The End of Season Title Reckoning: Updated Probabilities

Only ten days ago, Manchester City had according to our Model an 84% chance of retaining their title, making them heavy favourites, though down from the 92% chance the Model gave them before a ball was kicked this season.

Things have changed massively over the Christmas period. The feature image (also shown below) plots the Model’s simulation based probabilities of each team winning the Premier League as the season has progressed so far. This is up to date as of 28th December (i.e. before Spurs just lost this afternoon at home to Wolves). Liverpool have now overtaken Man City in the title reckoning, with their chances rising as high as 48%. The chances of Tottenham had increased to 33%, driven by their recent free-scoring form. Man City meanwhile have dropped down as far as 11%, with Arsenal at 4%.



Half-term Reports

We can always consult the league tables to find out where teams are – but are they where we expected them to be? It’s hard to avoid the idea that some teams are doing better than expected (Liverpool? Leeds?), and others are performing much worse than expected (Burnley, Millwall, Notts County). Shouldn’t tables reflect that?

Elo rankings offer such an opportunity. They give each competitor (team, individual) a strength score, from which a prediction can be generated for each match that lies between 0 and 1. In football, 0 would be an away win, 1 would be a home win, and 0.5 would represent a perfectly evenly matched event. So if our outcome variable is 0 for an away win, 0.5 for a draw, and 1 for a home win.

So we can look at every match so far this season, and see whether or not teams have exceeded expectations. If a home team had an Elo prediction of 0.45 and won, then the outcome is 1, and the Elo improvement is 1-0.45, hence positive. If on the other hand the Elo prediction was 0.7 and the visiting team won, then the home team’s adjustment would be 0-0.7, hence negative.

So teams that have consistently exceeded expectations would have a sum of adjustments that are positive, but a team that has under performed would have a sum of adjustments that is negative.

In the featured image for this post, we plot the story so far for the Premier League. Watford’s strong start is clear, and Liverpool’s seemingly relentless journey to the summit of the table on Christmas Day is there. However, up until two games ago, when Arsenal lost at Southampton, Arsenal were actually the most improve team.

Champions Manchester City are ninth placed in this table, falling from third on the eve of their match at Chelsea.

At the bottom, things are not surprising. Fulham, despite their summer investment, have struggled badly, as have Burnley following their success last season. Southampton and Crystal Palace are the two fastest improving sides at the moment.

Into the Championship, and indeed Leeds are the team most exceeding expectations, following on from their strong start, somewhat muted October, and strong November and December. Millwall are the biggest disappointment at half way.


Into Leagues One and Two (below), Macclesfield and Notts County stand out in League Two for seriously, seriously bad performances relative to expectations.

The scourge of the goalless draw

It’s the classic trope wheeled out by those who don’t like football – goalless draws, boring! Even those of us who live and breathe football have to confess we’d rather see a game with goals, even if those goals are all a bit comical, as they were in the 2-2 draw between Man United and Arsenal in the week.

Just how frequent are goalless draws? Mark Lawrenson and Paul Merson spectacularly under-predict them; prior to the current season, Lawro had called just 8 0-0 draws in 2,617 recorded predictions, and Merson just 4 in 1,483 recorded predictions (thanks to @MyFootballFacts and @EightyFivePoints¬†for the data). That’s low (about 0.3%), but how low compared to outcomes?

The featured pic for this post shows the frequency per season (northern hemisphere) over the history of data collected on Soccerbase. There’s been quite a bit of variation over time, and perhaps surprisingly for someone who got into football in the late 1980s and early 1990s, that isn’t the period when the most goalless draws were recorded – it’s actually the 1920s.

We can use the econometric technique of Indicator Saturation to determine shifts and outliers in this time series. The R package gets gives us the following plot:


So we see that since the late 1960s, things have been fairly constant, with (persistent) variation around about 8%. The middle panel gives the residuals, hence the difference each year from that mean level of 8%. We’re on a run now of 12 consecutive seasons with less than 8%, but not statistically significantly less than 8%. If the downward trend continues though, we may be looking at a new equilibrium sometime soon.

The art of defending, maybe, is a thing of the past?