Using Statistical Methods To Assess Relegation Odds

Which Premier League clubs will suffer relegation this season? Today Mark Taylor shows how statistical methods can help us assess relegation candidates as we head into the second half of the season.

January heralds the start of a new year and is also a convenient waypoint for the Premiership campaign. Just over half of the league matches have been played, so sides have played all of their rivals at least once, with the third round of the FA Cup proving either a pleasant or an unwelcome respite from the frenetic Christmas and New Year fixture list.

The upcoming transfer window also gives a final opportunity for teams to strengthen squads and foresighted chairman have usually already dispensed with the services of, what in their eyes have been substandard managerial appointments. For example, West Ham, alone of the current bottom five has retained the manager with which they started the 2013/14 season.

Unusually, the top of the Premiership is proving numerically more competitive than usual, where affluent sides such as Manchester City and Chelsea are engaged in close combat with older, established winners such as Arsenal and Liverpool. Whilst Manchester United’s continued struggles to adapt to a new manager continues to amuse or frustrate, depending upon your allegiance.

Busy At The Bottom

However, it is the bottom of the table where the greatest team involvement always lies. 52 points is the average number of points gained by a Premiership side in the history of the 20 team league and with 40 points universally regarded as the pre-season target for survival, few sides outside of the elite can consider themselves safe, even with over half of the season elapsed.

The competitive balance throughout the Premiership over the years has made identifying the leaders and the strugglers a relatively simple task and the league positions occupied by sides once Premiership hostilities resume after the FA cup break offer a strong indicator of where a side will finish in May.

We can demonstrate the predictive quality of a January league position by testing the historical strength of the correlation between a side’s league ranking now and their ultimate finishing position. If the league position of every side in January were to be repeated in May, the value of the correlation coefficient would be exactly one and while this obviously hasn’t been the case historically, the average January to May coefficient is very nearly 0.9. By comparison, league positions after just five matches have coefficients of around 0.7 when compared to final finishing places.

So for the majority, a team’s place in the pecking order becomes apparent relatively quickly, strengthens, and by January each side is going to finish relatively close to the position they occupied at the turning of the year.

Projecting Finishing Positions

Historically, eleven out of the eighteen sides which were bottom in terms of points accrued per game after the New Year’s Day matches, ended up occupying the same position after 38 matches and only three managed to claw their way out of the three relegation places. The escape rate for teams becalmed in 19th at near midway improves very slightly, with teams such as the 2010 Fulham side even climbing all the way into the top half of the table. If we move one place higher, more teams than not gain another Premiership season despite occupying 18th at the start of the year.

League position is a fairly unrefined indicator of a side’s performance so far and their likely course over the remaining five months of the season, so for it to be a decent indicator of finishing position is fairly encouraging. The historical rate of survival for sides increases the further up the table they find themselves in January.

However, an obvious improvement would be to quantify how close these teams which currently occupy the relegation spots are to their immediate rivals, as well as how many others side are closely within reach. A tightly packing field is likely to see more movement than one that is strung out affording the strugglers few realistic targets to catch.

The most “impressive” 20th placed side after a New Year’s Day was the Wolves team in 2010/11, which propped up the table with 18 points, but was just four points adrift of 13th placed Everton. By contrast, 1995/96’s Bolton team had just 10 points, had played more games than others at the foot of the table and were a dispiriting eight points adrift of 19th spot. Clearly the opportunity for Wolves to survive was likely to be greater than the chances enjoyed by Bolton and so it proved. Ultimately the latter were relegated by a ten point margin and Wolves survived, for one more season at least, by a single point. The close New Year proximity of numerous similarly limited teams proved a lifeline for the team from the West Midlands and the absence of any lingering rivals an insurmountable obstacle to the Trotters.

Grading Teams By Standard Scores

This grading of the quality of teams occupying the lower reaches of the Premiership can be reasonably quantified by converting their January points total or points per game rate into standard scores. A standard score reveals how far from the average a measurement lies, expressed in terms of the standard deviation or dispersal of that measurement.

In the case of escapologists, Wolves, the average Premiership side had gained 1.35 points per game up to the end of December 2010, and the league as a whole had a fairly typical standard deviation of 0.38 points per game. Wolves themselves had gained just 0.9 points per game. Or 0.45 points per game below the average, which equates to 1.18 standard deviations below the mean.

Bolton (10 points from 22 games for 0.45 ppg) in a season where the average ppg was running at 1.37 with a standard deviation of 0.44, by contrast earned a parlous standard score of 2.09 standard deviations below average, from (0.45-1.37)/0.44.

A standard score is a decent proxy to compare the relative achievements of sides from different competitions and despite both occupying 20th position in their respective editions of the Premiership, Wolves’ standard score indicated and quantified that they were probably much closer to a lifeline of 17th spot than Bolton had been fifteen years earlier.

Therefore, if instead of using simply raw position we now look at the historical performance of teams with differing standard scores, we can extend the already useful correlation between tables formed in January and completed in May.

The best and worst performing 19th placed sides were both relegated, although those that did survive clustered towards the top of that particular standard score table. The trend for higher standard scores to correspond with better survival rates continued in 18th spot. A January 18th place, Stoke City, boasting a standard score of -0.85 in 2008/09 saw them finish 12th, but Sunderland’s minus 1.48 score from the same 18th position in 2002/03 led to relegation.

Assessing The Relegation Candidates Of 2014

So although no account is made for any activity in the January transfer window or factors such as returning injured players, league position at the start of the year does appear to capture a fair amount of the likely outcome in May, especially if we include how close or otherwise sides are from the relative safety of mid table by using standard scores.

TeamPosition On January 2ndPPG expressed as a Standard ScoreAssessed Probability Of Relegation
Hull 10th -0.45 5.5%
A Villa 11th -0.45 5.5%
Stoke 12th -0.54 8.3%
Swansea 13th -0.64 12.0%
WBA 14th -0.64 12.0%
Norwich 15th -0.73 17.2%
Fulham 16th -0.83 24.4%
Cardiff 17th -0.93 32.3%
C Palace 18th -1.03 41.7%
West Ham 19th -1.22 62.5%
Sunderland 20th -1.31 71.4%

In the table above I’ve listed the current point totals expressed as standard scores for the bottom ten Premiership sides going into the 3rd round FA Cup weekend. Using the historical experiences of sides with similar point gathering profiles over first half of the season during the 18 seasons when the Premiership contained 20 teams, I’ve further expressed the chances of each side falling back into the Championship.

Let's Look At The Odds

Compared to the available odds, for the current bottom five, this model is slightly more optimistic about the chances of Fulham, Cardiff and Crystal Palace, while West Ham and Sunderland are considered slightly more likely to slip down a division in May than their currently available odds would suggest.

TeamProbability Of RelegationBest OddsBookmaker
Hull 5.5% 7.50
A Villa 5.5% 11.00
Stoke 8.3% 11.00
Swansea 12.0% 21.00
WBA 12.0% 11.00
Norwich 17.2% 4.00
Fulham 24.4% 3.00
Cardiff 32.3% 2.75
C Palace 41.7% 1.57
West Ham 62.5% 2.62
Sunderland 71.4% 1.67

The generated odds illustrate that few teams outside of the top six are free from the threat of relegation, even after 20 or more matches. Teams such as Villa and Hull currently top the bottom half of the table, but decimal odds for relegation, implying a probability of around 6% would hardly constitute a major upset if they occasionally occurred.

Blackpool in 2010/11 are the only side so far that have posted a positive and therefore, above average standard score based on points per game at the start of January and then been relegated. They tumbled from 7th to finish 19th, which at least provides a small crumb of comfort for Manchester United, whom currently occupy that same 7th spot, but with a much superior standard score compared to Blackpool’s three years earlier. Standard scores of 0.1 for Blackpool in the first week of 2011, compared to 0.6 for David Moyes’ team today, see the current champion’s odds of relegation at well over 4,000/1.

 

 

Read more of Mark's work on his The Power Of Goals blog

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