Is strength of schedule a strong argument against a frozen table?

By Andrew Puopolo, @andrew_puopolo


While it pales in comparison to the many societal, economic and public health challenges posed by the ongoing COVID-19 epidemic, the football world is grappling with the challenge of determining a suitable and equitable way for completing the remainder of their seasons. UEFA have recently published guidelines stating that "if a domestic competition is prematurely terminated for legitimate reasons" the procedure adopted by a National Association for selecting clubs for participation in 20/21 UEFA tournaments should be "based on objective, transparent and non-discriminatory principles". Although there is still talk of playing out competitions behind closed doors, some leagues, most notably in Belgium and Scotland, have decided to end the season by ‘freezing in place’ such that the current standings become the final standings, the leaders become Champions, and the teams in the relegation zone go down.

This method for settling the end of the season has been especially cruel on Scottish Championship club Partick Thistle, who have now been relegated despite having a game in hand and being only two points behind the team above them. In the English Premier League, freezing the season in place would result in a similar situation, as 19th placed Aston Villa have a game in hand and are also within two points of safety. Given the financial cost of relegation from the Premier League is at least £50 million, this method of ending the season would be controversial. Using points per game -- rather than the current points -- to determine final rankings would help to alleviate the issue of unequal numbers of games played.

Another argument against freezing the current table is that it crystallizes what would normally be a temporary advantage for teams that are facing a difficult run of fixtures to end the season. For example, in the EPL relegation battle, Brighton & Hove Albion are 15th with 29 points, but still have to play four of the current top five if the season were to be completed. Despite this, Brighton owner Tony Bloom has commendably been one of the biggest critics of freezing in place. Teams with a relatively benign run-in would, correspondingly, be at a disadvantage as they have already completed their matches against the strongest teams in their league.

Clubs that are advocating playing out the season behind closed doors can point to the obvious unfairness that differences in strength of schedule introduces in the frozen-table solution. But how big is this effect in the hard currency of points? Are the variations in difficulty sufficiently large that we might expect them to have a significant impact on the final rankings? We have previously seen that the rankings at this point in the season typically have over a 90% correlation with the final rankings at the end of the season, so most teams should already be very close to their final league position. On the other hand, adding or removing a point or two could have huge consequences for teams broiled in the fight against relegation.

To answer this question, we have developed a method for calculating adjustments to the current point totals that would remove the advantage that some teams would gain from avoiding a difficult remaining schedule. Do the clubs fighting relegation or competing for European slots have a legitimate grievance, or are these adjustments sufficiently small that they have no meaningful impact on the outcome of the 19/20 season?

Quantifying Strength of Schedule

To answer this question, we leverage the use of three statistical methods. First, we take the current Elo ratings for each EPL team from clubelo.com. Second, we use a Poisson regression fit using historical Elo values and match results to predict the number of goals either team would be expected to score in a match, based on the difference between their Elo ratings. Finally, by drawing from a Poisson distribution, we can simulate the match to evaluate the probability of each team winning or a draw.

We run two different simulated experiments for the remaining EPL fixtures in the 2019/20 season. In the first experiment we simulate each of the fixtures 50,000 times. In the second experiment, we repeat the simulations using randomly generated fixture schedules for each team. We randomise the schedules as follows:

1. We simulate the two matches that were postponed due to the Carabao Cup Final (Manchester City vs Arsenal, Aston Villa vs Sheffield United) and compute the expected points these teams would have gained from the matches and add them to their current totals. This ensures that each team has nine remaining fixtures.
2. We randomize the pairings in the 90 remaining fixtures under the constraint that each team can only play an specific opponent once. Home advantage effects are not included.

By generating random fixtures between teams, we are effectively exploring the expected points totals for a neutral fixture schedule, a schedule of average strength. To quantify the strength of schedule for each team we take the difference in their average points gained in the two experiments. A negative points difference indicates that the true schedule is more difficult than a neutral schedule and that the team therefore gains an advantage from not having to play those matches. A positive difference indicates that the true schedule is easier than a neutral schedule and so a team would lose the benefit of playing out these matches.

Figure 1 shows the results. With the exception of Crystal Palace (-1.2 points), Brighton (-1.0) and Man United (+1.2), the difference between the actual and randomized fixture schedules is less than a single point; for eleven of the twenty EPL teams, the variations in the strength of their remaining schedules is equivalent to less than half a point.

Figure 1: The points value of variations in strength of schedule. Chart shows the difference in average points between the simulations of the actual and randomized fixture schedules for each team. A negative points difference indicates that the true schedule is more difficult than a neutral (random) schedule; a positive difference indicates that the true schedule is easier than a neutral schedule. 

We then use these fixture strength differences, along with the expected points from the postponed matches, to adjust the current points total for each EPL team to gain an insight into how the ranking might change in a 'fair' table; that is, with the strength of schedule effects removed.

Table 1: The adjustments to current point totals for games in hand and fixture difficulty to determine an estimate of 'fair points' and how this would affect final league position.

The two teams that would have the most to lose (in terms of points) from a frozen table are Manchester United and West Ham United, who are, respectively, 1.2 and 0.9 points better off with their true schedule relative to a neutral schedule. However, correcting their current points totals to reflect this does not have an impact on their league position. The only teams that switch places in the fair table would be the teams in sixth and seventh: Wolverhampton Wanderers and Sheffield United (because of the upward adjustment to the latter's points total from their game in hand). Assuming Manchester City’s UEFA competition ban is upheld (and the FA Cup is not won by a team outside the top seven) both of these teams would still enter next season’s Europa League in the group stage^[1].

The identity of the Champions, Champions League qualifiers, Europa League qualifiers and relegation places remain unchanged^[2]. The fair table actually adds clarity to the relegation battle: while Bournemouth are currently in the relegation zone on goal difference, they fall further behind West Ham and Watford after adjusting for strength of schedule. Aston Villa, despite having a game in hand, are also still in the relegation zone after the adjustments are applied.

There are other factors that aren’t accounted for in this analysis, most notably some teams being on the beach and having little motivation, players being out of contract on June 30, and an overall lack of match fitness. While some teams might be better or worse off after the pandemic due to these factors, it is not clear who the beneficiaries would be, and similar factors are present in a normal Premier League season.

In conclusion, variations in the strength of each club's remaining fixtures do not appear to provide substantial evidence to those arguing that freezing the current table is a manifestly unfair method of determining the final standings. The financial impacts of lost commercial and match revenue are probably a much larger concern.

Follow Andrew Puopolo on twitter @andrew_puopolo

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[1] This assumes that the access and format to next season’s Europa League remains the same after COVID-19.

[2] If points per game is used to determine the final table, then Arsenal and Tottenham Hotspur would switch places in the table, with Arsenal qualifying for the Europa League at Tottenham’s expense. Wolves and Sheffield United would then finish in their “fair” positions