EPL Matchday 37 – Simulation

With only two games left in the Premier League season, many of the questions that I’ve been tracking with this simulation have been resolved, or it’s at the point where simulation analysis seems like overkill. In addition, some of the assumptions I’ve made in the simulation study – including how goal differential changes – may start to get in the way of useful analysis.

This will be the last update for the season, though I might run the simulation one more time just to see what it says before May 22. So here we go:

As always, the table shows the results of 10,000 runs of my simulation of the Premier League (background info here). Man Utd has every right to call the trophy engravers and Maserati dealerships after its win against Chelsea last week; while it’s still not a mathematical lock until they take a point from BlackX (where X = {burn, pool}), the chances of Chelsea pipping them for the title is 0.63%, or about 157-1.

Peter “praying mantis” Crouch (and, let’s be honest, their recent form) sunk Spurs hopes of another year in the Champions League (thankfully, this mathematical certainty reflects in the simulation, evidence I’m doing something right).  But the reality is that since March, City has been ahead of Tottenham on probabilities even if the standings didn’t always reflect it.

On the other end of the table, the relegation picture is clearer and clearer, even though there are still 5 teams which were relegated in the simulation. West Ham’s 33 points give their chances of going down at 97%, and their game against Wigan this weekend, while not a “clinch” game, does make the path to the Championship much clearer. Blackpool was relegated 79% of the time, while in 35% of simulation runs Wolves went down.  The two other teams that were relegated in the simulation were Birmingham (3%) and Blackburn (6%).

This is a useful example of how the simulation doesn’t predict every outcome. I have assumed that a win or loss changes each involved team’s goal differential by 1. This is a reasonable assumption when there are many games left, since blowout wins get offset by tight losses, and because when I update the stats every week the *actual* goal differential is brought to bear. However, with only a couple of games left, changes of +/- 1 to goal differential can overlook possibilities that might play out.  My simulation did not have any runs where Villa was relegated. However, their survival is not guaranteed. Granted, to be relegated they would have to lose both of their games while 5 teams below them win at least one, which is unlikely. But more importantly for the simulation, Villa’s -13 goal differential is a lot better than the teams below them. In a tie on points they would win every time even though it’s possible that a blowout by Arsenal or Liverpool could erode their goal differential if things go sideways for Gerard Houlier’s side.

Here’s a chart summarizing the outcomes of each simulation I’ve run since the end of March:

 
This chart shows the results for the 6 simulations I ran beginning on 28 March, and graphs how each team’s expected finishing position has changed as the season has progressed. It uses a ranking based on the weighted average of each team’s position (for example, this week Man Utd’s weighted average rank is 1.006, which is obviously the #1 ranking). So even though Man City and Tottenham fought for that 4th spot, Man City was consistently more likely to get there in the end. It also shows Everton consistenly ranked over Bolton, though in reality the teams were hard fought right up to the last couple of weeks. Things below the top 8 were decidely more mixed. West Brom had a wild ride, as did Newcastle. And two of the three teams most likely to be relegated way back in March are still expected to go down.

Just one game-based analysis this week, and it’s the critical Wigan-West Ham battle. Here’s how the numbers play out:

The numbers show how critical this match is for both teams. West Ham will come out of the game with a high likelihood of going down regardless of what happens; even a win only improves their chances from “almost completely certain” to “somewhat less certain.” But a home win for Wigan lowers their chances of relegation from 80% to 60%, and sets up a chance to clear the drop in their last game in Stoke. The loser of the match is almost certainly relegated.

Okay, one more game analysis. Wolves have a chance to virtually book a place in the Premier League next season if they win against Sunderland this weekend. Even a draw slightly improves their chances.  But a loss gives them essentially a 50-50 chance going into their final game against Blackburn Rovers.

As always, I would love to hear comments, questions, or rampant criticisms. Please feel free to drop me a line.

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