Monday 21 April 2014

Which Summer Premiership Buys Bloomed in the Spring?

The summer and winter transfer windows afford Premiership teams their only chance to substantially strengthen their squads with quality players. Considered judgement is made and opinions are backed with hard cash to acquire players who will hopefully form a nucleus for a successful squad for the foreseeable future.

In a sport with notoriously short term agendas, it is perhaps unfair to attempt to assess the winners and losers from last summers transfer spending spree, but in the spirit of the current awards season, we'll give it  go.

Transfers, of course involve defensive players, mid fielders and attackers and in view of the lack of really objective measures at the moment for the defensive side of the ball, a rating system based on player statistics would prove problematical. Therefore, we perhaps should fall back onto a much more valuable resource in evaluating a successful transfer, namely the experienced opinion the man at the top, the manager.

Playing time can be used as a good proxy for talent in assessing such things as ageing characteristics. Premiership teams have reasonably deep squads and a player who is appearing regularly is likely to be one of the top performers within his team.

However, playing time alone, requires context as well if we are looking at the success or otherwise of a transfer. The playing time achieved by a player is likely to be correlated to his transfer fee. Better players cost more and overall should perform to a higher level than those who cost less.

Age will also be a factor. Most players who attract a fee are generally aged in their twenties, but a player just out of his teens may be bought as much as a future investment than as a potential ever present in the current season of his purchase. By contrast, a player in his mid twenties would be more likely to be purchased as an immediate and useful full time starting player, before age related injury and depreciation sets in.

The third major consideration revolves around the talent levels of the side making the transfer. A £5,000,000 purchase for a promoted side would be a considerable investment and the expectation would be that the player would command a regular starting spot and considerable projected playing time. Whereas, a similarly priced player would be much less likely to make a similar impact at a top side, where talent levels would be higher. He may even initially be purchased as loan fodder with which to inconvenience the ambitions of his parent club's rivals.

These parameters can be used to create a baseline for playing time for particular transfer profiles.

For example, if a struggling Premiership side, had paid around £8 million for 24 year old in the summer transfer window, the average expected playing time, based on historical precedent, for your purchase would be around 60% of the time available in his first season. A more experienced player, nearing 30 would be expected to be on the field for the same side nearly 70% of the time.

Compare that to under 40% of playing time if a similar transfer had been to a top four side instead.

 The Ten Best Transfers Made in the Summer Window, 2013/14.

Player. Club. Cost.
(£ millions)
Age. Proportion Of  Playing Time.%
A Elmohamady. Hull. 2 26 97
S Caulker. Cardiff. 8 22 100
E Pieters. Stoke. 3 25 88
C Davies. Hull. 2.25 29 97
J McCarthy. Everton. 13 23 81
L Bacuna. Aston Villa. 3 22 79
M Olsson. Norwich. 2.5 25 85
T Huddlestone. Hull. 5.25 27 93
D Lovren. Southampton. 10 24 80
N Redmond. Norwich. 3.2 20 62

Above, I've listed the summer purchases whom have bettered their projected playing time by the greatest amount and thus may be considered to have exceeded the hopes and expectations placed in them by their new club.

Hull's Amhed Elmohamady tops the list, although he and Hull had the advantage of a season long loan to bed in at the KC Stadium during their Championship season of 2012/13. Therefore, England prospect, Steven Caulker should probably take the accolade. His transfer fee was four times that of Elmohamady, but he is considerably less experienced at 22 and under this simple metric, his ever present status at an inferior team, Cardiff, only just failed to overhaul the Hull player for outright leader.

A couple of modestly priced, relatively mature (in age anyway) players follow closely, Erik Pieters at Stoke and Curtis Davis, again continuing the apparently impressive team building done by Hull in the summer window.

Steven Caulker prepares to say "Pob Hwyl" to Spurs and "Helo" to Cardiff.
Of the higher priced purchases in the top 10, McCarthy at Everton and Lovren at Southampton stand out and mega pound, but relatively successful purchases bubbling just below, include Fernandinho at Manchester City, Eriksen and Paulinho at Spurs and Bony at Swansea.

I've omitted keepers, purely because they tend to have few pretenders to their place in the starting lineup, but Mignolet, Mannone and McGregor (at Hull) top the list of newly acquired stoppers.

Inevitably there is a bottom ten, but a metric based partly on appearance minutes is obviously susceptible to injuries.

Everton's Kone prove the least successful summer purchase, a £6 million pound, 30 year old player should be expected to play nearly half of the available minutes at a top 6 side in his first season. Although injuries are partly out of the control of a team or player, his history and age perhaps suggested the price paid was too high for the potential risk. He has been absent through injury since mid October.

Cardiff's John Brayford was a non injured failure from Derby. The fee was relatively modest, £1.5 million, but as a 26 year old he would  have expected to feature in around 45% of playing minutes. Instead he failed to play a single minute and is now out on loan. Cardiff suffered a similar disappointment with the transfer of Peter Odemwingie, a more costly and older investment who failed to impress enough to command a regular starting place and his swap move to Stoke was bi-laterally agreed in the winter window.

Palace, Sunderland, and Villa spent moderately, but with a fair few underperforming individual returns at this end of the ledger and big priced summer disappointments, some partly injury mitigated, include Fellaini at United, Osvaldo at Southampton, Jovetic at Manchester City and Lamela at Spurs.

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.

Sunday 13 April 2014

Norwich Slip Towards The Championship.

Just when it seemed the day couldn't get any worse for Norwich following their 1-0 defeat at Craven Cottage, the news arrived that the least likely result from the three relegation shaping games had actually materialized. A win for Cardiff at Southampton should have been expected around 12% of the time and Cala's goal (inevitably "Super Cala" for the punning headline writers) had made the result a reality.

The Canaries knew that defeat would see Fulham emerge as serious contenders to snatch away their Premiership place come May, but they must have hoped that Cardiff wouldn't also advance to within touching distance.

The result also took some of the shine off Fulham's narrow win as they failed to shake off the Welsh side.

Sunderland had begun the day as the most likely of the bottom two to take points from their fixture, but although the Black Cats scored the only goal of their game, it was sadly in the wrong net. Instead Cardiff's unexpected three points revived their hopes and chunks of survival probability were claimed from both Norwich and Fulham.

Leaving so soon?  Norwich's EPL Status Hangs by a Thread.
Norwich now lie 17th with 32 points and four matches remain, two points in advance of Fulham and Cardiff a further point back. Their goal difference is superior, but not so far in advance that it would remain so with a series of heavy defeats. The killer for them is a borderline unfair run in that takes in visits to Manchester United and Chelsea and visits from Arsenal and Liverpool. A schedule that would pitch them against three of the top four sides in any normal EPL season before a ball was kicked in August.

Norwich's average points expectation from their final four games is around 2.3 points, compared to 4.1 and 4.4 for Cardiff and Fulham respectively and this disparity is best illustrated by plotting the likelihood that each side will gather particular points totals from theses matches.

Norwich's expectations dominate the left side of the graph where fewer points lie and their rivals dwarf the chances of Norfolk's finest as we move towards the higher totals. Both Cardiff and Fulham's most likely total is four points and Norwich's is a single point.

These totals do need to be viewed with regard to how likely they are to occur, but the plot does reiterate the threat to Norwich from two currently trailing teams, but each with significantly easier final fixtures.

We can further confirm the task facing Norwich by comparing the record this season of teams at the foot of the table in their corresponding fixtures against the Canaries final four opponents to create a general baseline. It gives a small sample sized indication of how difficult Norwich's task may be perceived, even if the reality of their task may be slightly different when framed from longer term results.

Sunderland are yet to visit Old Trafford or Stamford Bridge, but are still pointless from the visits of Liverpool and Arsenal. Cardiff took nothing from the four games, as did Villa. Palace are also pointless with a visit from Liverpool to come. Fulham, Swansea and West Ham took just a single point each and only WBA bucked the trend, defeating United at Old Trafford at the depth of their slump and taking a point from each of the other three fixtures.

Overall, sides from Stoke downwards took just 15 points from a possible 105 against the four sides and venues confronting Norwich. Therefore, the upside for the Canaries appears very limited and now they have two legitimate pursuers.

Despite very nearly half the Premiership still not mathematically free from relegation worries, the main contenders still remain any three from the current bottom four.

Sunderland's failure to take anything from Saturday's home game with Everton has pushed them to near certainties for the drop, even with a brace of games in hand. Cardiff looked all but gone following defeat by Palace, but their against the odds win over Southampton has given them renewed hope, while simultaneously damaging the fortunes of Fulham and principally Norwich.

The results of simulating the remainder of the season is shown above.

On a weekend when honours at both ends of the table could have been virtually settled for the season, every result that needed to happen to prolong the enjoyment of the neutral or the agony of the committed, did happen.

Friday 11 April 2014

Premiership Showdowns at Liverpool and Fulham.

Get ready for a weekend of football action by seeing how two pivotal matches could decide the fate of the Premiership title race and the fight to stave off relegation. Norwich's visit to Fulham is followed on Sunday afternoon by Manchester City's trip to Liverpool.

In this guest post I outline what each possible match outcome will mean for each side.

Share the pain or the glory.

Monday 7 April 2014

Crystal Palace Survival Update.

For the length of his Premiership tenure at Stoke City, Tony Pulis always managed to pull of at least one late season victory over a fellow struggling team that virtually guaranteed safe passage through to May. Two goal margin wins at the Hawthorns in Stoke's first Premiership campaign and at QPR in Pulis' last season, sandwiched similarly important victories over the likes of Middlesbrough, Hull and Wolves in the intervening years.

For all his critics at the Britannia and beyond, Pulis never allowed the fans' fingernails to be bitten all the way to the quick and it was frequently Stoke's opponents whom were staring into the abyss on the final day of the season.

Whether that was a talent or just a happy quirk of fate, the Premiership's marmite figure virtually guaranteed himself a shot at a full season in Premiership charge of newboys, Crystal Palace, following a comprehensive 3-0 victory over Cardiff on Grand National Saturday.

Three goal margin wins are an extravagance that rarely appears on the Welshman's CV, where defence is prized above all else and few can disputed the marvelous turn around he has engineered using his tried and trusted approach. When Pulis arrived at Palace after 11 matches, they had fewer points than Derby had at a comparable point in their miserable 2007/08 season when they ultimately finished bottom with just 11 points.

As Palace fan and Infostrada's data guru, @SimonGleave points out on Twitter,

Since Pulis was named, Palace have kept nine clean sheets. Only Chelsea (12) and Arsenal (10) have kept more during the same period.

In those 21 PL matches, Palace have conceded 18 goals. Only Chelsea (14) and Man City (17) have conceded fewer in the same period.

Whether you use cold hard numbers or gut instinct, the picture is rosy for a second season of Premiership football. Last weeks post combined these two approaches by simulating the fate of each side given they attain a particular number of points. 

A fan whom watches his side over the course of a season is well placed to give a valid opinion as to the likelihood of their team taking all three points away at Cardiff, So the wisdom of the (Selhurst Park) crowd can provide a strong indication of the number of league points their side will finish with at this late stage of the season.

Above is the updated plot, summarizing the simulated relationship between points and how frequently each team survived in the 2013/14 EPL season. Palace's current total of 34 points is already sufficient for the team to survive in over half of the 10,000 simulations, even if they fail to gain another point. A single draw bumps their survival rate in excess of 80%.

For completeness, here's also the target figures for the remaining struggling teams.

The really good news for Palace is that Cardiff wasn't their easiest game in the final run in. They have a better opportunity to gain additional points in their upcoming home game with Villa and a similarly "easy" away match, comparable to Saturday's win at Cardiff, at Fulham on the final day. So points are there to be taken to push their likely end of season points haul to even more comforting probabilistic levels.

Again by simulating the remainder of the campaign, it's possible to arrive at how likely Palace are to finish with a particular points total and those predictions are shown in the plot above. Each fan will have his or her individual attainable total in mind, but even allowing for a degree of pessimism, the high 30's should be easily reached.

By combining the two plots above, we can arrive at a more conventional graphical depiction of the likelihood that Palace could, through the unlikely combination of a really poor set of results over the last half dozen games, combined with Europa League qualifying form from one or more of the teams currently cut adrift at the bottom, find themselves relegated in May.

So to summarize, Palace has a less than 2% chance of being relegated prior to Sunderland's Monday night game at Spurs. By defeating Cardiff, they almost certainly sealed the Welsh sides fate.

Norwich reacted to an extremely damaging loss at home to WBA by sacking their manager and face a massively important game at Fulham next week, followed by a run in that takes in visits to Old Trafford, Stamford Bridge and visits from Liverpool and Arsenal.

Should Fulham defeat Norwich, the Cottagers may face Palace on the final Sunday having to win to stay up, while the Palace fans celebrate another resounding success for the Pulis sorcery.

Wednesday 2 April 2014

Where To Draw the Line for Premiership Survival.

The expectations of football fans at the start of the season can be broadly split into two camps. Supporters of around half a dozen teams can look forward to a season where the anxiety revolves around title aspirations and UCL or Europa league qualification. Some even organise a flypast to celebrate the latter. The remainder of have-nots can't wait to get to the magical 40 points quick enough and reach the generally accepted threshold for continued membership of the top flight.

The 40 point target usually leaves quite a bit of room for error, the mid to high thirties has generally been sufficient to finish outside the bottom three throughout the history of the 38 game Premiership. Only West Ham (42 points) in 2002/03 have been relegated with more than 40 points, although Everton needed a superior goal difference to go with their two score points to survive in 1997/98 and Sunderland found 40 points insufficient a year earlier.

Each of these seasons were atypical of the current EPL. Everton's near miss-hap and Sunderland's demise came in a period when fewer than 80 points were needed to win the title, so "extra" points filtered down the league and West Ham suffered partly through the generous nature of the other two relegated sides, WBA (26 points) and Sunderland (19 points).

This demonstrates that while historical precedence can give a baseline figure, factors unique to particular seasons also wield some influence.

If the likes of Derby, Coventry and Sheffield Wednesday hadn't embarked on unlikely goal scoring sprees against Bolton in 1997/98, Everton would have suffered relegation on goal difference instead of clinging to their top flight status.

And if WHU had swapped an impressive 3-2 win away at Chelsea for a much more valuable win at lowly Bolton in 2002/03 instead of the narrow 1-0 defeat they actually suffered, the Hammers 42 points would have been sufficient and Bolton would have dropped into the Championship with 41 points.

Therefore, goal difference, an intertwined fixture list (14 of the remaining matches are head to heads between teams currently occupying one of the bottom nine places) and the proximity of the relegation candidates to each other, each add layers of uncertainty to the survival target of the threatened sides. And these effects become more apparent as the season winds to an end.

The case of Crystal Palace illustrates some of these factors. Their run in is tough and two matches away at both Cardiff and Fulham present them with one of their best opportunities to pick up points in their remaining matches. If they do take points from these games they will deny one or more of their pursuers the chance to take maximum points. Additionally they have a superior goal difference and this is likely to be the case after 38 games.

Palace's goal difference under Pulis' 20 matches in charge is -4, compared to -15 in the first 11 matches before his arrival. Even if they only limp to 34 points by May, simulations indicate that they will still have just over a 50% chance of beating the drop.

34 points is not only at the lower end of the points estimate for Palace by the end of the season, (their most likely total is 38 points), but it also gives them a better than even money shot at staying up.

But what about their relegation rivals, Sunderland, currently lying in 19th place with 25 points from 30 games. Palace are an obvious target for Sunderland, but their fixture lists don't cross again this season, although their goal differences are very similar. However, they do play WBA whom are also struggling at the foot of the table, but the Baggies have an easier run in than Palace, as well as a superior goal difference. To complicate matters further, Cardiff also visit the Stadium of Light at the end of April.

If Sunderland reach 34 points, (an over-achievement on current evidence), how will all these intertwined factors play out in terms of their survival chances?

The easiest way to unravel this is to again simulate actual seasons and see how often 34 points sees Sunderland safe compared to others marooned at the foot of the table.

The table above appears to indicate that rather than a single survival line at this late stage of the season, each team has its own individual target. The chances of enough teams emerging from the bottom of the pack to relegate Palace if they end the campaign with just 34 points is around 53%.

In contrast, the likelihood that Sunderland will find enough sides to catch should they gain 34 points in a multitude of different iterations of the remaining 64 matches is only 30%. Cardiff, especially with their poor goal difference, need a near superhuman 36 points before they are more likely than not to remain in the top flight, as most of the birds will have flown to a slightly higher perch.

The playing field is level in August, but by May the really struggling teams appear to be required to clear a slightly higher bar just to give themselves a similar shot at surviving the drop.

*although Fulham aren't on the (slightly cluttered) plot, they are of course included in the simulations. Their potential fate is slightly worse than that projected for Cardiff.