Manchester United's Chances of Being Relegated.

In the short history of the Premiership there have been just four different Champions.Manchester United top the list with 12 titles,followed rather distantly by Arsenal and Chelsea with three a piece and the group is completed by Blackburn.Three perennial contenders and a Blackburn team,built on a cash influx from a committed owner who was lucky enough to secure the services of Alan Shearer for the then not inconsiderable sum of £3.5 million.The presence of Blackburn's name on the list,especially in view of their recent and present struggles may surprise some,but Jack Walker's millions merely confirms that winners of the Premiership title are always sourced from the best and wealthiest teams of that particular time.

At the other end of the table the end of year booby prizes have been spread around much more liberally,not least because the teams who make the roll call of failures aren't allowed to make a reappearance for at least one season.Around a third of the current members of the Premier League  have at one time or another been relegated from the exclusive club and leading lights from the past such as Leeds,Nottingham Forest,Sheffield Wednesday and even Wimbledon have slipped through the trapdoor.

Football fans as a group tend to be a fairly realistic bunch especially when focussing on the likely prospects of their teams in a forthcoming season.Sights may be momentarily raised or lowered to suit the mood but most mid table supporters will hope for Premiership safety first.Then dream about a possible attempt to reach the foothills of a minor Europa League campaign,but will also harbour the fears about being dragged into a possible relegation scrap.

Perennial strugglers and new arrivals will hope to have still retained their star defender and the same manager by Christmas and their Premiership status come May.Any excursion into mid table will usually be seen as temporary respite,rather than a great leap forward.

Fans of the big four or five naturally set the bar highest. Championship ambitious usually depend on their recent spot in the top pecking order and any back sliding into the lower reaches of the stratosphere is viewed as an almost unthinkable catastrophe.

Naturally these views will be formulated from hours of watching or reading about our teams from previous seasons and assessing any team changes that may have occurred during the summer windows.Usually fans and pundits are reasonably accurate in these informal appraisals.You don't have to even be a particularly avid follower to game to be able to name the likely top four or bottom half dozen teams.However,occasionally there are surprises when a team busts clear of the limits of their usual station or falls below the levels of those predicted by their worst pessimists.

Often these bursts of unpredictable results are achieved by teams consisting of the same bunch of players who trundled unremarkably through the previous year.So what has changed? Often the answer is absolutely nothing and the team is merely experiencing the kind of randomness that exists when a process is repeated enough times even when the underlying event probabilities are similar to values seen previously.

Toss a coin enough times and you sooner or later you'll see ten consecutive heads,it's a natural sequence that will be thrown up by a fair coin.But if you're a supporter of "tails" and you see that sequence and in you horror you momentarily forget the "good times" that had gone previously,it's easy to think that your favourite coin has gone bad.

The Premiership Trophy....look,but Don't Touch for all but the best.

 If small sample size fluctuations occur in coin tosses that lead to apparently abnormal results even when the underlying chances have remained the same,we should see teams sometimes experiencing similar over the short 38 game Premiership season.If we simulate and repeat enough seasons,then just as a coin can churn out head after head through random bunching,so can a mid table outfit gain enough wins to climb higher in the natural order or enough defeats to possibly drop out of the Premiership all together and George Burley's Ipswich are the best Premiership example of the former as we can see here.

To see how likely it was that a team could rise above or fall well below their true talent,I used a simple goals based rating system to produce the kind of win/draw and loss probabilities a side would expect to encounter over a EPL season.I did this for a top four side expected to average around 84 points in a season,a slightly above average mid table team who would amass 52 points and a struggling team who would fail to break the 40 point barrier.

I then ran 1,000 simulations for each generic team for a 38 game season using the game probabilities that teams of such quality would encounter and for each "season" I totalled the number of points each team would have ended the season with.From each season to the next,each team had the same chance of winning or drawing each individual game as they had had in a previous "season" and the only variation in points total arose from the random bunching or none bunching of results picked by a randomly generated number.The better teams of course were more favoured to win their individual games.

Outcome per 1,000 EPL Simulations for Teams of Varying True Quality.

	One of the Best Top Four Teams.	A Good Mid Table Team.	A Relegation Candidate.
Number of Championships.	404	1?	0
Number of Relegations.	0	66	587
Highest Points Total.	106	82	67
Lowest Points Total.	60	28	19

The results of this simplified exercise appear to mirror the kind of subjective opinions you would hear if you talked to fans of these types of sides and good and bad news is equally shared between the three groups.

If you support the best of the best,as a team averaging 84 points would be then you have every right to think that the league title is a likely outcome.A 100+ points is unlikely,occurring 5 times in each 1,000 simulations,but definitely attainable.More realistically,teams who are destined to perform well enough to even approach 100 points will almost certainly wrap the title up long before end of season games take place.So desire or lack of it may be why this simple model perhaps over estimates the likelihood of 100+ years.The lowest points total such teams achieved was 60,dropping them into the ignominy of Europa Cup participation without the benefit of a pre Christmas Champions League campaign.Although,points deductions aside,a team of this true talent will never have an "unlucky" enough year to fear relegation.So to answer the original question,the current Manchester United side would almost certainly not be relegated this side of the Norman Conquest.

Things can look less rosy for our other two teams.Good mid table teams like Everton or Villa from the recent past may sneak one Championship once every 1,000 or so seasons,although their maximum haul of 82 points would hardly indicate a vintage year.Much more of a worry for fans and managers and a conundrum for chairmen are the 66 occasions when a true middle ranker gets randomly relegated.It's probably much better to dream about the 17or so times when fortune smiles and 70 or more points are banked.

The pessimism of fans of lowly teams is well justified with relegation an odds on proposition.They can expect half a dozen forays into the 60's,but a shade over 100 seasons every 1,000 when they don't reach into the 30's. They can certainly forget any chances that they might just win the Premiership Trophy by accident.