Forecasting the 2015 UK General Election

UPDATE: here is the spreadsheet with predict vote share and probability for every party in every constituency. SNP and Plaid are both under “nationalists”.

prediction_breakdown

This post provides a forecast of the 2015 UK general election based exclusively on the 2010 results and the Ashcroft constituency polls. No national polls of any kind were used as input. The left-wing block of parties (Labour, SNP, Plaid, Greens, SDLP) has a chance of about 90% of securing a majority in the House of Commons, thereby locking David Cameron out of number 10.

The most likely total of seats in Great Britain for each party after the election, and the 95% probability intervals, are as follows:

• Labour – 276 (253/325)
• Conservatives – 267 (214/291)(including speaker John Bercow)
• SNP – 57 (52/59)
• Liberal Democrats – 23 (16/35)
• Plaid Cymru – 5 (3/7)
• UKIP – 3 (1/8)
• Greens – 1 (1/1)

These add up to 339 seats for the center-left block, 293 seats for the center-right block, and 18 Northern Irish seats for which we have no polling data. This is a moderately comfortable lead for the center-left. A map of the party that’s projected to win each constituency is below:

Methodology

The idea behind this forecast is to split the difference between uniform national swing and pure constituency polling. The forecast for every constituency is a function both of the polling in that constituency and of the polling in similar constituencies. This is why Labour leads in places such as Bermondsey & Old Southwark, where it was nominally behind in the polls with a swing of 9%; the swing from the Lib Dems to Labour has been slightly greater in other Labour-Lib Dems marginals than indicated by the Ashcroft poll there, so we should include that information in the forecast. The result is that the national swing tips the scales in Labour’s favor there, resulting in a forecast swing of 11%.

There is reason to believe this Ashcroft polling-only method overestimates UKIP’s share of the vote. Many of the Ashcroft polls date from the fall, when UKIP was polling significantly higher than it is now. The projected vote percentage for UKIP using this method is over 16%, but the party has been polling closer to 13% in the past month. Nevertheless, this shortcoming shouldn’t have a big effect on the marginal seats; these are the seats that are polled most frequently, so the information from the most recent polls places UKIP at a lower level.

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The seats you should be watching for on election night/How can David Cameron keep his job

I will now list for each region of Great Britain all seats where the result is less than 90% certain.

Scotland

You will notice that Scotland wasn’t included in the map above. That is for two reasons. First, it is very big and makes it difficult to see everything else. Second, the election there is very boring; the SNP is projected to win almost every seat comfortably:

Marginal seats in Scotland:

• 1. Berwickshire, Roxburgh & Selkirk (45% SNP, 44% Con, 10% LD)
• 2. Coatbridge, Chryston & Bellshill (89% SNP, 11% Lab)
• 3. Glasgow North East (74% Lab, 26% SNP)
• 4. Orkney & Shetland (61% LD, 39% SNP)

The main story here is that the SNP is an odds-on bet to carry 56 out of 59 Scottish constituencies this election, which is stunning compared to the 6 they carried in the last election. They also have a very real chance of winning all the seats in Scotland. There are only three seats in which they are the underdogs, losing one to each of Labour, Tories and Lib Dems. Ashcroft polls put them slightly behind in Berwickshire and a bit further behind in Glasgow North East, but they have been improving their vote share over the past few months, so there is reason to think that they may have closed the gap since those polls were conducted. They have led in every other poll in Scotland.

London

Marginal seats in London:

• 1. Bermondsey & Old Southwark (81% Lab, 19% LD)
• 2. Croydon Central (75% Lab, 25% Con)
• 3. Ealing Central & Acton (88% Lab, 12% Con)
• 4. Finchley & Golders Green (52% Lab, 48% Con)
• 5. Harrow East (70% Lab, 30% Con)
• 6. Ilford North (72% Con, 28% Lab)

Labour will be one of the most important battlegrounds on election night. There are four seats here where Labour are currently favoured but that the Tories must win if they hope to stay in power. The polling in Croydon Central has been mixed, but Labour only need a 3% swing, which is below the 5% average swing they have been getting in most seats. Labour should also easily pick up two Lib Dem seats, Brent Central and Hornsey & Wood Green, and are favoured in a third, Bermondsey & Old Southwark. If these results are confirmed on election day, the Lib Dems will be confined to four seats on the Southwestern suburbs of London.

South East and East of England

Marginal seats in the SE and E of England:

• 1. Brighton Kemptown (88% Lab, 12% Con)
• 2. Castle Point (78% Con, 22% UKIP)
• 3. Chatham & Aylesford (83% Con, 17% Lab)
• 4. Crawley (77% Con, 23% Lab)
• 5. Great Yarmouth (79% Con, 21% Lab)
• 6. Milton Keynes South (73% Lab, 27% Con)
• 7. Norwich North (74% Lab, 25% Con)
• 8. Peterborough (61% Lab, 39% Con)
• 9. Portsmouth South (71% Con, 29% LD)
• 10. Reading West (78% Con, 22% Lab)
• 11. Rochester & Strood (89% Con, 11% UKIP)
• 12. Stevenage (87% Lab, 13% Con)
• 13. Thanet South (50% UKIP, 50% Con)
• 14. Thurrock (72% UKIP, 28% Lab)
• 15. Watford (84% Con, 15% Lab)

This is just as important a battleground as London. The theme here is medium-to-small sized towns. The Tories’ path to victory lies through the 5 seats where they are underdogs here: Stevenage, Brighton Kemptown, Milton Keynes South, Norwich North and Peterborough. If Labour carries a few of the ones where they are not favoured, such as Great Yarmouth and Reading West, we will know they are having a great night.

This is also UKIP’s heartland. They have a lock on Clacton, are favored to win Thurrock, and have an outside shot of keeping Rochester & Strood and winning Castle Point. And then there’s Thanet South, where Nigel Farage is running, and the race is extremely close; it’s as close to a toss up as it comes.

South West and Wales

Marginal seats in the SW and Wales:

• 1. Aberconwy (77% Con, 16% Plaid, 6% Lab)
• 2. Carmarthen West & Pembrokeshire South (84% Con, 16% Lab)
• 3. Ceredigion (50% Plaid, 50% LD)
• 4. Cornwall North (87% LD, 13% Con)
• 5. Devon North (87% Con, 13% LD)
• 6. Dorset South (87% Con, 13% Lab)
• 7. Filton & Bradley Stoke (87% Con, 13% Lab)
• 8. Gloucester (67% Con, 33% Lab)
• 9. Llanelli (79% Lab, 21% Plaid)
• 10. St Ives (74% LD, 26% Con)
• 11. Swindon North (85% Con, 15% Lab)
• 12. Swindon South (58% Lab, 42% Con)
• 13. Taunton Deane (76% Con, 24% LD)
• 14. Torbay (78% LD, 22% Con)
• 15. Ynys Mon (64% Plaid, 36% Lab)

The South West is ground zero for the battle between the Tories and the Lib Dems.   It is, however, not very important for deciding who will be the next PM, since both the Tories and the Lib Dems are in the coalition; the results of their marginals don’t matter very much. Perhaps the only constituency worth watching out for is Swindon South, which has had extremely balanced polling between the two main parties.

Amidst all the talk about the SNP, Plaid Cymru has been a bit neglected. They have a very good chance of picking up a few seats in Welsh-speaking West Wales, and that’s based on polls conducted before Leanne Wood appeared on the TV debates, which should certainly improve Plaid’s fortunes.

Midlands

Marginal seats in the Midlands:

• 1. Birmingham Yardley (81% Lab, 19% LD)
• 2. Boston & Skegness (52% Con, 48% UKIP)
• 3. Burton (79% Con, 21% Lab)
• 4. Derbyshire South (85% Con, 15% Lab)
• 5. Dudley South (79% Con, 21% Lab)
• 6. Halesowen & Rowley Regis (75% Lab, 25% Con)
• 7. High Peak (58% Con, 42% Lab)
• 8. Leicestershire North West (87% Con, 13% Lab)
• 9. Lincoln (88% Lab, 12% Con)
• 10. Northampton North (82% Lab, 18% Con)
• 11. Northampton South (83% Con, 17% Lab)
• 12. Redditch (81% Con, 19% Lab)
• 13. Rugby (79% Con, 21% Lab)
• 14. Stafford (69% Con, 31% Lab)
• 15. Staffordshire Moorlands (88% Con, 12% Lab)
• 16. Stourbridge (78% Con, 22% Lab)
• 17. Tamworth (80% Con, 20% Lab)
• 18. Warwick & Leamington (78% Con, 22% Lab)
• 19. Worcester (63% Con, 37% Lab)
• 20. Wyre Forest (66% Con, 34% UKIP)

There are a lot of “marginal” seats in the Midlands, but most of them are Labour longshots. If Labour win in places such as Stafford and Stourbridge, it will be pretty obvious that they have won very early in the night. If they win most of these seats, they may even be able to avoid depending on the SNP (and depending on the Lib Dems instead). If they fail to win seats such as Halesowen & Rowley Regis or Lincoln, to say nothing of seats like Nuneaton, which is not listed, Ed Miliband has reason to be worried about his future. UKIP have two potential gains here; Boston & Skegness is one of their top targets, whereas Wyre Forest is a seat that had an independent MP for many years, and where UKIP were polling well last year.

The North

Marginal seats in the North:

• 1. Berwick-upon-Tweed (75% Con, 25% LD)
• 2. Blackpool North & Cleveleys (82% Con, 18% Lab)
• 3. Brigg & Goole (74% Con, 26% Lab)
• 4. Calder Valley (78% Con, 22% Lab)
• 5. Cleethorpes (65% Con, 35% Lab)
• 6. Colne Valley (73% Con, 27% Lab)
• 7. Crewe & Nantwich (30% Con, 70% Lab)
• 8. Elmet & Rothwell (76% Con, 24% Lab)
• 9. Leeds North West (71% Lab, 29% LD)
• 10. Pudsey (54% Lab, 46% Con)
• 11. Rossendale & Darwen (50% Con, 50% Lab)
• 12. South Ribble (51% Con, 49% Lab)

Again, some Labour longshots, but there are three constituencies here that are almost perfectly balanced between the two main parties: Pudsey, Rossendale & Darwen, and South Ribble. The result in these three constituencies should be a good indication of whether the parties will over- or underperform their forecasts.

The keen-eyed will have noted that Sheffield Hallam didn’t make the list. the model gives Nick Clegg only a 5% chance of hanging onto his seat. There have been 3 polls of Sheffield Hallam and in all 3 the Labour candidate has been consistently leading the Lib Dem leader.

A Bayesian rating system for football teams

This post provides an introduction to a system I devised for rating football teams called Footbayes. The goal of this project is to rate football teams in a coherent, principles-based way using game results.

There are of course many other projects that do the same. In my opinion, the two most prominent are ClubElo and the Euro Club Index. These are similar in that both are based to different degrees on the Elo rating system originally developed for chess players. They are both very good overall; I’m especially fond of ClubElo due to its careful attention to predictive checks.

However, I have never been satisfied with Elo as a definitive solution to rating football teams, or anything else for that matter. For one, what is considered to be one of its virtues, I actually consider to be a terrible feature: a team’s rating doesn’t change at any time except when it plays a match. This is counter-intuitive, and not how people usually think about things. Take the example of group B in the last World Cup. The Netherlands thrashed Spain 5-1 in the fourth game of the tournament, and everyone’s opinion of the Netherlands improved a lot. When a couple days later Chile also beat Spain convincingly, should our opinion of the overall quality of the Dutch remain unchanged? Elo says no; FootBayes says most certainly yes! If Spain got beaten again it provides us with some evidence they were never very good in the first place, and that in turn makes the Netherlands’ achievement of beating them by four goals less impressive in retrospect.

Another problem is that Elo was originally designed to predict binary outcomes, but football games are not binary. Any rating system will need at least three outcomes: home win, loss and draw. The technique used to work around this is to count a draw as a half-win for either side. This is relatively reasonable. On the other hand, the adjustment for goal difference is not. The number of points exchanged between the teams is multiplied by a coefficient that varies with the goal difference. This is very unelegant; it is mixing two different rating systems, but it also leads to strange results. If Real Madrid beat Ludogorets at home by 1-0 Real’s rating will increase; however, that can’t be right. The difference in abilities is taken to be so great that a narrow 1-0 victory should make one downgrade their estimate of Real’s ability. If Real wants to keep being considered one of the best teams ever, it really should be beating minnows at home by larger margins.

So how does FootBayes actually work? It is based on a few principles:

1. Each team is described by a unique number, its rating. The ratings are transitive, meaning that there is no situation such as Arsenal beats Spurs, Spurs beats Stoke, Stoke beats Arsenal; if the first two are true, then Arsenal must be better than Stoke. This rating is normalized so that the mean is 500 and the standard deviation is 250, for interpretability
2. The probability distribution of the different outcomes of a match is a function of exclusively the difference in ratings between the home team and the away team. Specifically, the outcomes follow an ordered discrete logistic regression.
3. The ratings, as well as the coefficients for the regression, are those that make the data most likely. For those of you who know this, it’s just simple maximum likelihood, with flat priors on the coefficients. The ratings follow a normal distribution by construction.

That’s it. There is nothing else involved. These assumptions are used to fit a Bayesian inference model in Stan, a probabilistic programming language. A major flaw of this model is that it doesn’t take time into account anywhere, thus a team’s ratings are assumed to be universal, and can’t vary with time. I have an idea to incorporate time into the ratings, but for the time being the ratings are given by team by season, and there’s no link between a team’s rating last season and this season. For the last Premier League season, the ratings look like this:

They mostly follow the final league table, although not perfectly. This is to be expected; in such a low-scoring games, some teams can go on hot streaks that do end up altering their position in the table at the end of the season. This is the same data, but in table form:

The ratings are designed such that an average team has a score of around 500, and a good team has a score of at least 750. One thing that is striking is that the standard deviations for the estimates are all fairly large. Even though Man City is rated as being 100 points better than Liverpool, on average, the standard deviation of around 90 points allows for a small possibility that Liverpool were actually better than City, and that the results on the field just didn’t reflect this.

Now, imagine for a moment City and Liverpool were going to play a match. A static rating system, such as Elo, would calculate win/draw/loss probabilities from point estimates for the ratings. FootBayes, on the other hand, incorporates uncertainty into its estimates. Ratings only make sense if they include uncertainty.

Of course, if the uncertainty is too big ratings don’t mean anything. But the FootBayes ratings allow us to be very sure of at least some things. For comparison, here is the difference between City’s and Arsenal’s ratings for last season:

Very clearly different, though you probably didn’t need any math to get to that conclusion independently if you watched any games last season.

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The nice part of having these ratings is being able to get probabilities not only for upcoming matches, but also for who is going to win the league, who is going to be relegated, etc. Here are the ratings for this season so far:

A few comments:

• Chelsea and City have a very clear lead over the rest of the field, as they should
• United are actually almost not any better than last season; their rise in the league table is the result of the collapse of Arsenal and especially Liverpool
• The model rates Southampton relatively high, on the same level as Arsenal and United
• Spurs and Liverpool are very mediocre
• The three worst-rated sides are the three promoted sides: Burnley, QPR, Leicester
• These ratings do NOT take the team’s performances in previous seasons into account (yet). So it probably overrates underdogs like Southampton, and underrates big teams like Liverpool

Good, we have the ratings, now we can use them to make predictions about the future. All of the following are the results of 4000 simulations. First, W/D/L probabilities for the next round of matches:

Next, title probabilities:

Chelsea is favored but City have a chance. That is the consensus anyway. Next, Top 4 probabilities:

Chelsea and City have already guaranteed their places in the next Champions League. The other two spots seem likely to go to two of United, Southampton and Arsenal. Both Spurs and Liverpool have very low chances of getting one of the spots; the model rates them very poorly. Finally, relegation:

A tighter battle. Leicester and Burnley are the most endangered, but each still has only a two-thirds chance of being relegated. QPR comes after, and this is remarkable because the model does not know at all who was promoted this year. Could it be that the three are going down?