League forecasts

We predict scorelines each week. We try to forecast using the most up-to-date information, and as close as we can to matches, since that reflects the best information.

But what if, instead, we tried to carry on forecasting to the end of the season? That is, forecast the outcomes of every match between now and next May (or whenever the 2020-2021 season ends)? If we do so, we can get some idea about what overall outcomes are going to look like – what’s the chance of Liverpool winning the title? Of Fulham being relegated?

We input results based on our forecasts for all remaining matches, creating each time we do this an alternative reality. We input results for the next week, then use those simulated results to update Elo ratings and other variables that affect forecasts, before making forecasts for the following week, inputting scorelines, and updating again. We carry on to the end of the season. Then we calculate the final league table, store that alternative reality and start again with the next alternative reality.

We do this a thousand times or more – the more the merrier, for statistical purposes.

What do we get from this? Well, we can ask: how often did Liverpool win the title in those 1000 different alternative realities? If they won it 500 times, then that says they have a 50% chance of winning the title.

We can do this for a range of leagues, and we can keep updating each week. We’ll post those updates here. Here are the forecasts made on November 3 after Monday’s Premier League results were in.

Here are the summary tables for each English division (Premier League down to League Two). There’s probabilities of different important outcomes in the first three columns, then the difference in goals score and goals conceded from the average. They are heat map coded too, so the redder, the more likely. Liverpool and Man City are nailed on for the top 4 in the Premier League, for example.

So, Premier League:

Championship:

League One:

League Two:

Here are the full matrices giving probabilities of each of the possible final positions (rows) for each club (columns):

Premier League:

Championship:

League One:

League Two:

What’s wrong with our model? Our model does alright, according to published evidence. Still to be factored in though:

  1. The impact of promotion and relegation,
  2. The impact of personnel changes (players in/out).