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.