Improving the Premier League Simulator

I recently built a quick from-scratch Premier League season simulator. For the game simulator, I simply took the Squad’s average goals in the season and fed that into a Poisson model generator (rpois in R) and ran against the opposing squad’s simulated distribution. This is OK, but it doesn’t take into account a few things : home/away splits, strength of defense, or noise in the data.

Home/away is easy enough to grab. We have goals allowed. Noise can be reduced by using Expected Goals (xG) instead of Goals. My biggest challenge was how to capture the interaction between Goals and opposing defense. I eventually found a really helpful article that used the following methodology:

For the home team, calc their average home xG and divide by league average xG.
Then calculate the opposition average home Expected Goals Allowed (xGA) and divide by league average.
Multiply these two numbers together, then multiply by league average home xG.

For example, let’s look at Man City’s match against Sheffield United. City went into the game with a home xG of 1.78, which is 1.03 from league average of 1.73. Sheffield United had an away xGA of 1.29, which of 1.05 from league average of 1.23. So we get 1.03 * 1.05 * 1.73, or 1.87 xG for City. It’s a relatively small adjustment, but worth the trouble.

Note these are done using 12 week exponential moving averages (another concept I took from the article linked above). This is in Premier League / Champions league only, and uses the most recent data to forecast the rest of the season. The idea being that we can capture change in team performance without giving up too much historical data. At some point it’d be nice to update the model to adjust the moving average after each simulated match, but I’m saving that for another day.

OK, I made all this effort, how well does it work? We’ll calculate each match’s Brier scores., using matchweeks 18 and 19 for testing. The total is simply the average of the Brier for Win, Draw, and Loss.

Show the code

library(gt)
library(gtExtras)
library(hrbrthemes)
library(patchwork) 
library(pracma)
library(plotly)
library(rvest)
library(tidyverse)
library(worldfootballR)

#https://beatthebookie.blog/2021/06/07/the-predictive-power-of-xg/

#set seed for reproducibility
set.seed(20231228)

#use this to for the season end year
#makes it easier to update stuff later
season_end <- 2024
ema_duration <- 12

#how many seasons we want to simulate
number_of_sims <- 20000

#rather than use a case statement over and over, just make this a function
calculate_points <- function(a, b){
  case_when(a > b ~ 3,
            a == b ~ 1,
            a > b ~ 0,
            TRUE ~ 0)
}

#fetch current table using the worldfootballr package
prem_2024_table <- fb_season_team_stats(country = "ENG", 
                                        gender = "M", 
                                        season_end_year = "2024", 
                                        tier = "1st", 
                                        stat_type = "league_table")

pl_table <- prem_2024_table %>%
  select(Squad, MP, Pts, W, D, L, GF, GA, GD, xG, xGA, Rk) %>%
  rename(Points = Pts,
         Goals = GF,
         Goals_Allowed = GA,
         Rank = Rk,
         Goal_Dif = GD,
         xG_Allowed = xGA)

#get match results for current season and prior season
#also grab champions league so we have something for clubs that got promoted
match_pl_cs <- fb_match_results(country = "ENG", 
                 gender = "M",
                 season_end_year = season_end,
                 tier = "1st")

match_pl_ps <- fb_match_results(country = "ENG", 
                       gender = "M",
                       season_end_year = season_end - 1,
                       tier = "1st")

match_efl_ps <- fb_match_results(country = "ENG", 
                       gender = "M",
                       season_end_year = season_end - 1,
                       tier = "2nd")

#set aside unplayed matches for later
pl_future_matches <- match_pl_cs %>%
  filter(is.na(HomeGoals) | Notes == 'Match Suspended') %>%
  select(-MatchURL) %>%
  as_tibble()

#get max date with a game
Max_Date <- match_pl_cs  %>%
  filter(!is.na(HomeGoals)) %>%
  summarise(Max_Date = max(Date)) %>%
  pull()

#get home/away goals for the league using moving average
leaguge_exp <- match_pl_ps %>%
  rbind(match_pl_cs) %>%
  rbind(match_efl_ps) %>%
  mutate(Wk = as.numeric(Wk)) %>%
  group_by(Competition_Name, Season_End_Year, Wk) %>%
  summarise(mean_Home_xG = mean(Home_xG, na.rm = TRUE),
            mean_Away_xG = mean(Away_xG, na.rm = TRUE),
            d = min(Date)) %>%
  arrange(d) %>%
  group_by(Competition_Name) %>%
  mutate(lg_ema_Home_xG = movavg(mean_Home_xG, n = ema_duration, type = 'e'),
         lg_ema_Away_xG = movavg(mean_Away_xG, n = ema_duration, type = 'e')
         ) %>%
  select(-mean_Home_xG, -mean_Away_xG, -d)

#get club expected goals relative to league average for both home and away
#using a expoential moving average for each, i.e. compared to league over 
#last n matches, how good/bad are they at scoring and preventing goals
club_xg_ema <- match_pl_ps %>%
  rbind(match_pl_cs) %>%
  rbind(match_efl_ps) %>%
  mutate(Wk = as.numeric(Wk)) %>%
  select(Competition_Name, Season_End_Year, Wk, Home, Away, Home_xG, Away_xG) %>%
  gather(key = Location, value = Squad, Home, Away) %>%
  filter(!is.na(Home_xG)) %>%
  filter(!(Season_End_Year == 2024 & Wk == 20)) %>%
  mutate(xG =  case_when(Location == 'Home' ~ Home_xG, TRUE ~ Away_xG),
         xGA =  case_when(Location == 'Home' ~ Away_xG , TRUE ~ Home_xG)) %>%
  select(-Home_xG, -Away_xG) %>%
  arrange(Squad, Season_End_Year, Wk) %>%
  group_by(Squad, Location) %>%
  mutate(ema_xG = movavg(xG, n = ema_duration, type = 'e'),
         ema_xGA = movavg(xGA, n = ema_duration, type = 'e')) %>%
  inner_join(leaguge_exp) %>%
  mutate(rel_xG = case_when(Location == 'Home' ~ ema_xG / lg_ema_Home_xG,
                            TRUE ~ ema_xG / lg_ema_Away_xG),
         rel_xGa = case_when(Location == 'Home' ~ ema_xGA / lg_ema_Away_xG,
                            TRUE ~ ema_xGA / lg_ema_Home_xG)) %>%
  group_by(Squad, Location) %>%
  filter(Season_End_Year == season_end) %>%
  filter(Wk == max(Wk)) %>%
  select(Wk, Squad, lg_ema_Home_xG, lg_ema_Away_xG, rel_xG, rel_xGa)

sim_games3 <- function(home, away){
  n_sims <- number_of_sims
  
  home_table <- club_xg_ema %>%
    filter(Squad == home & Location == 'Home')
  
  away_table <- club_xg_ema %>%
    filter(Squad == away & Location == 'Away')
  
  home_exp <- (home_table$rel_xG  * away_table$rel_xGa) * home_table$lg_ema_Home_xG
  away_exp <- (away_table$rel_xG  * home_table$rel_xGa) * away_table$lg_ema_Home_xG
  
  home_goals <- rpois(n_sims, home_exp)
  away_goals<- rpois(n_sims, away_exp)
  
  results <- cbind(home_goals, away_goals) %>%
    as_tibble %>%
    mutate(goal_dif = home_goals - away_goals,
           home_points = calculate_points(home_goals, away_goals),
           away_points = calculate_points(away_goals, home_goals),
           sim_num = row_number()) %>%
    relocate(sim_num)
  
  results  
}

#old version of simmer just in case
sim_games <- function(home_goals, away_goals){
  n_sims <- number_of_sims
  home_goals <- rpois(n_sims, home_goals)
  away_goals<- rpois(n_sims, away_goals)
  
  results <- cbind(home_goals, away_goals) %>%
    as_tibble %>%
    mutate(goal_dif = home_goals - away_goals,
           home_points = calculate_points(home_goals, away_goals),
           away_points = calculate_points(away_goals, home_goals),
           sim_num = row_number()) %>%
    relocate(sim_num)
  
  results  
}

sim_new <- match_pl_cs %>%
  filter(Wk %in% c(18, 19) & !is.na(HomeGoals)) %>%
  select(Wk, Date, Home, Away, HomeGoals, AwayGoals) %>%
  inner_join(pl_table %>% select(Squad, Goals, xG, MP) %>% rename(Home_Goals = Goals, Home_xG = xG, Home_MP = MP), join_by(Home == Squad)) %>%
  inner_join(pl_table %>% select(Squad, Goals, xG, MP) %>% rename(Away_Goals = Goals, Away_xG = xG, Away_MP = MP), join_by(Away == Squad)) %>%
  mutate(Home_G_per_Match = Home_Goals / Home_MP,
         Away_G_per_Match = Away_Goals / Away_MP) %>%
  mutate(simmed_games = map2(Home, Away, ~sim_games3(.x, .y))) %>%
  unnest(simmed_games)

sim_agg_with_brier <- sim_new %>%
  mutate(W = case_when(HomeGoals > AwayGoals ~ 1, TRUE ~ 0),
         D = case_when(HomeGoals == AwayGoals ~ 1, TRUE ~ 0),
         L = case_when(HomeGoals < AwayGoals ~ 1, TRUE ~ 0)) %>%
  mutate(W_sim = case_when(home_goals > away_goals ~ 1, TRUE ~ 0),
         D_sim = case_when(home_goals == away_goals ~ 1, TRUE ~ 0),
         L_sim = case_when(home_goals < away_goals ~ 1, TRUE ~ 0)) %>%
  group_by(Wk, Home, Away) %>%
  summarise(W = mean(W),
            D = mean(D),
            L = mean(L),
            HomeGoals = mean(HomeGoals),
            AwayGoals = mean(AwayGoals),
            W_sim = mean(W_sim),
            D_sim = mean(D_sim),
            L_sim = mean(L_sim)) %>%
  mutate(Brier_W = case_when(W == 1 ~ (W_sim - 1)^2, TRUE ~ W_sim ^ 2),
         Brier_D = case_when(D == 1 ~ (D_sim - 1)^2, TRUE ~ D_sim ^ 2),
         Brier_L = case_when(L == 1 ~ (L_sim - 1)^2, TRUE ~ L_sim ^ 2),
         Brier_T = (Brier_W + Brier_D + Brier_L) / 3
  )

bw <- sim_agg_with_brier %>%
  ggplot(aes(x = Brier_W))+
  geom_density()+
  geom_rug()+
  theme_ipsum()+
  labs(title = 'Brier Win')+
  xlim(0, 0.85)

bd <- sim_agg_with_brier %>%
  ggplot(aes(x = Brier_D))+
  geom_density()+
  geom_rug()+
  theme_ipsum()+
  labs(title = 'Brier Draw')+
  xlim(0, 0.85)

bl <- sim_agg_with_brier %>%
  ggplot(aes(x = Brier_L))+
  geom_density()+
  geom_rug()+
  theme_ipsum()+
  labs(title = 'Brier Loss')+
  xlim(0, 0.85)

bt <- sim_agg_with_brier %>%
  ggplot(aes(x = Brier_T))+
  geom_density()+
  geom_rug()+
  theme_ipsum()+
  labs(title = 'Brier Total')+
  xlim(0, 0.85)

(bw | bd) / (bl | bt)

This isn’t bad - the average sits around 0.35, so we’re better than a coin toss. It’s doing suspiciously well on draws, while win and loss only look OK. Let’s compare our average prediction for each outcome with the average outcomes overall.

Show the code

sim_agg_with_brier %>%
  ungroup() %>%
  summarise_if(is.numeric, mean, na.rm = TRUE) %>%
  select(-HomeGoals, -AwayGoals,) %>%
  pivot_longer(everything(), names_to = 'type', values_to = 'value') %>%
  mutate(Class = case_when(grepl('_sim', type) ~ 'Sim', 
                           grepl('Brier_', type) ~ 'Brier',
                           TRUE ~ 'Actual'),
         type = str_replace(type, '_sim', ''),
         type = str_replace(type, 'Brier_', ''),
         type = ifelse(type == 'T', 'Total', type)) %>%
  pivot_wider(names_from = 'Class', values_from = 'value') %>%
  gt() %>%
  gt_theme_espn() %>%
  fmt_percent(columns = c(Actual, Sim), decimals = 1) %>%
  fmt_number(columns = c(Brier), decimals = 2) %>%
  sub_missing(columns = everything(),
              rows = everything(),
              missing_text = "-")

type	Actual	Sim	Brier
W	42.1%	37.8%	0.31
D	15.8%	20.7%	0.13
L	42.1%	41.6%	0.29
Total	-	-	0.24

Not too shabby, with an overall Brier score of 0.24. We’d like it to be closer, it overestimated draws and underestimated wins in our test data. Where is it missing? Let’s check our top 10 Brier scores. Win/loss perspectives are from the home team’s perspective.

Show the code

sim_agg_with_brier %>%
  ungroup() %>%
  arrange(desc(Brier_T)) %>%
  top_n(10) %>%
  gt() %>%
  gt_theme_espn() %>%
  fmt_percent(columns = c(W_sim, D_sim, L_sim), decimals = 1) %>%
  fmt_number(columns = c(Brier_W, Brier_D, Brier_L, Brier_T), decimals = 2) %>%
  cols_label(HomeGoals = 'Home Goals',
             AwayGoals = 'Away Goals')

Wk	Home	Away	W	D	L	Home Goals	Away Goals	W_sim	D_sim	L_sim	Brier_W	Brier_D	Brier_L	Brier_T
19	Arsenal	West Ham	0	0	1	0	2	67.5%	17.1%	15.4%	0.46	0.03	0.72	0.40
18	Wolves	Chelsea	1	0	0	2	1	16.2%	16.9%	66.9%	0.70	0.03	0.45	0.39
19	Newcastle Utd	Nott'ham Forest	0	0	1	1	3	64.8%	17.0%	18.2%	0.42	0.03	0.67	0.37
18	Luton Town	Newcastle Utd	1	0	0	1	0	18.3%	17.2%	64.5%	0.67	0.03	0.42	0.37
18	Aston Villa	Sheffield Utd	0	1	0	1	1	63.1%	22.0%	14.8%	0.40	0.61	0.02	0.34
18	Crystal Palace	Brighton	0	1	0	1	1	27.1%	23.2%	49.7%	0.07	0.59	0.25	0.30
18	Fulham	Burnley	0	0	1	0	2	50.4%	24.9%	24.7%	0.25	0.06	0.57	0.29
18	Liverpool	Arsenal	0	1	0	1	1	32.2%	25.1%	42.7%	0.10	0.56	0.18	0.28
18	Tottenham	Everton	1	0	0	2	1	28.0%	19.2%	52.9%	0.52	0.04	0.28	0.28
19	Sheffield Utd	Luton Town	0	0	1	2	3	48.5%	23.9%	27.6%	0.24	0.06	0.52	0.27

Our highest score comes from Arsenal vs. West Ham. The model pegged the Gunners with a 67.4% chance of winning and a 17.3% chance of losing, leaving West Ham with a mere 15.3% win probability. They won it 0-2, while the xG was 2.7 to 1.4 suggests it was a tough loss it was nonetheless a loss. (It was a great game to watch, too - both squads played very well.) I think we’d all have been suspicious of a model that heavily favored West Ham going in - if anything, 15.3% was too high a win probability for them - so we won’t worry about this match.

Going down the list, most of these are upsets. I like the Wolves and all, but wouldn’t pick them to beat Chelsea (even considering how lousy Chelsea’s been lately), yet here we go. Nottingham Forest* beating Newcastle was another great game to watch, and yet again an upset.

*Caveat: Nottingham is quickly becoming my favorite underdog squad. Just a lot of fun to watch.

What about the cases where the model did well?

Show the code

sim_agg_with_brier %>%
  ungroup() %>%
  arrange((Brier_T)) %>%
  top_n(10, -Brier_T) %>%
  gt() %>%
  gt_theme_espn() %>%
  fmt_percent(columns = c(W_sim, D_sim, L_sim), decimals = 1) %>%
  fmt_number(columns = c(Brier_W, Brier_D, Brier_L, Brier_T), decimals = 2) %>%
  cols_label(HomeGoals = 'Home Goals',
             AwayGoals = 'Away Goals')

Wk	Home	Away	W	L	Home Goals	Away Goals	W_sim	D_sim	L_sim	Brier_W	Brier_D	Brier_L	Brier_T
19	Everton	Manchester City	0	1	1	3	11.6%	14.7%	73.8%	0.01	0.02	0.07	0.03
19	Burnley	Liverpool	0	1	0	2	15.7%	19.7%	64.6%	0.02	0.04	0.13	0.06
18	Nott'ham Forest	Bournemouth	0	1	2	3	17.5%	20.3%	62.2%	0.03	0.04	0.14	0.07
19	Bournemouth	Fulham	1	0	3	0	54.2%	23.9%	21.8%	0.21	0.06	0.05	0.10
19	Chelsea	Crystal Palace	1	0	2	1	47.1%	22.2%	30.6%	0.28	0.05	0.09	0.14
19	Brighton	Tottenham	1	0	4	2	46.4%	19.0%	34.7%	0.29	0.04	0.12	0.15
19	Brentford	Wolves	0	1	1	4	45.3%	21.0%	33.7%	0.21	0.04	0.44	0.23
18	West Ham	Manchester Utd	1	0	2	0	32.8%	23.8%	43.4%	0.45	0.06	0.19	0.23
19	Manchester Utd	Aston Villa	1	0	3	2	30.8%	21.4%	47.8%	0.48	0.05	0.23	0.25
19	Sheffield Utd	Luton Town	0	1	2	3	48.5%	23.9%	27.6%	0.24	0.06	0.52	0.27

The model thought City had a 73.5% chance of beating Everton, and guess what City did? Most of these are really good clubs beating up weaker clubs, though there are also some mid-table clubs in there as well.

The chief thing here is that the model is being perhaps too conservative. City’s odds for winning against Everton were surely higher. (Yeah, the Brier for their win was 0.07, but if it’d given 80% odds the score would’ve been 0.04, a 43% improvement.) As a rule, the higher the odds, the lower the Brier score when you’re right. So that’s definitely something to look tweaking going forward. For now, it’ll do.

With this done, we can update the projected table for the rest of the season.

Show the code

pl_simmed <- pl_future_matches %>%
  select(Wk, Date, Home, Away) %>%
  inner_join(pl_table %>% select(Squad, Goals, xG, MP) %>% rename(Home_Goals = Goals, Home_xG = xG, Home_MP = MP), join_by(Home == Squad)) %>%
  inner_join(pl_table %>% select(Squad, Goals, xG, MP) %>% rename(Away_Goals = Goals, Away_xG = xG, Away_MP = MP), join_by(Away == Squad)) %>%
  mutate(Home_G_per_Match = Home_Goals / Home_MP,
         Away_G_per_Match = Away_Goals / Away_MP) %>%
  mutate(simmed_games = map2(Home, Away, ~sim_games3(.x, .y)))

#unnest our sims, split into home and away
pl_simmed_long <- pl_simmed %>%
  select(Wk, Date, Home, Away, simmed_games) %>%
  unnest(simmed_games)

pl_simmed_home <- pl_simmed_long %>%
  select(sim_num, Home, home_points, home_goals,  away_goals) %>%
  rename(Squad = Home,
         Goals = home_goals,
         Goals_Allowed = away_goals,
         Points = home_points
  ) %>%
  mutate(W = case_when(Goals > Goals_Allowed ~ 1, TRUE ~ 0),
         D = case_when(Goals == Goals_Allowed ~ 1, TRUE ~ 0),
         L = case_when(Goals < Goals_Allowed ~ 1, TRUE ~ 0))

pl_simmed_away <- pl_simmed_long %>%
  select(sim_num, Away, away_points, away_goals, home_goals) %>%
  rename(Squad = Away,
         Goals = away_goals,
         Goals_Allowed = home_goals,
         Points = away_points
  ) %>%
  mutate(W = case_when(Goals > Goals_Allowed ~ 1, TRUE ~ 0),
         D = case_when(Goals == Goals_Allowed ~ 1, TRUE ~ 0),
         L = case_when(Goals < Goals_Allowed ~ 1, TRUE ~ 0))

#we need actual in the data as well, so we repliate the table 
#to match our number of sims
table_rep <- seq(1:number_of_sims) %>%
  as_tibble() %>%
  rename(sim_num = value) %>%
  crossing(pl_table %>% select(Squad, Points, Goals, Goals_Allowed, W, D, L))

#take all of our sims and summarize. Note this includes the sim number if we want to play with that
pl_aggregated <- pl_simmed_home %>%
  rbind(pl_simmed_away) %>%
  rbind(table_rep) %>%
  group_by(sim_num, Squad) %>%
  summarise_if(is.numeric, sum, na.rm = TRUE) %>%
  mutate(Goal_Dif = Goals - Goals_Allowed) %>%
  group_by(sim_num) %>%
  arrange(desc(Points), desc(Goal_Dif)) %>%
  mutate(Rank = rank(desc(Points), ties.method="first"),
         win_PL = case_when(Rank == 1 ~ 1, TRUE ~ 0),
         qualify_UCL = case_when(Rank <= 4 ~ 1, TRUE ~ 0),
         relgated = case_when(Rank >= 18 ~ 1, TRUE ~ 0))

pl_team <- pl_aggregated %>%
  ungroup() %>%
  select(-sim_num, -Rank) %>%
  group_by(Squad) %>%
  summarise_if(is.numeric, mean, na.rm = TRUE) %>%
  arrange(desc(Points))

pl_sim_table <- pl_table %>%
  inner_join(pl_team, by = join_by(Squad)) %>%
  select(-xG, -xG_Allowed) %>%
  arrange(desc(win_PL), relgated) 

pl_sim_table %>%
  gt() %>%
  gt_theme_espn() %>%
  tab_spanner(
    label = "Current Table",
    columns = c("MP", "Points.x", "Goals.x", "Goals_Allowed.x", "Goal_Dif.x", "Rank", "W.x", "D.x", "L.x")
  ) %>%
  tab_spanner(
    label = "Projected",
    columns = c("Points.y", "Goals.y", "Goals_Allowed.y", "Goal_Dif.y", "win_PL", "qualify_UCL", "relgated", "W.y", "D.y", "L.y")
  ) %>%
  gt_add_divider(columns = "Rank", style = "solid", color = 'lightgrey') %>%
  data_color(
    columns = c("win_PL", "qualify_UCL", "relgated"),
    method = "numeric",
    palette = c('#00ff85', '#ffffff'),
    #omain = c(0.01, 1),
    na_color = "white",
    reverse = TRUE
  ) %>%
  fmt_percent(columns = c("win_PL", "qualify_UCL", "relgated"), decimals = 1) %>%
  fmt_number(columns = c("Points.y", "Goals.y", "Goals_Allowed.y", "Goal_Dif.y",
                         "W.y", "D.y", "L.y"), decimals = 1) %>%
  cols_width(win_PL ~ px(95),
             qualify_UCL ~ px(95),
             relgated ~ px(95)) %>%
  cols_label(
    Points.x = "Points",
    Goals.x = "G",
    Goals_Allowed.x = "GA",
    Goal_Dif.x = "GD",
    W.x = "W",
    D.x = "D",
    L.x = "L",
    Points.y = "Points",
    Goals.y = "G",
    Goals_Allowed.y = "GA",
    Goal_Dif.y = "GD",
    win_PL = 'Win PL',
    qualify_UCL = 'Qualify UCL',
    relgated = 'Relegated',
    W.y = "W",
    D.y = "D",
    L.y = "L",
  ) %>%
  tab_header(title = 'Premier League Projected Standings',
             subtitle = paste('Using data from matches played through ', Max_Date)) %>%
  tab_footnote('Table data courtesy of fbref.com') %>%
  tab_style(
    style = cell_text(align = "center"),
    locations = cells_column_labels()) %>%
  cols_hide(columns = c(W.x, D.x, L.x, W.y, D.y, L.y))

Squad	Current Table						Projected
Premier League Projected Standings
Using data from matches played through 2024-01-02
Squad	MP	Points	G	GA	GD	Rank	Points	G	GA	GD	Win PL	Qualify UCL	Relegated
Liverpool	20	45	43	18	25	1	79.4	81.7	41.0	40.6	43.7%	99.0%	0.0%
Manchester City	19	40	45	21	24	3	77.2	87.0	43.9	43.2	28.1%	97.3%	0.0%
Arsenal	20	40	37	20	17	4	77.0	75.4	38.7	36.7	24.1%	97.4%	0.0%
Aston Villa	20	42	43	27	16	2	70.9	75.1	52.7	22.3	4.0%	78.9%	0.0%
Tottenham	20	39	42	29	13	5	61.4	75.3	68.1	7.2	0.0%	10.1%	0.0%
Newcastle Utd	20	29	39	29	10	9	59.7	79.9	60.2	19.7	0.0%	7.2%	0.0%
Chelsea	20	28	34	31	3	10	57.9	73.1	61.9	11.3	0.0%	4.0%	0.0%
Brighton	20	31	38	33	5	7	57.3	72.9	66.1	6.8	0.0%	2.9%	0.0%
West Ham	20	34	33	30	3	6	56.3	61.4	63.3	−1.9	0.0%	1.8%	0.0%
Manchester Utd	20	31	22	27	-5	8	55.1	53.2	60.0	−6.8	0.0%	1.1%	0.0%
Bournemouth	19	25	28	35	-7	12	51.3	58.3	65.6	−7.3	0.0%	0.2%	0.2%
Brentford	19	19	26	31	-5	16	48.6	61.0	61.3	−0.3	0.0%	0.1%	0.5%
Wolves	20	28	30	31	-1	11	47.1	55.4	66.9	−11.5	0.0%	0.0%	0.9%
Crystal Palace	20	21	22	29	-7	14	44.1	48.6	58.8	−10.3	0.0%	0.0%	3.7%
Fulham	20	24	28	35	-7	13	43.7	52.5	68.3	−15.8	0.0%	0.0%	4.5%
Everton	20	16	24	28	-4	17	39.9	53.6	59.6	−6.0	0.0%	0.0%	13.5%
Nott'ham Forest	20	20	24	35	-11	15	40.1	51.3	71.3	−20.0	0.0%	0.0%	14.2%
Burnley	20	11	20	41	-21	19	30.5	40.8	69.8	−29.1	0.0%	0.0%	82.9%
Luton Town	19	15	23	37	-14	18	30.7	43.3	75.8	−32.5	0.0%	0.0%	83.8%
Sheffield Utd	20	9	15	49	-34	20	26.5	36.4	82.8	−46.4	0.0%	0.0%	95.7%
Table data courtesy of fbref.com

Liverpool is sitting pretty nice right now, with City and Arsenal in contention. Liverpool also just beat Newcastle 4-2, with an xG line of 7-0.6 (!), so their numbers are a bit inflated right now.

The takeaway here is that bootstrapping is relatively trivial, but making sure that what you’re bootstrapping is solid is a lot more difficult. Soccer has a fair amount on unpredictability which should adjust our expectations, but that doesn’t mean there’s no room for improvement.