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# The professor's Premiership probabilities

 By Professor David Spiegelhalter Professor for the Understanding of Risk, Cambridge University

 Professor David Spiegelhalter analyses the football table

Why should anyone take any notice of what a Cambridge professor of statistics, who knows little about football and does not even support a team, says about this weekend's matches?

The answer lies in the increasingly sophisticated mathematical models that are being used by sports betting companies to set odds and identify potentially good bets.

Let us look at Arsenal playing Stoke City at home on Sunday, and ask - how many goals is Arsenal going to score?

The average number of goals scored by a Premier League team at home this season is 1.36.

But Arsenal is not average - in fact they have scored 39% above average at home, so we could add this "strong attack factor" of 39% to get 1.89 expected goals.

Now we need to take into account the defence strength of the opposition, and we find that this season Stoke City has conceded 11% more goals than average, so we add a further "weak defence factor" of 11% to get a final total of 2.1 expected goals from Arsenal.

Now no team is going to score 2.1 goals, but we can use some probability theory (rather bizarrely called a Poisson distribution after Monsieur Poisson) to estimate a 12% chance that Arsenal will score 0 goals, a 26% chance of getting 1 goal, a 27% chance of scoring 2, and so on.

Meanwhile, Stoke City is estimated to have a 51% chance of not scoring at all, a 34% chance of getting 1 goal, and only 15% chance of getting 2 or more goals.

 MORE OR LESS BBC Radio 4's More or Less is broadcast on Friday, 22 May at 1330 BST and repeated on Sunday, 24 May at 2000 BST Subscribe to the More or Less podcast Listen online

We can then easily work out the chance of a particular score - it turns out that the most likely score is 2-0 but even this only has a 14% chance.

This is the simplest possible analysis and can be easily done on a spreadsheet.

With my student Yin-Lam Ng we have been looking at all the major league results in Europe for the past 20 years and found that better predictions can be made by including something called the pitch-factor.

This reflects the fact that there is a slight but measurable relationship between the conditions on the pitch and the number of goals scored by both teams.

This means that teams have some tendency to either both score high or low.

This needs special software and gives the predictions shown in the table.

One thing the model makes very clear is that although we can sometimes be reasonably confident who will win certain games, it is much harder to nail down the exact scores.

For example, although the model suggests a 72% chance that Arsenal will beat Stoke on Sunday, there is only a 14% chance that the final score will be exactly 2-0.

There is 13% chance it will be 1-0, and a 9% chance of 2-1.

So with even the best mathematical models, predicting the exact scores involves a lot of luck, which means Mark Lawrenson is still in with a good chance of beating the computer this weekend.

One final word of caution: These techniques are not as sophisticated as the models the bookies use, and they do not respond to public opinion as bookies' odds do.

So we only give Hull City a 9% chance of beating Manchester United on Sunday, which may be reasonable if we just look at past performance.

But judging from the betting, people clearly feel Hull has a better chance than this given their perilous circumstances and with Man U conserving their strength.

Maths can find it difficult to deal with these factors.

So I would not recommend anyone using these odds for betting.

You have been warned.

PREMIER LEAGUE PROBABILITIES

ARSENAL V STOKE

Home win: 72%

Draw: 19%

Away win: 10%

Verdict: 2-0 (14%)

ASTON VILLA V NEWCASTLE

Home win: 62%

Draw: 21%

Away win: 17%

Verdict: 1-0 (10%)

BLACKBURN V WEST BROM

Home win: 54%

Draw: 23%

Away win: 23%

Verdict: 1-1 (10%)

FULHAM V EVERTON

Home win: 35%

Draw: 35%

Away win: 30%

Verdict: 0-0 (10%)

HULL V MAN UTD

Home win: 9%

Draw: 19%

Away win: 72%

Verdict: 0-2 (14%)

LIVERPOOL V TOTTENHAM

Home win: 72%

Draw: 20%

Away win: 9%

Verdict: 1-0 (10%)

MAN CITY V BOLTON

Home win: 59%

Draw: 22%

Away win: 19%

Verdict: 2-1 (10%)

SUNDERLAND V CHELSEA

Home win: 10%

Draw: 25%

Away win: 65%

Verdict: 0-1 (20%)

WEST HAM V MIDDLESBROUGH

Home win: 57%

Draw: 28%

Away win: 15%

Verdict: 1-0 (19%)

WIGAN V PORTSMOUTH

Home win: 44%

Draw: 32%

Away win: 25%

Verdict: 1-0 (16%)

HOW DID DR SPIEGELHALTER DO?

(All fixtures were played on Sunday 24th May at 1600 BST)

SUNDAY

Arsenal 4-1 Stoke

The professor's probable score: 2-0 (14%)

Aston Villa 1-0 Newcastle

The professor's probable score: 1-0 (10%)

Blackburn 0-0 West Brom

The professor's probable score: 1-1 (10%)

Fulham 0-2 Everton

The professor's probable score: 0-0 (10%)

Hull 0-1 Man Utd

The professor's probable score: 0-2 (14%)

Liverpool 3-1 Tottenham

The professor's probable score: 1-0(10%)

Man City 1-0 Bolton

The professor's probable score: 2-1 (10%)

Sunderland 2-3 Chelsea

The professor's probable score: 0-1 (20%)

West Ham 2-1 Middlesbrough

The professor's probable score: 1-0 (19%)

Wigan 1-0 Portsmouth

The professor's probable score: 1-0 (16%)

In summary: Nine out of 10 win/draw/lose probabilities were correct, with two actual score results being exact.

BBC Radio 4's More or Less is broadcast on Friday, 22 May at 1330 BST and repeated on Sunday, 24 May at 2000 BST.

Subscribe to the More or Less podcast.

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