Towards Condensing the Season
So I had an idea to complete the Premier League season in fewer matches. There is a fixture list of remaining fixtures, but not all fixtures are created equally. For example Liverpool vs Aston Villa would put a bit more shape to both the title race and the relegation battle, or Man Utd vs Sheff Utd would add significant information to the race for Champions League spots.
It may even increase the fairness as the most relevant matches are prioritised. It is more likely that you get a fair run in where Villa and Brighton both play Liverpool full strength and less likely the case where Liverpool field reserves as they will not be required to play many meaningless games.
One process to consider would be to rank the remaining fixtures by relevance based on title/relegation/Champions/Europa League "battle", based on which "battle" is most open and which teams are most involved in those battles.
1. Rank the remaining fixtures.
2. Play the most relevant next.
3. Check the table if all "battles" are mathematically decided then stop, else repeat from 1.
It may even increase the fairness as the most relevant matches are prioritised. It is more likely that you get a fair run in where Villa and Brighton both play Liverpool full strength and less likely the case where Liverpool field reserves as they will not be required to play many meaningless games.
Following this process I have simulated a number of seasons and condensed the season from 92 remaining fixtures to on average 76 fixtures. So for one example the "final" table would end up looking like below.
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| Man City expelled from European competition. Just one simulation of 10,000. City not enough points available to pass Liverpool. Everton, Palace, Newcastle, Southampton not enough points availbale to pass Burnley for Europa League place. Relegation and Champions League more or less had to fully play out. |
This obviously is a non starter. Re-ranking the fixtures after each game is ridiculous. Nobody would know who or when they are playing until a couple of days in advance. The algorithm could pick the same team to play 3, 4 or 5 games in a row to try and sort out their position. If you play Man Utd vs Sheff Utd and you have capacity to play fixtures concurrently (which you should unless you have only a limitted number of venues) then you may as well play that full round of fixtures anyway. Everton may be comfortable in midtable obscurity and Leicester may have the Champions League spot nailed down but out of title contention - there is little benefit to resting both teams.
In reality you will have a few teams on the critical path that will require their full list of fixtures to be played to separate them. A gap of 3 or 4 days between fixtures for these teams would require a minimum of 5 weeks to complete. So even if you can reduce the amount of fixtures left, it will be much harder to condense the amount of weeks left.
There still may be some use from this analysis. It could be used to dictate which order to schedule the remaining rounds (not fixtures) - so if we have a further interruption hopefully we have played some of the most relevant matches first.
Everyone wants to see Man City vs Liverpool and instinctively you would think this is highly relevant to decide the title chase. In truth though, from the relegation contenders, and the Champions League contenders a number of those teams will have to play out their full list of remaining fixtures which would include their matches versus Liverpool or Man City. A couple of wins for Liverpool vs the relegation sides would then render the Man City match meaningless. Based on my simulations it was the match that least needed to be played.
The full list of fixtures are below and the number of times out of 10,000 simulations that the fixture was required to sort the "battles" out mathematically.
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