# How Predictable is the English Premier League?

The reason why football is so exciting is uncertainty. The outcome of any match or league is unknown, and you get to watch the action unfold without knowing what’s going to happen. Watching matches where you know the score is never exciting.

This weekend the English Premier League season will conclude with little fanfare. Bar one relegation place, the league positions have already been determined. In fact, these positions were, for the most part, decided weeks ago. The element of uncertainty seems to have been reduced this season.

With this in mind, I wanted to look at uncertainty over the long run in English football. To do this used the data provided by http://www.football-data.co.uk/ and analyzed these with R. These data consist of 34,740 matches played in the top 5 divisions of English football between 2000 and 2015, containing information about both the result and the odds offered by bookies on this result.

To measure the uncertainty of any given match I used the following strategy. First, I averaged across all bookies’ odds for the three possible events: home win, draw, and away win. Next I mapped these aggregated odds into probabilities by inverting each of the odds and then dividing by the summed inverted odds. This takes care of the over round that helps bookies to make a profit. For example, if the odds were 2.1/1 that an event happens and 2.1/1 that it doesn’t then the probability of the event occurring is:

(1/2.1)/ (1/2.1 + (1/2.1)) = 0.4761905/(0.4761905+0.4761905) = 0.5.

Finally, to measure the uncertainty of each match, I subtract the probability that the event occurred from 1, to calculate a “residual” score. Imagine a home win occurs. The “residual” in this case will be 1-P(home win). If P(home win)=1, then there is no uncertainty, and this uncertainty score will be zero. Since there are 3 outcomes, we would expect an uncertainty measure to be bounded between 0 (no uncertainty) and 0.67 (pure uncertainty) where we get 1 out of 3right by just guessing.

After importing these data into R and calculating the uncertainty measure, I looked at this uncertainty measure over time. The plot in the above shows fitted smoothed trend lines of uncertainty, stratified by division. These trends are striking. Going by this graph, the Premier League has gotten more predictable over the analysis period. In 2000, the uncertainty measure was around 0.605. Given that we expect this measure to be bound between 0 (complete certainty) and 0.67 (completely random), this tell us that the average league game was very unpredictable. Over time, however, this measure has decreased by about 5%, which does not seem like much. Despite, the somewhat unexciting end to the 2014/15 season, the outcome of the average game is still not very predictable.

Noticeably, in lower league games there is even greater uncertainty. In fact, the average uncertainty measure of League 2 games approached a value of 0.65 in 2014. This indicates that the average League 2 game is about as unpredictable as playing rock-paper-scissors. Interestingly, and unlike the Premier League, there does not appear to be any discernible change over time. The games are just as unpredictable now as they were in 2000. Please see my R code below.

```# clear
rm(list=ls())

# libraries
library(ggplot2)

# what are urls

years = c(rep("0001",4), rep("0102",4), rep("0203",4), rep("0405",4),
rep("0506",5), rep("0607",5), rep("0708",5), rep("0809",5),
rep("0910",5), rep("1011",5), rep("1112",5), rep("1213",5),
rep("1314",5), rep("1415",5))
divis = c(rep(c("E0","E1","E2","E3"),4), rep(c("E0","E1","E2","E3","EC"),10))

urls = paste(years, divis, sep="/")
urls = paste("http://www.football-data.co.uk/mmz4281", urls, sep="/")

odds = c("B365H","B365D","B365A",
"BSH","BSD","BSA",
"BWH","BWD","BWA",
"GBH","GBD","GBA",
"IWH","IWD","IWA",
"LBH","LBD","LBA",
"PSH","PSD","PSA",
"SOH","SOD","SOA",
"SBH","SBD","SBA",
"SJH","SJD","SJA",
"SYH","SYD","SYA",
"VCH","VCD","VCA",
"WHH","WHD","WHA")
home = odds[seq(1,length(odds),3)]
draw = odds[seq(2,length(odds),3)]
away = odds[seq(3,length(odds),3)]

# load all data in a loop
full.data = NULL
for(i in 1:length(urls)){
# calculate average odds
temp\$homeodds = apply(temp[,names(temp) %in% home], 1, function(x) mean(x,na.rm=T))
temp\$drawodds = apply(temp[,names(temp) %in% draw], 1, function(x) mean(x,na.rm=T))
temp\$awayodds = apply(temp[,names(temp) %in% away], 1, function(x) mean(x,na.rm=T))
temp = temp[,c("Div","Date","FTHG","FTAG","FTR","homeodds","drawodds","awayodds")]
full.data = rbind(full.data, temp)
}

full.data\$homewin = ifelse(full.data\$FTR=="H", 1, 0)
full.data\$draw = ifelse(full.data\$FTR=="D", 1, 0)
full.data\$awaywin = ifelse(full.data\$FTR=="A", 1, 0)

# convert to probs with overrind
full.data\$homeprob = (1/full.data\$homeodds)/(1/full.data\$homeodds+1/full.data\$drawodds+1/full.data\$awayodds)
full.data\$drawprob = (1/full.data\$drawodds)/(1/full.data\$homeodds+1/full.data\$drawodds+1/full.data\$awayodds)
full.data\$awayprob = (1/full.data\$awayodds)/(1/full.data\$homeodds+1/full.data\$drawodds+1/full.data\$awayodds)

# bookie residual
full.data\$bookieres = 1-full.data\$homeprob
full.data\$bookieres[full.data\$FTR=="D"] = 1-full.data\$drawprob[full.data\$FTR=="D"]
full.data\$bookieres[full.data\$FTR=="A"] = 1-full.data\$awayprob[full.data\$FTR=="A"]

# now plot over time
full.data\$time = ifelse(nchar(as.character(full.data\$Date))==8,
as.Date(full.data\$Date,format='%d/%m/%y'),
as.Date(full.data\$Date,format='%d/%m/%Y'))
full.data\$date = as.Date(full.data\$time, origin = "1970-01-01")

full.data\$Division = "Premier League"
full.data\$Division[full.data\$Div=="E1"] = "Championship"
full.data\$Division[full.data\$Div=="E2"] = "League 1"
full.data\$Division[full.data\$Div=="E3"] = "League 2"
full.data\$Division[full.data\$Div=="EC"] = "Conference"

full.data\$Division = factor(full.data\$Division, levels = c("Premier League", "Championship", "League 1",
"League 2","Conference"))

ggplot(full.data, aes(date, bookieres, colour=Division)) +
stat_smooth(size = 1.25, alpha = 0.2) +
labs(x = "Year", y = "Uncertainty") +
theme_bw() +
theme(legend.position="bottom") +
theme(axis.text=element_text(size=20),
axis.title=element_text(size=20),
legend.title = element_text(size=20),
legend.text = element_text(size=20))
```

# Coal and the Conservatives

Interesting election results in the UK over the weekend, where the Conservatives romped to victory. This was despite a widespread consensus that neither the Conservative or Labour party would get a majority. This was a triumph for uncertainty and random error over the deterministic, as none of the statistical forecasts appeared to deem such a decisive victory probable. The UK election is a lot harder to model, for numerous reasons, when compared to the US.

This means that a lot of pollsters and political forecasters will have to go back to the drawing board and re-evaluate their methods. Obviously, the models used to forecast the 2015 election could not handle the dynamics of the British electorate. However, there is a high degree of persistence within electuary constituencies. Let’s explore this persistence by looking at the relationship between coal and % Conservative (Tory) votes.

Following a tweet by Vaughan Roderick and using the methodology of Fernihough and O’Rourke (2014), I matched each of the constituencies to Britain’s coalfields creating a “proximity to coal” measure. What the plot below shows is striking. Being located on or in close proximity to a coal field reduces the tory vote share by about 20%. When we control (linearly) for latitude and longitude coordinates, this association decreases in strength, but not by much. For me, this plot highlights a long-standing relationship between Britain’s industrial revolution, the urban working class, and labour/union movement. What I find interesting is that this relationship has persisted despite de-industrialization and the movement away from large-scale manufacturing industry.

```> summary(lm(tory~coal,city))

Call:
lm(formula = tory ~ coal, data = city)

Residuals:
Min      1Q  Median      3Q     Max
-42.507 -10.494   2.242  10.781  29.074

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)  42.9492     0.7459   57.58   <2e-16 ***
coal        -24.9704     1.8887  -13.22   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 14.36 on 630 degrees of freedom
Multiple R-squared:  0.2172,	Adjusted R-squared:  0.216
F-statistic: 174.8 on 1 and 630 DF,  p-value: < 2.2e-16

# robust to lat-long?
> summary(lm(tory~coal+longitude+latitude,city))

Call:
lm(formula = tory ~ coal + longitude + latitude, data = city)

Residuals:
Min      1Q  Median      3Q     Max
-44.495  -8.269   1.485   9.316  28.911

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 246.4355    18.9430  13.009  < 2e-16 ***
coal        -15.1616     1.8697  -8.109 2.68e-15 ***
longitude     1.4023     0.4015   3.493 0.000512 ***
latitude     -3.8621     0.3651 -10.578  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 12.76 on 628 degrees of freedom
Multiple R-squared:  0.3838,	Adjusted R-squared:  0.3809
F-statistic: 130.4 on 3 and 628 DF,  p-value: < 2.2e-16

```