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Nov 25, 2016
Nov 25, 2016

# Predicting the finishing table of the Premier League 2016/17

The ability to make predictions about the future based on past data is key to sports bettors who use statistics to increase their winnings. But how reliable are predictive models? In this article, Joseph Buchdahl explains how the true score theory applies in sports betting and uses it to calculate the finishing table of the Premier League this season. Read on to find out his predictions.

In a previous article, Dominic Cortis examined extensively the design and use of forecasting models to predict future outcomes. In one of his articles dealing with inaccuracy in prediction models he reminds us that “prediction is not prophecy,” as it can be “influenced by error."

Error or uncertainty, more commonly known as chance or luck, is the reason why models can often be seen to underestimate the range of possible realities when trying to predict what we should expect to happen in the future. A nice way to illustrate this is by means of true score theory and its application to the prediction of the Premier League points table.

### Predictions should be narrower than real life

On his blog, Phil Birnbaum explains why model predictions should be narrower than real life.

“Every year since 1983 at least one MLB team finished with 97 wins or more. More than half the time, the top team had 100 wins or more. In contrast, if you look at ESPN's 2014 team projections, their highest team forecast is 93-69. What's going on? Does ESPN really expect no team to win more than 93 games? Nope. I bet ESPN would give you pretty good odds that some team will win 94 games or more, once you add in random luck.”

The key word here is ‘luck’. A model simply attempts to forecast expectation, with good and bad luck evened out. In contrast, real life gives us realities where some teams have more good luck than bad, whilst for others it’s the other way around. The most skilful team may not be expected to surpass 93 wins, but with a few lucky wins, they could conceivably do better. Is there any way we can determine how much actual outcomes are influenced by skill and how much by luck?

### The True Score Theory

One way of determining the relative contribution of luck and skill to outcomes is what is known as True Score Theory. This is a theory about measurement and is a very simple one, if not necessarily proven: observed outcome is true ability (skill) plus random error (luck).

More specifically, it states that the variance in outcome is the sum of the variance in skill and the variance in luck. Variance is a statistical measure of the amount of variability in a set of data, for example finishing points in the Premier League table. It is equal to the square of the standard deviation.

The table below shows the actual finishing points for the 20 Premier League teams at the end of the 2015/16 season.

Premier League 2015/16 finishing table

## EPL 2015/2016 finishing table

 Team Actual Points Leicester 81 Arsenal 71 Tottenham 70 Manchester City 66 Manchester United 66 Southampton 63 West Ham 62 Liverpool 60 Stoke 51 Chelsea 50 Everton 47 Swansea 47 Watford 45 WBA 43 Crystal Palace 42 Bournemouth 42 Sunderland 39 Newcastle 37 Norwich 34 Aston Villa 17

Much has been written about how lucky Leicester City were to win the Premier League last season, whilst most of the big teams underperformed relative to expectation. Similarly, Aston Villa’s meagre points total might arguably contain an element of bad luck too. Just how much might luck, good and bad, contribute to this table?

### The influence of luck

Perhaps the simplest method to determine the role of luck is to start by assuming that all teams are of equal ability; that is to say, they have the same chance of  a home win, a draw or an away win. Since the inception of the Premier League in 1992, about 46% of matches have finished with a home win, whilst draws and away wins have each seen about 27%.

Since the inception of the Premier League in 1992, about 46% of matches have finished with a home win, whilst draws and away wins have each seen about 27%.

If every team managed such a ratio, they would all finish on about 52 points. Of course, because of good and bad luck, that wouldn’t happen all the time. In the same way as we don’t always see exactly five heads and five tails in ten coin tosses.

Using a Monte Carlo simulation we can model how much good and bad luck will influence the spread of points around this average. From a 1,000-run simulation the standard deviation was 7.8 points, meaning roughly two-thirds of points totals lay between about 44 and 60.

#### The role of skill

According to True Score Theory, the variance in skill should equal the observed variance minus the variance due to luck. We can easily calculate the observed variance from the 2015/16 Premier League points table above. With the standard deviation equal to 15.4, the variance is roughly 238. We can now also calculate the variance due to luck: 7.8 squared equals approximately 61. Consequently, the variance due to skill should be about 177 and the standard deviation of roughly 13.3 points.

### Who will win the Premier League 2016/17?

It is clear from True Score Theory that the observed Premier League table is a mixture of the skill of individual teams and some luck. Furthermore, since any forecasting model seeks to determine expected outcomes with luck factored out, the variation in actual Premier League points should always be greater than that which we might model.

Sure enough, this is typically what we find. The following table shows the modelled finishing points totals as we would have expected based on Pinnacle’s match betting odds for the 380 games played during the 2015/16 season. Constantinos Chappas shows how to calculate expected points from raw match betting odds.

Premier League 2016/17 finishing table forecast*

## EPL 2016/16 finishing table forecast

 Team Expected Points Manchester City 76 Arsenal 75 Chelsea 68 Manchester United 67 Tottenham 65 Liverpool 65 Southampton 58 Everton 54 Leicester 53 Bournemouth 47 Crystal Palace 46 West Ham 46 Swansea 45 Stoke 45 Watford 42 Norwich 42 Newcastle 41 WBA 38 Sunderland 37 Aston Villa 34
*Aston Villa, Norwich and Newcastle are included in the 2016/17 table as the above predictions are based on the 2015/16 season data.

Compare the variation of these expected points to the observed points in the earlier table. It’s obvious that the range is narrower. In fact, the standard deviation is about 13 points, with variance 170, very close to the figures predicted by True Score Theory.

Writing for Scoreboard Journalism, Simon Gleave, head of analysis at Gracenote Sports, confirmed a similar finding for model predictions submitted to him for the 2013/14 Premier League season. Whilst average model standard deviation was 15 points, the standard deviation in the actual finishing table was 19 points

### Model limitations

Given that the outcome of a Premier League season is a combination of team skill and luck we have to accept that no model can be perfect and that it will always underestimate the range of possible realities. Given that luck is unpredictable, no forecasting model should exhibit a variance greater than actual outcomes. If it does, then either there is something wrong with the model or, as Phil Birnbaum says, it’s “a sign that someone is trying to predict which teams will be lucky. And that's impossible.”

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