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.

Winning Contribution in Soccer.

Expected Points graphs are the natural tool to visualise how many league points a team is likely to acheve during certain phases of a game.However,if we are interested in their chances of winning (or drawing) the match then plotting success probability is much more useful.

As the game progresses a team's success probability will ebb on flow dependent upon such things a current score,relative strengths of both team and whether a red card has been shown.By adding a team's chances of winning the match to half it's chances of drawing the game we can chart a teams expected success probability at various stages of the match.

At full time a team will have either won,gaining a success probability of 1.0 or drawn the game and shared the win equally with it's opponent gaining 0.5 wins each or of course lost.

By looking at the changes in success probability from the start of the game to full time,we can start to assign how much success probability should be attributed to the 11 or more participating players.

There are generally four fundamental stages to consider.

1) Change in SP due to time elapsed.

Each team will start a game with a likely success probability (SP) based on their relative strengths compared to today's opponents.This can be calculated by taking a weighted view of both team's recent results.How far you go back in time is a matter for individual taste,but I would suggest the last 25 games as a bare minimum requirement.
Since goals,both scored and conceded determine football games,it's sensible to expess the relative team merits in terms of how many goals each team will on average score in today's game,given the relative merits of both attack and defences.We can therefore use the pre game goal expectancies for both teams to calculate the expected success probability at the start of the game.This is the starting point and it's also team specific for today's game.

As the game develops without any goals occuring,the pregame goal expectancies for each team will start to decay.Thus we can re calculate each team's SP up to the point when a goal is scored.What generally happens is that a much superior team will see it's SP trend downwards towards 0.5 (as the teams are still level) and an inferior oppenent will see it's SP trend upwards.We can assign this change in SP respectively to each team along with any changes that occur in the lulls between significant events such as goals,penalty awards or red cards.

2) Goals scored.

To state the obvious,goals change games.If you score you always increase your success probability.The real bone of contention is how to distribute the credit for the goal between the scorer and the creator,similar to the situation in American Football where the QB throws a TD to his WR.I currently split the credit 80/20 in favour of the scorer.Some goals will be relative tap ins,although as Torres demonstrated recently,there maybe no such thing as a tap in,while other goals may result from a relatively simple pass from a team mate.

3) Goals conceded.

Allowing goals always decreases your SP and again we need to apportion the "blame".Harsh though it may seem,I've given the keepers 20% "credit" for the goal.The remaining 80% I've distributed between the 10 outfielders.55% of remaining fall in SP is divided amongst the defenders.I've chosen this figure because if we use goals scored as a proxy for "attacking play" we find that forwards score 55% of the goals,midfielders 35% and defenders 10%.Therefore it seems reasonable to flip these percentages when  trying to apportion the less transparent skill of defending.Blaming forwards partly for goals conceded may seem strange,but firstly the proportion of fault is relatively small, they do actively defend at corners and goals often develop from failure to maintain possession higher up the field.

4) Red Cards.

It's not harder to play against ten men that eleven,it's easier.Reduced in numbers,a team finds it harder to score and harder to prevent goals being scored against them.A red card reduces that team's SP  and the entire amount by which the SP is reduced counts against the transgressing player.

These are the (very) bare bones of a system to apportion blame and credit for team wins or draws amongst the individual players.So lets use a real example.I've chosen the Fulham Man City game from last week to illustrate the methodology and I've started with a pared down Success probability graph,illustrating the six major incidents from the game.Namely,kick off,two goals apiece and full time.

Significant Events from the Fulham Man City Draw.

Goals.
0-1,Aguero ,18 mins,assist,Silva.
0-2,Aguero,46 mins,assist,Dzeko.
1-2,Zamora,56 mins,assist,Dempsey.
2-2,Murphy,75 mins,assist,Zamora.


Subs.
Kasami on for Duff,61 mins.
Ruiz on for Dembele,84 mins.


Zabaleta on for Silva,69 mins.
Johnson on for Nasri,81 mins.
Tevez on for Aguero,83 mins.


A deeper look at some of the SP changing events from the game.


Kick Off).

Man City are the away side,but unsurprisingly given their vast investment are still considered more likely winners.If this game were to be repeated a large number of times I'd expect Man City to score on average 1.9 goals,concede 0.8 goals,win just over 60% of the time and draw just over 20% of the time.
So at kick off Man City have a SP of 0.741 compared to Fulham's 0.259.Just prior to the first Man City goal after 18 minutes,City's SP has declined to 0.722 and that fall is shared amongst the 11 starting players.Fulham's has risen to 0.278 from 0.259 and that is also shared amongst their starters.

Aguero's first goal).

Aguero scores from a Silva assist and Man City's SP goes from 0.722 to 0.902.80% of the credit goes to Aguero and 20% to Silva.By contrast Schwartzer is debited 20% of the 0.18 his team's SP has fallen,another 44% is shared by each member of the back four,28% by the four midfielders and 8% by the the two strikers.

Murphy's equaliser).

His goal raises Fulham's SP from 0.07 to 0.39 of which 80% is attributed to him and 20% to Zamora,who set up the chance.

Last 20 minutes).

Fulham's SP rises from 0.39 at the time of the Murphy goal to 0.5 at the final whistle,this is shared amongst the players on the field at the time of the goal.Man City's players lose the same amount as their SP falls to 0.5 from 0.61 as they were still the most likely winners with the game tied at 2-2.

A summary of each players win shares from the game.

FULHAM.

Player.	Win Conribution.	Comments.
Schwartzer.	-0.018	Conceded 2 goals,but benefitted from Fulham being big underdogs and claiming a point.
Kelly.	0.005	Unless they score,assist or are sent off,defenders score identically.Tackles won for example would re distribute the SP.
Baird.	0.005
Hangeland.	0.005
Riise.	0.005
Duff.	0.006	He was substituted while Fulham were still trailing,so didn't reap the completed comeback rewards.
Sidwell.	0.015
Murphy.	0.271	A late equaliser is always going to be a big SP mover.
Dempsey.	0.030	Assist for Zamora goal.
Zamora.	0.145	His goal could have just been a consolation.Assist for Murphy's leveller.
Dembele.	0.016
subs.
Kasami.	0.010	Limited game time,but gained from coming on before the equaliser.
Ruiz.	0.007
Total.	0.5

MAN CITY.

Player.	Win Contribution.	Comments.
Hart.	-0.021
Richards.	0.015
Kompany.	0.015
Lescott.	0.015
Clichy.	0.015
Silva.	0.097	Supplied an assist and had left the field before the equaliser.
Barry.	0.021
Toure.	0.021
Aguero.	0.259	Two goals.
Dzeko.	0.063
Nasri.	0.056	He wasn't on the pitch at the very end when City's SP was slipping away quickly and,as a forward he wasn't heavily penalised for Fulham's goals.
subs.
Zabaleta.	-0.039	Appeared when City still led,but couldn't help them protect the lead.
Tevez.	-0.007	Appeared with the game stalemated,but couldn't grab a winner.
Johnson.	-0.008
Total.	0.5

This initial system rewards or penalises players for being involved in events that are integral to the score and the final result.Consequently,players who aren't involved in game changing incidents tend to score similar shares.As in American Football,it' quite easy to assign a number to depict how influential a quarterback has been to the game,but much more difficult when dealing with a lineman.An improvement to players being scored as a unit would be to re distribute the unit's total by using stats such as tackles made or passes completed.The problem here is that these kind of stats,even if they correlate well with talent,aren't readily available in an easy to use format.So at the moment it's a work in progress and the more obvious contributors to the fore.