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Friday, 18 October 2013

England Qualify For Brazil 2014. How Hodgson Defied The Odds.

Waldemar Fornalik and Roy Hodgson led their respective teams out at Wembley on Tuesday night at the conclusion of the 2014 World Cup qualifying campaign. Of the two, Fornalik, looked relaxed and at ease and was almost certain to be sacked regardless of the result against England. Roy Hodgson knew that only a win against Poland would prevent a unwelcome visit to the November playoffs before the trip to Brazil could be confirmed.

The odds had been stacked in favour of Hodgson reaching game ten in a relatively comfortable position at the initial drawing of the 2014 qualifying groups. Despite this kind draw, the anguish etched on his face was evident, as forward after forward snatched shots wide of a gaping goal in the opening half. Jan Tomaszewski sat in the stands and the specter of 1973 hung over a nervy opening half hour.

Back in the more relaxing surroundings of Rio in July of 2011, an out of place France in pot two had been avoided during the initial draw for the nine qualifying groups and Group H had pitched England in with four lowly ranked teams from pots three to six, with only Montenegro, ranked second to France in pot two, appearing to represent a less than ideal group rival.

The random element in drawing qualifying groups, often years before the final match is played has been excellently documented by Simon Gleave here and the mechanics of the procedure illustrate how arbitrary group makeup can become. Poland, England's final group opponents were one ranking place away from being in pot 5 rather than pot 4. In addition as Simon points out, Ukraine may have started the draw process as FIFA ranked 45 and a place in the bottom two of pot 3, but they ended the campaign, over two years later ranked 20th in FIFA and a seeded playoff side.

So the fluid nature of national sides can see the protracted timescale of a qualifying campaign transform the strength and difficulty of each group.

The pained, first half expressions on Hodgson's face were possibly down to an appreciation of the chances of a favourable outcome materializing on the night. A 73% chance of an England victory was a huge comfort blanket against a national expectation that tends to think in more stark outcomes, where defeat (or a draw) is virtually inconceivable, but that still left ample room for a two game shootout in November if randomness drew 74 or above.

Even greater levels of  World Cup "certainty" were overturned at Wembley in 1973. Coincidentally, and largely irrelevantly, also against Poland, as the product of numerous, low quality chances, repelled by a massed defence and marshaled by a future Polish politician, could only equal the goal count from one, clearer cut Jan Domarski shot on the rapid counter.

Certainty of outcome, as Hodgson may have reflected, only arrives after 93 minutes of actual play, no matter how much ability and national entitlement is bought to the table. Somewhere in the mass of possible, probable and improbably outcomes on Tuesday, lurked a quickfire Polish break that ended with a shot that squirmed under a largely untroubled English goalkeeper....but on this occasion, under the full glare of live, HD TV, the ball rolled uncomfortably wide of the target.

Defying the odds is usually expressed as being exclusively the preserve of the underdog, but every result defies some outcome, even if it is "only" the 27% chance that Tuesday evening's result would send Hodgson's England into an unwanted two legged playoff. In topping Group H, England turned the combined uncertainty and myriad of possible combinations of results from thirty qualifying matches played across 13 months into the certainty of confirmed qualification.

It is difficult to make an intuitive guess at the likely true size of the task faced by each team at the outset of qualification. The average FIFA ranking of England's opponents on the day of the draw was 84 and this had been pushed out to 89 by last week, as Montenegro fell and Ukraine rose. The task faced by England ranged from the near certainty of victory at home to San Marino, up to barely deserved favouritism on the road in Ukraine.

The final margin of group victory, a single point, hardly denoted a simple, alarm free passage.

Simulating the Group H qualifying matches, using the relative abilities of each side at the time of each individual match, allows us to record the range and frequency of both finishing position and points totals that may have been achieved by each team. With it comes a better understanding of the odds Hodgson's England defied to claim their spot in Brazil.

The 22 points actually gained by England was their second most likely points haul (~10% of the time), behind 23 (14%). 75% of the time, the 22 points were sufficient to send England straight to Brazil, either as outright winners or winners on goal difference. 20% of the time they fell into the playoffs when amassing 22 points. Once every 60 occurrences, 22 points was insufficient to place them any higher than 3rd place in the group and their World Cup campaign ended, as in 1973 with a final match against Poland. It is only when 25 points are breached that the need for a playoff begins to entirely disappear. A perfect 30 points certainly guarantees qualification, but England only met that target once in every 50 or so of the simulated leagues.

The lowest ebb for England was a fifth place finish in the six team group, occurring once every 200 or so iterations with a points total of around 13. It is a sobering thought for all aspiring national team coaches, that you can be demonstrably the best side in the group, favourite in all 10 of your matches and still, on very rare occasions, finish below Montenegro, Ukraine, Moldova and Poland.

No amount of iterations could force San Marino above England. 21 minutes of barely believable supremacy against the founders of the game in Bologna seems to be as good as it will get for FIFA's perennial minnows and England's national footballing pride was maintained, at least in the virtual world of number crunching and spreadsheets.

Possible Finishing Positions For England From Simulations of Group H.

Position in Group H. Frequency per 100.
Top. 61
2nd. 22
3rd. 12
4th. 4.5
5th. 0.5
6th. 0

The bottom line, for a nation obsessed with World Cup qualification is the 61% figure, denoting the likelihood that England might turn a favourable draw into a top of the table finish. A further 22% of the time England fell into the playoffs and as one of the likely seeded sides, they would expect to progress to the finals by this route well in excess of 50% of the time. So as a conservative estimate, Hodgson has just completed a campaign where his chances of successfully negotiating a route to the 2014 finals could be put at around 75% prior to a ball being kicked.

It may not have felt like it on Tuesday night, as Hodgson waited for Rooney to temporarily discarded his padded headband before heading England into the lead, but his side went into the final match with an improved chance of qualifying compared to their chances at the outset. Their 73% chance of winning the match, combined with a 27% chance of entering the playoffs if victory wasn't achieved, equated to a near 90% chance of appearing in Brazil via the route of either automatic or playoff progression.

The possibility of a hoped for outcome had increased, but the anxiety had been compressed into one single match, rather than spread over a 13 month campaign.

Poland, as widely expected sacked Fornalik and his coaching staff following their 4th place finish and a respectable 13 point haul. A 3rd or 4th place finish was almost equally their most likely outcome in the group. Fornalik's side had a near 70% chance of occupying one of those positions in the final group table, but they did fall 4 points below their most likely tally of 17 league points.

Where Hodgson had inexorably, if at times unconvincingly, dragged his team over the line, Fornalik failed to build on his side's meagre 10% chance of qualifying and with it went their World Cup hopes, his job, those of his collegues and judging by his demeanor on Tuesday night, the ever present pressure of turning possibles into probables and finally into certainties.  

Wednesday, 16 October 2013

Can Seven Games Change The World?

Seen in the context of recent Premiership history, Manchester City's 4-1 win over cross city rivals, United on match day five was a most impressive result. The champions of 2011/12 put the champions of 2010/11 and 2012/13 to the sword in a convincing win. However, when viewed through the lens of the early 2013/14 table, the outcome was much less noteworthy. Following the derby, United shared 8th spot with four other sides, including newly promoted Hull  and Newcastle, while City stood third, two points off joint leaders, Arsenal and Spurs. Had City beaten say Newcastle by a similarly large margin, the result wouldn't have been as noteworthy.

If United's defeat at City was embarrassing, their late September home 1-2 demise at the hands of WBA a week later, was probably even more disappointing. United now shared 12th to 16th, again with Newcastle and they found themselves gazing up towards two of the three promoted teams, Cardiff and Hull.

Untangling the mess that is early season results, as opposed to longer term class is fraught with problems. Ignoring home field advantage for a moment, City's 4-1 win taken in isolation indicted a single performance that may imply that they were superior to United by three goals. But one performance, heavily influenced by random chance isn't really sufficient to even show that City are the better side. Repeated matches between the sides are extremely unlikely to see City's average margin of victory maintain the heady heights of three clear goals. Indeed, they may not even win the majority of such games. In 2011/12, City recorded an even more impressive 6-1 win at Old Trafford, yet both sides ultimately finished on identical points totals, once 37 respective, additional games were added to that single result from late October, 2011.

The unwanted intervention of WBA also adds to the confusion. A single goal win away at United is the equivalent of a near two goal margin of victory on home soil. An achievement of similar, but slightly inferior magnitude to City's 4-1 win. So in a pecking order derived solely from three early season matches, the only possible conclusion is that City are better than WBA, whom are superior to United.

Interlocking formlines soon appear in league based tournaments. Stoke haven't played United yet, but both sides have entertained Premiership new boys, Crystal Palace, so an interconnected relationship does exist between the two sides. By the end of week seven, sufficient matches have taken place for common opponents to exist directly or indirectly for every side. Therefore, twenty connected simultaneous equations exist with the fixture list as the input and a result based parameter such as goal difference as the output and goal based ratings, that best describe these actual sequence of results can be relatively easily produced.

Least squares regression, usually via a matrix based approach is the standard way to solve simultaneous linear equations and provide team ratings based around a number of inter-related match outcomes. However, if City's 6-1 win in 2011 proved an unreliable indicator as to the true, long term worth of each side, how useful are such strength of schedule adjusted conclusions even after nearly 1/5th of a season.


An Inverted 20 x 20 matrix narrowly avoids meltdown.

Just as raw supremacy figures, derived from a single match, invariably greatly over or understate the likely long term talent gap between teams, the problem persists when the best ratings fit is produced by solving the linear equations for a two month season. The supremacy gap between the best and worst sides in the EPL over one completed season is usually in the order of 2.4 goals. The "gap" between United and City two likely top four finishers, on a single day was 3 goals and solving the 20 inter connected form lines after seven matches also produces wider than usual goal ratings gaps between the sides. The best side under this strength adjusted ranking is Manchester City, around 3 goals ahead the two worst sides in the 2013/14 EPL.

Strength of Schedule Adjusted Ratings After Seven EPL Games.

Team. League Position. SOS Adjusted Rating.
 (in Goals).
Change in Position.
Arsenal 1 2.19 -3
Liverpool. 2 2.13 -4
Chelsea. 3 2.64 +1
Southampton. 4 1.98 -5
Man. City. 5 3.12 +4
Spurs. 6 1.81 -4
Everton. 7 2.18 +2
Hull. 8 1.99 0
Man. Utd. 9 1.73 -2
Aston Villa. 10 2.31 +7
Newcastle. 11 1.63 -2
WBA. 12 1.62 -2
WHU. 13 2.09 +6
Cardiff. 14 1.69 +2
Swansea. 15 1.26 -2
Stoke. 16 1.33 0
Fulham. 17 1.02 -1
Norwich. 18 1.46 +3
Crystal Palace. 19 0.32 0
Sunderland. 20 0 0

The method combines a side's recorded goal difference and the "to date" records of their opponents, to seemingly quantify the difficulty of the task against the size of the achievement. West Ham jump six places under a revised, goal based, SOS appraisal. Manchester City jump to the top of the  new league by partly by virtue of an ability to score many and concede relatively few, coupled with a universal inability of teams to fully control how they distribute their scoring patterns. But disappointingly for WBA, they actually fall two places despite playing leaders, Arsenal because their outstanding win at Old Trafford came against a side currently in 9th.

The biggest climbers once SOS is factored in is predictably Aston Villa, who has faced the current 1st, 2nd, 3rd and 5th sides. The Villains are rated the 3rd best side over seven matches, despite their more lowly 10th actual placing. On Sunday, Villa entertain Spurs, an over achieving side based on their narrow wins against mediocre sides and failure to beat Chelsea or Arsenal from the top three. Therefore, if this short term methodology, when based around goals, is to have any validity, it would be expected that Villa should have an excellent chance of beating Spurs at Villa Park.

The goal gap between Villa and Spurs, corrected after seven matches is half a goal, stretching to 8 tenths once home advantage is allowed for, indicating a win% of around 55% for the hosts if these figures are to be taken wholly at face value. However, in the real world of bookmakers odds, Villa aren't even favourites, being afforded less than half the winning probability based around strength of schedule adjusted form from 2013/14 alone.

Villa are a mid to lower league side in the eyes of the bookmakers and Spurs are top four potential, despite the results of any manner of tinkering with their relative seven game achievements in an apparently unbalanced early season.

What should be evident from this exercise is that just as random variation can see equals thrash near equals on a single day, the record of a side over single figure matches can also be greatly influenced by chance. Villa benefited from an Arsenal red card on opening day (and red cards can be a disproportionately large influence on the goal difference acquired over a run of a few games) and they then recorded an unlikely, but permitted victory, both pre-game and in running against Manchester City.

What happened, happened, but even attempting to allow for differences in schedule strength, seven games are extremely unlikely to even partly remove chance from skill

In short "luck" influences short term results both in recorded, individual records and in the results of their opponents, which then are sometimes used to "better understand" a side's win loss record. Luck is recycled on both sides of the ledger to add certainty, but it merely replaces a much better arbiter of team ability, namely their record over a much longer stretch of matches.

As a way of celebrating recent, short term achievement, such as manager of the month awards, these methods are fine (as long as achievement is recognised as a combination of both the best and most likely the luckiest), but they fall well short, at least in the case of football's universal currency, goals, if they are used as an improved indicator of actual repeatable skill....or Villa would be 4/5 on Sunday against Spurs, rather than 3/1 and Manchester United would be 6/4 and not 8/15 to see off high-flying Southampton at Old Trafford.

Wednesday, 2 October 2013

The Premiership After Six Games.

It has been a turbulent first two months of the season for Manchester United and Arsenal. After all of one game, it was business as usual for the former (a 4-1 win away at the Liberty) and chaotic meltdown for the latter (a 3-1 home defeat at the hands of Villa).

Five games later and the narrative has flip flopped. Arsenal lead the table and United are tied on points with Stoke. Three of United's games have been against possible title contenders, but Arsenal have faced just one in local rivals Spurs and strength of schedule issues are bound to be more keenly felt early in a campaign.

In this post  I look at the impact of an unbalanced, short term fixture list as well as the impact of random variation over just six games and try to see how likely it is that United and Arsenal's core talent is little changed from the last campaign, despite the current 11 place gap between the sides.