Those Contentious Arsenal Decisions and Expected Points.

Firstly a brief description of the methodology.

The win probability for each team is tracked on a minute by minute basis throughout each EPL game.At any point in a game a team will have a probability of winning the game outright and an associated probability of drawing the game.By multiplying the probability of winning the game by 3 and the probability of drawing by 1 and adding the results together you will get an expected longterm average for the number of points that team will achieve from that position or Expected Points (EP) for short.

In the previous post we saw that the Expected Points that Arsenal would likely gain after the first goal was scored in their 2010/11 matches over estimated the actual number of points they achieved by between 6 and 10%.This isn't unusual because the EP is averaging all possible outcomes that may occur after the goal,so a particularly unlikely event such as Liverpool's last kick equaliser or Arsenal's capitulation at Newcastle will tend to move the two totals apart in a run of only 38 games.

An alternative explanation could be that the ratings,which at times uses matches from the previous season overrated Arsenal's actual ability this season and they should have been downgraded quicker.Again bringing the two figures closer together.Or it could be just down to small sample size variation.

Here's Arsenal's Expected Points for each contentious match if we assume the "correct" decision was given.Allowances are fully made for any red cards that may have resulted.All the hard work collecting the incidents comes from Tim Long's site.

Arsenal 6-0 Blackpool.Arsenal were given a penalty and Blackpool a red card.The red card still stands,but the foul was outside the box.Arsenal's EP for "correct" decision would have been 2.868

Arsenal 4-1 Bolton.Bolton's Cahill should not have been red carded in the 64th minute with the score at 2-1. Arsenal's EP for "correct" decision would have been 2.762

Arsenal 0-1 Newcastle. An incident so very late in the game.If Arsenal hadn't been reduced to ten men their EP would have been 0.10 in the 92nd minute instead of 0.023.

Arsenal 2-1 Birmingham.Squallaci's disallowed 19th minute goal.Arsenal's EP for the "correct" decision would have been 2.766.Arsenal lose out here even though the decision on the day went against them.Playing "what ifs" means you can't assume Arsenal will go onto win as they did on the day.You have to allow for the possibility of a Birmingham win or draw under the new,unknown conditions.

Wolves 0-2 Arsenal.No 88th minute red card for Fabregas with the score still at 1-0.Red cards reduce on average the amount of goals you score and increase the amount you concede.So a red card even his late would have marginally increased Wolves' chances of a draw or a dramatic win.Arsenal's EP for "correct" decision would have been 2.773

Everton 1-2 Arsenal.The absence of a leading attacking player can reduce the average number of goals you score by about 10%.So we could calculate Arsenal's EP from kick off due to Fabregas' potential suspension.However,we'll go with the 61st minute penalty that wasn't given to Everton with the score at 0-2.That would have reduced Arsenal's EP to 2.106.

Aston Villa 2-4 Arsenal.Villa's Clark should have had his 51st minute goal disallowed when Arsenal led 2-0.Again,you can't assume Arsenal would have certainly gone onto win as they did,even though that outcome is extremely likely and is reflected in their corrected EP of 2.845

Arsenal 2-1 Fulham.Kamara was wrongly given offside,but no time is given for the incident.It was certainly before Arsenal made it 2-1 though.If we assume it was after around an hour and he had a 10% chance to convert the one on one,Arsenal's EP as he bore down on goal would have been 1.701

ManU 1-0 Arsenal.United denied a penalty mid way through the first half with the scores level.Swings and roundabouts for Arsenal.If we give ManU the penalty we can't assume they go onto win as they did on the day.With the award,Arsenal's EP would have fallen to 0.531

Wigan 2-2 Arsenal.Arsenal were denied an 89th minute penalty.If we assume the Gunners have a league average 75% chance of scoring and accept that there is still time for 10 man Wigan to respond,Arsenal's EP rises to 2.474 upon the award.

Birmingham 0-3 Arsenal.Birmingham were denied a 18th minute penalty when trailing 1-0.It's a 75% chance the game is tied and 25% it remains 1-0 to the Arsenal.The award drops Arsenal's EP to 1.910

Arsenal 0-0 Man City.After a touchline incident,Sagna and Zabaleta are red carded.The latter harshly.Had Zabaleta stayed on the pitch Man City would have been marginal favourites for what little time remained and Arsenal's EP would have dropped to 0.941

Arsenal 2-1 Everton.As we've seen if you change an event,the rest of the game has potential to change for the worst.Saha's 24th minute strike should have been disallowed.If it had been Arsenal would have had an EP of 2.213 at that point.Much more likely winners,but not guaranteed to get the three points they actually claimed from one down.

Newcastle 4-4 Arsenal.If Best's 74th minute goal had stood 10 man Arsenal would have had a 2 goal lead and 94 times out of 100 they'd have kept it.Their EP would have been 2.803.

Arsenal 0-0 Sunderland.Arshavin's 87th minute goal is wrongly disallowed.The goal would have made victory extremely likely,but not certain.To account for a possible Sunderland comeback the EP for Arsenal would have been 2.869

Blackpool 1-3 Arsenal.If Taylor-Fletcher had been awarded a 54th minute penalty,Blackpool would have had an opportunity the level the game.A penalty depresses Arsenal's EP to 2.300

Bolton 2-1 Arsenal.Walcott is denied a penalty that would have elevated his team's EP to 2.179

Arsenal 1-2 Aston Villa.Ramsey is denied a penalty after 30 minutes with Arsenal already 2 down.On average Arsenal would expect to claim 1.206 points when lining up to take a spot kick in those circumstances.

Arsenal 1-0 ManU.Vidic should have been red carded and a penalty awarded after 31mins with the game still level.Arsenal's position would certainly be strengthened and they'd expect to go on and claim an average of 2.548 points.

The Alternative Expected Points for Arsenal for the remainder of each 2010/11 matches where a contentious decision occurred.The EP has been calculated by assuming that the correct decision was made.

Opponent.	Arsenal EP for the Alternative Decision.	Actual Points Gained in Match by Arsenal.
Blackpool(H).	2.868	3
Bolton(H).	2.762	3
Newcastle(H).	0.100	0
Birmingham(H).	2.766	3
Wolves(A).	2.773	3
Everton(A).	2.106	3
Aston Villa(A).	2.845	3
Fulham(H).	1.701	3
ManU(A).	0.531	0
Wigan(A).	2.474	1
Birmingham(A).	1.910	3
Man City(H).	0.941	1
Everton(H).	2.213	3
Newcastle(A).	2.803	1
Sunderland(H).	2.869	1
Blackpool(A).	2.300	3
Bolton(A).	2.179	0
Aston Villa(H).	1.206	0
ManU(H).	2.548	3
Total Points.	39.895	37

The cumulative total at first appears to support Tim Long's view that Arsenal were deprived of some points by poor referring decisions in 2010/11.If the correct decision had been made,both for and against Arsenal the cumulative EP total predicts on average Arsenal acrue 39.9 (call it 40) points from each new game position.This compares with the 37 points that they actually gained in reality in those games.Therefore, a case can be made for Arsenal losing 3 points over the season.

However,as we saw in the previous post,EP over estimated Arsenal's actual points haul by between 6 and 10% when we looked at real games where,first Arsenal and then their opponents scored the game's opening goal.They similarly underperformed in their three goalless games that aren't recorded here.So it's legitimate to ask why they should perform any differently in  these new "in running" games compared to how they actually did in real life situations in 2010/11.

Accounting for this under performance,an EP of 40 for Arsenal is the equivalent of around 37 points in reality.37 points is what they got when the poor officiating calls stood and 37 points is what EP projects them to get if all the dubious calls are corrected for both teams.

So we have a reasonable case to support both sides of the argument.

Which scenario's correct?......It's probably a bit of both :-).

A big thanks to Mr Long for putting these kind of stats into the public domain.