion of goals each side scored after ten matches and their points haul and goal difference over the final 28 matches for 8 of the last 9 seasons. (2005/06 is omitted simply because the race to ten games was an abnormally spread out affair). In most of the years, the strength of the relationship seen in 2011/12 is confirmed and sometimes bettered.

To be usefully predictive of future performance a statistic should be capable of surviving changing context. But in the short term of the first 10 matches for each side during he 2011/12 season, shots, as a proportion of total shots, appear to be too dependent upon such external forces as game state and current score to pass that test.

Thursday 5 December 2013

World Cup Groups. The Numbers Sometimes Lie.

The 2014 FIFA World Cup becomes much more tangible and real on Friday when the draw for the group stages takes place.  Inevitably some sides will appear to be presented with a relatively easy passage to the later stages and others will fall foul of an imperfect seeding system and find themselves competing in the ritual group of death.

The FIFA rankings determine the seeded teams, continuing the influence they had over the prolonged qualifying stages. And while it is easy to pick flaws in both the rankings themselves and the manner of their use in deciding group make up, they do perform a reasonable job of sorting sides into a recognizable order of merit.

The non competitive nature of many of the friendly matches that contribute towards a side's FIFA ranking figure, along with the seemingly arbitrarily applied weightings to such games, can sometimes undermines the authority of the figures. Additionally, factors that are unique to international football, such as a continental advantage, akin to home field advantage in domestic games, also complicate their use as a predictive tool for future matches. As does the lack of meaningful, collateral form lines between the various FIFA confederations outside of the years of a World Cup.

In view of these issues, it is perhaps surprising that FIFA rankings for two sides can provide a decent indication of the likely match outcome when those sides do meet. Other systems of course exist to provide international team rankings, such as the many elo based ratings and these may be preferred by some.

So whether FIFA is your preferred starting point or not, much of the group analysis that will appear following the draw will rely on the use and interpretation of a rating figure for each of the four teams that will comprise the individual World Cup groups. Simulating the outcomes of the group games by use of a ratings differential based on historical outcomes of similar games is a well recognized way of evaluating the challenges faced by each side before a Brazuca is kicked in anger.

Ratings based analysis of individual matches in football bears a similarity to their use in horse racing, where it has long been realised that translating ratings to likely outcomes doesn't always follow a smooth and regular progression. A single rating figure may describe a weighted evaluation of a side's recent performances, but the expectation in a single upcoming match is likely to merely be centered around that figure. A team may perform better than their rating or they may perform worse. This scenario can be accounted for by randomly selecting figures to be used in simulations from values distributed around that mean.

This approach still requires assumptions to be made that may not accurately reflect reality. The more opportunity a team (or horse) has to truly demonstrate their ability, the more confident we may be that any future performance, independent of a multitude of other factors, such as venue (or going), will be close to that central number. Mature ratings are more likely to have readily identifiable up and downsides. However, in the cases of a lightly exposed horse, in particular, the upside and downside to their recorded rating may be considerably skewed in one direction or another, especially if that horse has shown itself capable of at least being competitive on a major stage.

"Potential for major improvement" may be a horse racing cliche, but a combination of increased opportunity to show their true worth, combined with increasing experience, often throws up cases of underrated talent as measured by traditional ratings.

Relatively few numbers of runs, combined with good, but not great ratings, often characterize horses with capabilities that may far outstrip a tight, normally distributed range of recent performances. Mining the extensive, commercially available racing databases can identify such cases where subsequent performance deviates markedly from the more usual progression. The FIFA ratings provide the footballing equivalent of the racing handicap, but it is less easy to define how "exposed" a team may be.

Horse Ratings Rarely Follow the Straight and Narrow.
One way is to look at the average number of caps gained by the current side. Player turnover can be relatively rapid in international sides. Only four of the starting England players who lost on penalties to Italy at Euro 2010, started the final World Cup qualifying win over Poland at Wembley three years later. So a rating forged over multiple seasons has partly been passed to the inexperienced likes of Andros Townsend, Chris Smalling and Daniel Sturridge. This fluctuating lineup doesn't guarantee improvement, but it may make any conclusion we draw from England's current rating prone to a distorted up or downside compared to a rating belonging to a more mature starting 11.

The number of caps gained by a starting eleven isn't readily available and there is a limit to the amount of data I'm prepared to collect, but below I've listed the average number of caps owned by the starting eleven for all of the European qualifying teams in their most impressive performance during the round of group matches.

Average No. of Caps Owned by Each Starting 11 in their Most Impressive WC Qualifying Game.

Team. Mean Number of Caps Owned by Starting 11. Median Number of Caps.
Netherlands. 32 13
England. 40 22
France. 33 26
Switzerland. 34 30
Bosnia & H. 37 32
Italy. 44 41
Belgium. 38 42
Germany. 48 44
Greece. 45 46
Russia. 49 47
Portugal. 58 57
Spain. 71 63
Croatia. 67 70

In comfortably beating playoff bound Romania, the Netherlands did so with a side that produced an impressive performance and did so with an under exposed side, by the standards of current international football. If a similar database existed in football as it does in horse racing, we could perhaps make a more informed prediction about the likely size and shape of any immediate upside for such a side. But in the absence of such data, when simulating the WC chances of the Dutch team, we should consider that their upside may be heavily skewed and inflated compared to their downside, especially if they persist with "proven inexperience".

Teams towards the lower end of the table, such as Spain and Portugal, will be fancied to do well as highly rated European teams, but their range of likely outcomes may not surprise.

Anecdotal evidence of a decidedly non linear progression for under exposed talent, will inevitably be tainted by survivor bias, but the handful of established players I have looked at do show an exponential increase in useful output, such as goals and assists as their cap count climbed into the 30's and 40's.

Equally non random in selection and therefore probably inadmissible as anything more than an interesting nugget of information, is the average cap count of sides that have shown performances at major tournaments that belied their more modest pre-tournament ratings.

2004 Euro champions and pre-tournament 250/1 outsiders, Greece, started the final with a side which had an average of just 30 caps per player. Senegal kick started their 2002 World Cup campaign with a 20 cap a man win over France. Caps largely gained in a partly isolated confederation. Republic of Ireland defeated Italy in a WC with a median of 26 caps and Bulgaria's run to the 1994 WC quarter finals was achieved with a 32 cap average.

Prediction can draw from many pots and while the potential for ratings to progress in a non linear manner for teams about which our information may be limited (even if that side's name is well known) is unlikely to be an over riding factor, it will add some degree of uncertainty. So an established higher ranked side that welcomes the likes of Bosnia and Hertzegovina should probably heed the example of an upwardly skewed Bulgaria from 1994.

For those who can't wait for Friday's draw, a nice primer can be found here at

Wednesday 4 December 2013

Free Kicks verses Shots From Open Play.

The spotlight continues to fall on the effectiveness of shooting from distance, but how does much of an advantage does a set piece shot from outside the box give to the shooter. In this guest post I try to quantify how much closer to goal you need to be before a shot from open play becomes roughly equivalent to a shot during regular play

Tuesday 3 December 2013

The Scoreline Isn't Everything.

One of the major problems when attempting to add context to football statistics is that many of the recorded events are highly situational. It is relatively easy to produce a chain of events from touches to passes to key passes through to shots and ultimately onto goals. But the urgency and frequency at which a side attempts these actions and the commitment in effort and manpower that their opponents put into preventing a successful conclusion, depends greatly on the state of the game. Current score, time remaining and the relative abilities and expectation of each side are the three most obvious indicators of the current game state.

It is hugely tempting to collect every positive action performed on the field of play and relate those numbers to match outcome and often the results appear to confirm a connection. Shooting at goal is to be preferred to having to stop a similar effort from your opponent. Therefore, it isn't surprising to see that the winning teams in the EPL during 2011/12 out-shot their opponents by an average of 3.5 shots per match.

However, averages almost always fail to capture the full nuance of a situation. Although 180 of the 2011/12  matches where there was an outright winner saw the winning side out-shoot their opponent, a not insignificant 110 matches saw the loser out-shot the victor. Nearly 40% of result games went to the loser or tie in terms of shots.

Goalscoring, in a low event sport such as football contains a lot of random variation and out and out luck in a single match. If Stoke had filled in the corners of the south stand as proposed in 2011, thus creating a windbreak to the gale that habitually blows towards the Boothen End, if Shawcross hadn't won the toss against Southampton and spurned tradition by turning the sides around, if Southampton's defenders had heeded the mantra of "never let the ball bounce", then Begovic might not have scored the fastest goal by a keeper on a Saturday in November.

However you define it, luck or randomness may play a part in an out-shot side winning the game, but other factors, such as the tactical approach of each side under the influence of the underlying game state is an obvious additional candidate.

Many sports that incorporate game state analysis have either greater numbers of scoring events than football, making a draw at full time much less likely or positively balk at the thought of a draw and actively legislate against such an outcome by incorporating overtime. Therefore, the draw is firstly, uncommon in these sports at the end of regulation and often eliminated by extra playing time.

This isn't the case in football, the relative low scoring nature of the game results in around half of the playing time being spent with the scores level. Secondly, the draw at full time does represent a safe haven for a side that is content with a point. So, a tied scoreline in football is much more likely to still see widely differing intentions displayed by a side and their opponents compared to other sports, because it is a scoreline that can persist at the final whistle.

In dealing with game states, therefore, we must address the issue of the tied scoreline. Once the massive rump of time spent level is given a more team specific outlook, we can begin to see if the out-shot teams took advantage of a fair wind or actively adjusted to a renewed and diversified challenge from a ultimately defeated rival.

Above are the 290 games in 2011/12 that ended with a winning team, showing the influence of average game state on the shot differential experienced by the winning side. Game state is customized stat, so as a general indicator, zero along the horizontal axis indicates a side that was consistently behind expectations for large parts of the match. For example, a good side that couldn't break down weaker opponents until very late in the game or a side that achieved a "come from behind" victory. Values of 1.5 or more comprise sides that were generally well in charge of the game from a relatively early stage or weaker sides that held superior opponents and won late on.

Correlations using single matches as a data point are notoriously weak, but even if a few outlying games may have pulled the line of best fit downwards, the correlation appears clear. The longer an ultimate winner was behind or a stronger team was held by a weaker rival (denoted by the decreasing size of the number along the horizontal axis), the more likely they were to have out-shot their opponents on their way to victory.

On the other side of the game state mirror, an acceptable scoreline for the majority of the game, denoted by a positive value along the horizontal axis appears to indicate that in 2011/12, either by design or through necessity (or a combination of the two), a majority of such sides won despite being out-shot in the match. A side sitting on a lead and defending shots or an underdog defending from the outset and catching their more illustrious opponent on an effective, but rare counter, for example.

Rather than averaging out the detail and manner of victory, by including average game state, the typical manner and frequency of how EPL sides achieved their wins when faced with particular in game situations starts to become more apparent.

Clearances, for example follow the opposite trend. A side that either led relatively early or held a superior rival, before winning tended to account for the majority of the clearances seen in the match.

The opportunity to make clearances depends partly on the willingness of the opponent to proved such opportunities. In short, the kind of stats a side records is greatly dependent upon the average game states they experience either during a single game, a run of matches or an entire season.

The full-time result tells you very little about how a side arrived at such a favourable outcome. A team may lead from the first minute or overturn an early deficit with a couple of late strikes. Sides that win from prolonged bouts of poor in running scorelines (by their standards), also tend to win the majority of the corners, attempt more aerial crosses, make more forward passes and accrue more key passes. They also take the majority of longer range shots and see more efforts blocked than their immediate opponents. These trends are reversed, in general for teams that win matches where they were satisfied with their position for large parts of the game. Paradoxically therefore, a play-maker whose side creates a couple of early goals is less likely to accrue a large amount of key passes in such a match because the team priority may have switched to defence.

An approach that adds game context to the stats could be used to look at the kind of actions individual sides take to achieve an acceptable result, this time compared to their own usual average. Swansea are known for their possession based passing style, but their commitment to passing the ball in the final 3rd was strongly dependent upon game state as shown in all their matches from 2011/12.

For example, they traveled to Anfield as big outsiders with just a 10% chance of winning the game at kick off. Therefore, they were perfectly happy for the game to remain scoreless, because with every passing goalless minute, their points expectation from the game edged upwards from it's paltry beginnings towards the reality of a single point gained. So they rarely ventured into Liverpool's final third when compared to their usual way of playing. And they similarly reproduced these lowly final 3rd figures when they enjoyed the benefit of any early goal during their much less onerous trip to Villa Park. By contrast the Swans attempted almost 100 more final third passes than was usual for them when they trailed early at home to Newcastle.

Talent may dictate a side's ability to attempt final third passes, but game state is also a powerful driver of their desire and need to exhibit that talent.

You were more likely to see Swansea passing in the final 3rd when they were doing poorly 2011/12.

As a further example, Spurs under Redknapp became a much more aerially orientated attack in poor game states. Once again there is a strong trend, this time for more aerial crosses to be played into the box as they tried to turn around the game state. Spurs' red card assisted romp against Liverpool was their most comfortable game during 2011/12, an early Modric goal was quickly followed by Adam's dismissal and the number of crosses into the box throughout the game was well below their seasonal average. Unlike the Sunday game in mid December at Stoke, where a couple of first half Etherington goals had them chasing the comeback for much of the game and they bombarded the box with well above numbers of crosses.

Plots like these may more clearly illustrate what you can/could expect from a team in certain circumstances. If you got the upperhand on Swansea in 2011/12 you could expect to have to deal with more passes in more dangerous areas, while Spurs increased the amount of aerial balls they played into the box. Just as importantly, Swansea's output of long balls for instance, remained relatively constant regardless of game state, so defenders were unlikely to find themselves chasing back into the corners with anymore frequency if they were defending a good game position against Swansea.

Equally, the individual player statistics are strongly tied to the game states and the needs of their side in that game state. An apparent decline or upswing in an individual raw stats, such as headed clearances, assists or final 3rd pass attempts could have as much to do with the ebb and flow within recent matches, as it has any real decline or improvement from the player concerned.

In short, quantifying a player or team's abilities is often tied to fully appreciating their need to show off that ability to the full.