Friday, 18 April 2014

Luck Can Make An Average Team Appear Special.

It is very easy to be drawn to extreme performances, either good or bad when looking at the analytical side of football. Exceptional performance stands out, is always highlighted in the media and talked about by the fans. It's difficult not to get carried along.

Liverpool's title charge and the consummate ease by which Crystal Palace cruised to 40 points, of course is partly down to the expertise of their respective managers, fans and players, but it is also likely that random fortune also pushed their sides higher, as well.

The temptation, though is to look for the cause to the effect and ascribe 100% of the former to the latter. But the praise is rarely fully deserved and the criticism is often unduly harsh when expected success fails to arrive promptly.

One way to avoid the almost irresistible rush to narrative, is to start with a singularly anonymous team, one that, for a season,at least is steeped in mediocrity. 52 points with a barely positive goal difference has been the average seasonal performance of a Premiership team over the last decade and the Spurs team of 2004/05 exceeded no one's expectations by recording this benchmark.

The side Martin Jol inherited mid term from Jacques Santini finished 19 points clear of the drop, 43 points from the summit, reached the 6th round of the FA Cup before losing to Newcastle and the 5th stage of the league cup before bowing out to Liverpool, despite taking the first kick in the penalty shootout. They failed to defeat any of the then Big 3 of Arsenal, Chelsea or Manchester United and their 52 points were exactly in line with expectations from their pre-match odds over the 38 games.

So the 52 points gained by Spurs in 2004/05 probably reflected the most likely outcome for a team of their ability playing in that season's Premiership. It is a comforting occasion when theory and reality combine to give the illusion of control without the appearance of outlying products of talent and a lop sided portion of random chance.

The range of possible outcomes from a group of games is most easily demonstrated by simulating seasonal outcomes using strength of schedule adjusted match odds. The usual method projects the range of league points that might be posted by a side of say Spurs talent once the vagaries of random chance are given full rein by continual repetition. However, it is a simple process to break down a team's match probabilities into individual slices that quantify the chances of winning or losing by a particular margin.

So alongside the usual range of points projections, we can add another commonly used statistic, namely goal difference.

How Likely Winning or Losing Margin Varies with the Chance of Winning the Game Outright.

Chance of Winning the Game. 65% 46%
Winning By a Margin of 1 25% 24%
Winning By a Margin of 2 20% 14%
Winning By a Margin of 3 12% 6%
Winning By a Margin of 4 5% 2%
Losing By a Margin of 1 10% 17%
Losing By a Margin of 2 3% 7%
Losing By a Margin of 3 0.8% 2%
Losing By a Margin of 4 0.1% 0.5%

Spurs' cumulative points expectation from the individual match odds for all 38 league games in 2004/05 was that they would get 52 points and typically that would result in a goal difference of small, single figures.

However, just as it is possible, but highly unlikely that an average side could either win or lose all 38 matches, a single iteration may see a side of Spurs' 2004/05 talent deviate from their expected average and in doing so produce atypically higher or lower goal differences.

The most likely goal difference is indeed centred around zero, but there is also a reasonable chance that our league average side might record multiple years when their goal difference drops well into negative double digits or rises to similar positive heights.

If we take the 2004/05 season as a benchmark, Spurs' range of possible goal differences only begins to peter out as they record values matched by Manchester United, who finished 3rd at one extreme and Norwich who were relegated at the other.

Even with thousands of repetitions, sample sizes start to fall as we look at the spread of actual points recorded by the same goal difference. But the spread of points gained with the same goal difference, in this case -2, is similarly wide, if slightly less well defined, falling into the low 40's and as high as the early 60's. If we again look at the 2004/05 season, Everton recorded a goal difference of -1, but won 61 points.

If average Spurs, mk 200405 can produce an impressive array of goal differences from the same talent base and an equally diverse range of league points from seasons with identical goal differences, the random walk should also be apparent within individual seasons.

Below are two final plots that trace individual seasons taken from just a couple of dozen simulations using our generic, average team and patterns and trends, that could be easily mistaken for real changes within the team are readily apparent. Even though they have been generated from the same game odds, used in an identical order.

The first graph could easily be depicted as a promising start that stalled after around a dozen matches and then got progressively worse as the side stumbled over the survival finishing line, before the season ends on a low point and four consecutive losses.

While the second plot, again drawn from the same match probabilities, show an almost polar opposite. A poor start is gradually arrested and followed by an impressive second half of the season, containing a 12 game winning streak and likely  UEFA Champions League qualification, probably in the first qualifying round.

Two very different outcomes to essentially the same talent laden season, made possible by the random distribution of rewards in a short 38 game period.

Fortunately, even when we try to chose a mundane, everyday side to illustrate how the same talent base can produce very different results, an event often intervenes to proved a potential narrative where none really exists.

Santini left to be replaced by his assistant, Jol after 12 matches. Jol's first match in charge was a 4-5 loss at home to rivals, Arsenal. And each of these graphs provides convenient inflexion points at or around 12 matches and it would be incredibly hard to resist attaching the cause of a managerial departure to the effects seen in either plot.

Even if we knew that both were merely produced as one possible reality out of many with the help of a spreadsheet.

Thursday, 17 April 2014

The Race For 1st and 4th.

A quick piece of housekeeping to follow up the relegation post after the weekend games.

Liverpool's win over Manchester City failed to settle the title race, but it did tilt the odds strongly in favour of the victors. The Reds and particularly Chelsea, then watched on as Sunderland came within minutes of taking all three points from City on Wednesday night, before gratefully settling for a draw.

The title now lies in the hands of Liverpool and Chelsea, win out and that side will be crowned champions by virtue of their head to head meeting at Anfield at the end of April.

Title Odds as of 17 April 2014. 

Team. Liverpool. Chelsea. Manchester City.
Title Likelihood. 65% 22.5% 12.5%

Chelsea will be the outsiders of three at Anfield, behind Liverpool and the draw, hence the large preference for Liverpool to take the title. However, match odds of around 47% for a Liverpool victory refer to longterm expectation, rather than a single iteration, so chance and luck will quite likely play a part as they did at Anfield on Sunday.

Goal difference has largely become cast in the title chase. There's around a 5% chance that Chelsea and Liverpool will end the season level on points, but virtually all of these ties would be settled in Liverpool's favour. A 5 goal margin of victory in the head to head would be needed to wipe out Liverpool's current advantage in one swoop, (somewhere in the order of 1,000/1), but even then the sides would also need to finish level, most likely on 84 points. Nine goals is too big a gap to bridge in just four games.

City trail both Chelsea and Liverpool, but have a superior goal difference. If they catch one or both (a triple tie is about a 0.5% chance), they almost certainly maintain or increase their current advantage.

The title is now Liverpool's to lose.

Goal difference is one straw that the blue half of Merseyside are currently clutching after Pulisball found its unlikely vindaloo factor by scoring one more than Everton as Crystal Palace reached 40 points in a 5 goal thriller. Should Liverpool falter, the clamour to crown Tony Pulis manager of the season may prove irresistible and the irony won't be lost in the Potteries, if clever defensive spoiling and set piece efficiency suddenly becomes fashionable five years after its inception.

Roberto Martinez is correct in stating that even Everton's current slender three goal difference superiority could prove decisive in the battle for 4th, although only in a minority outcome. If the teams are tied at the end of the season, Everton win nearly 90% of those occasions by virtue of goal difference. Unfortunately, ties are only likely to occur less than 5% of the time and overall Arsenal took a huge step towards securing UCL football on the back of a favour from their favourite pantomime villain and the honesty in the penalty area of West Ham's Matt Jarvis.

4th Place Odds as of 17th April 2014.

Team. Arsenal. Everton.
Likelihood of 4th. 85% 13%

As over at StatsBomb points out, Pulis is now cast in the role of Kingmaker. Having fatally wounded Everton and greatly inconvenienced Chelsea, he faces both Liverpool and Manchester City, against whom his record with a similarly hard working Stoke side was excellent in matches away from their home comforts.

During Pulis' reign at the Britannia Stadium, a Stoke side that was assured Premiership football next season looked and played very much like any other Stoke side and for all that he departed Stoke on relatively good terms, it must appeal if he could end the season with Palace positioned above Stoke.

Monday, 14 April 2014

Yaya Sanogo's "Goal" Would Have Been More Than A Consolation.

In a low scoring sport such as football, it is inevitable that perceived mistakes by the officials can be extremely important factors in determining the final scores of matches and even the outcomes of competitions. The introduction of goal line technology is a first step to eliminating error, although as Simon Gleave points out even this welcome addition should also come with an associated error bar.

Most contentious decisions involve the more subjective interpretation of fouls and the awarding of any subsequent penalties. Had Mark Clattenburg or his assistants spotted Skrtel's last minute penalty area handball or taken a less lenient view of Sakho's ill timed, first half tackle or Suarez's persistent infringing at Anfield on Sunday, the title race might already be over, settled in Manchester City's favour.

Offside decisions, by contrast have more in common with goal line innovation, but unlike other sports such as rugby, the officials in football are still given just one shot at calling correctly these often extremely close calls.

The ability to watch two different actions simultaneously, (the pass and the move), while correctly judging the relative movement of the striker and the marker, takes a rare talent and it is testament to the skill of the linesmen and women that the majority of such decisions are correct.

The nippy Grant Holt is flagged for offside (& a couple of fouls, probably).
One such call that may have been incorrectly flagged came with virtually the final kick of Arsenal's recent visit to Everton when Yaya Sanogo's 93rd minute goal was generally thought to have been incorrectly ruled out for offside.

The contest had already been comprehensively won by Everton, who led 3-0 and although replays suggested that Sanogo began his run from an onside position as the pass was made, few commentators thought the decision significant. Even Arsene Wenger's burning desire to see fair play remained in check.

Sanogo's disallowed goal would likely have been the game's final action, so the impact on the match can easily be calculated. It had none. Everton would have won the match whether Arsenal's goal stood or was struck off.

However, in a wider context the "goal" had a significant effect on the UCL ambitions of both Everton and Arsenal. As Liverpool v Manchester City and Fulham against Norwich demonstrated, head to head games against your rivals are immensely important, especially as the season winds to a close. Everything good you profitably do also ends up in the loss column of you rival.

Three points gained are three points that aren't available to your opponents, but less obviously goals scored boost your goal difference, while simultaneously depleting that of your current opponent.

If we ignore for a moment the unlikely resurgence of Spurs or the unexpected implosion of Manchester City, Arsenal and Everton have the fight for fourth place and UCL participation in 2014/15 between themselves. Everton currently top the Gunners by two points with five games each to play.

Everton's two point cushion is partly countered by Arsenal's markedly easier run in. Everton's schedule includes entertaining both Manchester sides and a visit to Southampton, while Arsenal taken on four teams from the bottom half along with Newcastle, which is arguably easier that playing basement teams at the moment.

Arsenal's points expectation from these 5 games is around 11 points compared to just 8 for their rivals and strength of schedule based simulations of the remaining matches give the Gunners the upper-hand prior to Tuesday's rearranged game at home to West Ham.

The Race for 4th on April 14th.

Teams. Arsenal. Everton. Teams Tied on Points.
Chance of Finishing 4th 58% 30% 9%

So Arsenal, despite trailing Everton appear to still have the better chance of claiming 4th spot. In addition, a significant, near 10% of the iterations result in both sides finishing with equal points, meaning goal difference would be the tie breaker and Everton currently have the superior figures, +22 to Arsenal's +16.

To break these ties we can run the simulations using correct scores, rather than simple win/draw and loss outcomes and add the margin of victory or defeat onto the current goal difference of each side. Once again Arsenal's easier schedule gives them a potential advantage. They are more likely to win by larger margins and less likely to lose by larger margins compared to Everton who face stronger overall opposition.

However, a current six goal deficit is a mighty obstacle to overcome in just five matches and Everton, in the event of a tie, edge 78% of these occasions where the teams finish the season level on points. Arsenal win 14% of the tie breakers and a further 8% of the 9% still cannot be split by goal difference and we have to move onto goals scored.

Overall, once ties have been broken, Arsenal finish 4th 59.8% of the time, Everton 37.8% with a small percentage left over for any other team. So the current goal difference of each side greatly favours Everton should the need arise.

At which point we should return to Sanogo's disallowed goal in the 93rd minute two weeks ago.

The apparent irrelevance of the event in the context of the single game, (except perhaps to Sanogo) begins to take on a much larger significance over the season as a whole.

Everton's currently superior goal difference shrinks if the match at Goodison finishes 3-1 with a last kick consolation and Arsenal, under these new conditions now win a much larger minority percentage of the occasions when both sides end with the same points tally. 4th place is also settled more frequently by goals scored, which also favours Arsenal who have at present scored three more than their Merseyside rivals.

What Was the Cost of Sanogo's Disallowed Goal at Everton?
Teams. Arsenal. Everton.
 4th Place if Sanogo Scores. 62.0% 35.6%
4th if Sanogo's Goal is Ruled Out. 59.8% 37.8%

Arsenal's chances of claiming 4th place increase by over 2% points simply due to a single goal. Underlining the importance of seemingly irrelevant goals scored in head to head matches, especially when two teams are locked closely together by both points and the subsequent tie breakers.

Liverpool at 2-0 against Manchester City briefly had the opportunity to press on and overturn City's superior goal difference and in view of their harsh run in, Norwich should be grateful that Fulham won on Saturday by the narrowest of margin, rather than the 5-0 they recorded over the Canaries in 2012/13.