Different winners under different criteria

A few posts ago (see here), I noted that there was a group of 7 teams in the English Premier League (EPL) that seem to be a cut above the rest:

  • Arsenal
  • Chelsea
  • Everton
  • Liverpool
  • Manchester City
  • Manchester United
  • Tottenham Hotspur

The team logos. (Photo credit: kadanewsmag.com.ng)

Who is the best among these 7 teams? In thinking about this question I realized that there are so many measures of what is best. So, instead of trying to figure out who is best (and get caught in between raging fans), I challenged myself to do the following: For each of the 7 teams, can I find a metric of success for which they are the best? Here, I am limiting myself to metrics that can be derived from just ranking and points.

tl;dr: I couldn’t find one for Everton, and the one I found for Liverpool is rather forced. Can you find measures against which Liverpool or Everton come out tops?

Code snippets used to obtain figures in this post are provided; the full R script can be found here.

Here is a glimpse at the data we are using (named under the variable standings):

Most championships in last 10 years: Chelsea, Man C, Man U (3)

 
standings %>% filter(Rank == 1) %>%
    group_by(Club) %>%
    summarize(Champions = n()) %>%
    arrange(desc(Champions))

Most top 3 finishes in last 10 years: Chelsea, Man C (7), Man U (6)

 
standings %>% filter(Rank <= 3) %>%
    group_by(Club) %>%
    summarize(`Top 3` = n()) %>%
    arrange(desc(`Top 3`))

Most top 5 finishes in last 10 years: Arsenal, Man C (9),Chelsea, Man U, Tottenham (8)

 
standings %>% filter(Rank <= 5) %>%
    group_by(Club) %>%
    summarize(`Top 5` = n()) %>%
    arrange(desc(`Top 5`))

Most points in last 10 years: Man U (783), Man C (764), Chelsea (762)

 
standings %>% group_by(Club) %>%
    summarize(`Total Points` = sum(Points)) %>%
    arrange(desc(`Total Points`))
 

Best median rank in last 10 years: Man U (2), Man C (2.5), Chelsea (3)

 
standings %>% 
    group_by(Club) %>%
    summarize(`Median Rank` = median(Rank)) %>%
    arrange(`Median Rank`)
 

Best median rank in last 5 years: Man C (2), Chelsea (3), Tottenham (3)

 
standings %>% 
    group_by(Club) %>% filter(Season >= 2013) %>%
    summarize(`Median Rank` = median(Rank)) %>%
    arrange(`Median Rank`)
 

Best worst rank in last 10 years: Arsenal (6), Man U (7), Liverpool (8), Tottenham (8)

 
standings %>% 
    group_by(Club) %>%
    summarize(`Worst Rank` = max(Rank)) %>%
    arrange(`Worst Rank`)
 

Best worst rank in last 3 years: Tottenham (3), Man C (4), Arsenal (6), Man U (6)

 
standings %>% filter(Season >= 2015) %>%
    group_by(Club) %>%
    summarize(`Worst Rank` = max(Rank)) %>%
    arrange(`Worst Rank`)
 

Most consistent ranking by standard deviation: Arsenal (1.14), Tottenham (1.72), Everton (2.12)

 
standings %>% 
    filter(Club %in% c("Arsenal", "Chelsea", "Everton", 
                       "Liverpool", "Manchester United", 
                       "Manchester City", "Tottenham Hotspur")) %>%
    group_by(Club) %>%
    summarize(sd = sd(Rank)) %>%
    arrange(sd)
 

Most consistent ranking by linear regression coefficient: Liverpool (-0.024), Arsenal (0.133), Chelsea (0.261)

 
standings %>% 
    filter(Club %in% c("Arsenal", "Chelsea", "Everton", 
                       "Liverpool", "Manchester United", 
                       "Manchester City", "Tottenham Hotspur")) %>%
    group_by(Club) %>%
    summarize(beta = lm(Rank ~ Season)$coefficients[2]) %>%
    arrange(abs(beta))
 

Most improved team in last 5 years by linear regression coefficient: Tottenham (-0.9), Man U (-0.8), Man C (0.1)

 
standings %>% filter(Season >= 2013) %>%
    filter(Club %in% c("Arsenal", "Chelsea", "Everton", 
                       "Liverpool", "Manchester United", 
                       "Manchester City", "Tottenham Hotspur")) %>%
    group_by(Club) %>%
    summarize(beta = lm(Rank ~ Season)$coefficients[2]) %>%
    arrange(beta)
 

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