2013-14 English Premier League – GW 19 Simulation

It’s back…

With the first half (190 games) of the 2013-14 English Premier League season in the books and 190 more games scheduled to unfold over the next 4 1/2 months, it seems the right time to start up my EPL simulation model. Please, contain your excitement.

The model was an outgrowth of a teaching tool developed in 2008 for a simulation class taught at the Alberta School of Business. That model – originally designed by Armann Ingolfsson – was used to track the last half of the NHL season, and specifically to determine whether the Edmonton Oilers would make the playoffs. It’s necessary to mention here that by the 2008 and 2009 all star break – when the simulation model started – the chances of the Oilers making the playoffs was slightly more than the current snowball’s chance in hell.

(For more information on the history and methodology, click here.)

My model uses a fairly simplistic equation to determine the probability of each game’s outcome, then repeats this process 9,999 more times to develop a sense of the probability of each team’s final table position after all 38 gameweeks are finished. Every week I update the data in the model with the most recent matches played and re-run the model.

So here’s where we are on December 31, immediately before the New Year’s Day fixtures (click to embiggen):



The title race is not a lock – and frankly, it shouldn’t be this early into the season or things would get really boring – but it’s much more wide open than I’ve seen in previous years. By Gameweek 21 in the 2012-13 season, for example, Man U’s chances of winning the title were better than 80%. However, in 2014 we see Arsenal with “only” a 44% chance, and both Man City and Chelsea in with a hope. Man U’s chances at this point are on par with Spurs. (Both of these facts delight me as an Arsenal fan, I should mention). It will be interesting to see how much these change over the next few weeks.

The race for the top is very apparent when looking at European prospects. There are no surprises about Arsenal, Chelsea, and Man City each having a better than 70% chance of a top-4 finish at the end of the season, but the ~50% chances of the two Merseyside sides are surely a pleasant change for Reds fans and an exciting prospect for their Toffee bretheren. Somewhat more dispiriting is the 20.7% chance for Robin van Persie et al to see Champions League action in 2014-15, a likelihood roughly equal to Tottenham.

And finally there is relegation. The roller coaster ride of the Hammers and their fans sees no likelihood of a slowdown, with relegation a 59% likelihood based on their play in the first half of the season. It’s even worse for Gus Poyet’s Sunderland side, whose 70% probability of relegation threatens our chance to watch the legendary Tyne-Wear derby. The 39.4% relegation probability for Crystal Palace belies their current 15th place position, as the three teams below them – Norwich, West Brom, and Cardiff – all have a lower likelihood of returning to the Championship come summer.


Above are the raw numbers that lead to the analysis above (click the pic to make it bigger). The numbers show how often, over 10,000 iterations, that a team reaches a given placement in the table. The figure in red is the most likely result for each team. The distributions for each team show the real story behind the averages. For example, Southampton has a 37% chance of a 9th place finish, but could do better. There’s even a chance of a 4th-place finish for the Saints.


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.

EPL Matchday 36

What a difference a week makes!

With most Premier League teams now looking down three more games in the regular season, the weekly simulation that I’ve been running (not so weekly) sees the numbers solidifying more and more. It’s been well established which 6-7 teams will occupy the top spot (though not quite as firm which would be in the bottom three). But the ordering is still wide open. Recent runs of form – both good and bad – by the top teams have kept the title race alive.

Without further ado, here’s the summary of my simulation after Sunday’s games were complete. Remember, the number indicates the number of times (out of 10,000 runs) that a particular team ended the season in a particular ranking:

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EPL Matchday 35 – Simulation

Here we are with only four matches left for most teams (Tottenham and Man City being the exception, since their match was postponed until May due to the FA Cup). Even at this late stage, there is still ambiguity about who will end up where, and there are some massive games ahead.

As always, for some background on how these numbers are derived (and why, other than because your author is a big fat nerd), please check this backgrounder.

As of April 28 (up to and including Fulham’s 3-0 defeat of Bolton), the probabilities of each team achieving each position in the league table are as follows:

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EPL Matchday 33 – Simulation

the curse of teams whose names begin with W is holding strong

Here’s the results of my simulation run for the Barclay’s Premier League after the weekend matches. For some background information, please visit this backgrounder.

As of April 11 (including Liverpool’s 3-0 drubbing of Man City), the outcome of the simulation is as follows:

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Premier League Probabilities – Backgrounder

In 2009 I taught a course at the U of A’s School of Business on simulation – the application of quantitative techniques to answer business questions where there is uncertainty or risk. For example, if you run a retail store and are trying to manage inventory, you need to have an idea of your demand so you can decide how much to stock. But demand is unknown – so, by using random variables based on previous demand, then repeating the analysis many times over, you can understand the effects of changes to your bottom line. That’s the power of simulation.

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