Haven't got much time these days, but I think it's about time to deliver a new post.
Inspired by an article from the homepage of my absolute favourite soccer magazine http://www.offside.org/de-tre-redaktorerna/2012/snallast-vinner-ibland?page=2 (Swedish), I decided to investigate the relationship between number of cards and league position. The article doesn't state any historical relationship, but gives concrete examples from last season, which indicates that the pattern could differ between leagues.
Once again I have looked at my favourite league, the English Premier League. I have collected cards data (yellow + red) for the last 17 seasons (1995-2012) from www.statbunker.com. The graphical representation of cards against league position is following:
Below you see the average number of cards for each league position.
The best linear fit is shown in the figures. The confidence interval for the position coefficient is (0.2305, 0.6669), which clearly rejects the hypothesis of no relation between position and number of cards. The assumptions of the linear model is verified by graphical inspection of the residuals, which indicates that the distribution of number of cards for each league position is approximately normal and has same variance.
The conclusion is that there exist a linear relation between league position and number of cards given in the English Premier League, and on seasonal average, bottom teams receive more cards than top teams.
But how about the distribution of cards between teams? Is there significant differences between teams?
43 teams has taken part in the English Premier League between 1995 and 2012. 30 of these 43 teams has played 3 or more seasons in the period, and they are represented in below figure.
If you find the details interesting, feel free to look into the team data below. Notice that among the earlier big four, that Chelsea and Arsenal on average have received 10-15 more cards per season than Liverpool and Manchester United.
The seasonal card distribution clearly differ from team to team as we see from the averages, and a boxplot of the two extreme observations makes it clear that there are differences between (at least) some of the teams.
Inspired by an article from the homepage of my absolute favourite soccer magazine http://www.offside.org/de-tre-redaktorerna/2012/snallast-vinner-ibland?page=2 (Swedish), I decided to investigate the relationship between number of cards and league position. The article doesn't state any historical relationship, but gives concrete examples from last season, which indicates that the pattern could differ between leagues.
Once again I have looked at my favourite league, the English Premier League. I have collected cards data (yellow + red) for the last 17 seasons (1995-2012) from www.statbunker.com. The graphical representation of cards against league position is following:
Below you see the average number of cards for each league position.
The best linear fit is shown in the figures. The confidence interval for the position coefficient is (0.2305, 0.6669), which clearly rejects the hypothesis of no relation between position and number of cards. The assumptions of the linear model is verified by graphical inspection of the residuals, which indicates that the distribution of number of cards for each league position is approximately normal and has same variance.
The conclusion is that there exist a linear relation between league position and number of cards given in the English Premier League, and on seasonal average, bottom teams receive more cards than top teams.
But how about the distribution of cards between teams? Is there significant differences between teams?
43 teams has taken part in the English Premier League between 1995 and 2012. 30 of these 43 teams has played 3 or more seasons in the period, and they are represented in below figure.
If you find the details interesting, feel free to look into the team data below. Notice that among the earlier big four, that Chelsea and Arsenal on average have received 10-15 more cards per season than Liverpool and Manchester United.
| Team | Cards/S | Seasons |
| Arsenal | 64,82 | 17 |
| Aston Villa | 58,47 | 17 |
| Chelsea | 67,06 | 17 |
| Everton | 65,18 | 17 |
| Liverpool | 52,88 | 17 |
| Manchester United | 55,47 | 17 |
| Tottenham Hotspur | 58,88 | 17 |
| Newcastle United | 59,63 | 16 |
| Blackburn Rovers | 72,80 | 15 |
| West Ham United | 69,86 | 14 |
| Bolton Wanderers | 68,92 | 13 |
| Middlesbrough | 69,31 | 13 |
| Manchester City | 61,58 | 12 |
| Fulham | 56,82 | 11 |
| Sunderland | 70,45 | 11 |
| Southampton | 59,10 | 10 |
| Leeds United | 76,22 | 9 |
| Charlton Athletic | 53,00 | 8 |
| Birmingham City | 65,29 | 7 |
| Derby County | 77,57 | 7 |
| Leicester City | 58,43 | 7 |
| Portsmouth | 61,43 | 7 |
| Wigan Athletic | 67,71 | 7 |
| Coventry City | 67,33 | 6 |
| West Bromwich Albion | 54,00 | 6 |
| Sheffield Wednesday | 51,20 | 5 |
| Wimbledon | 53,00 | 5 |
| Stoke City | 70,00 | 4 |
| Wolverhampton Wanderers | 67,50 | 4 |
| Nottingham Forest | 69,00 | 3 |
| Bradford City | 55,00 | 2 |
| Crystal Palace | 65,50 | 2 |
| Hull City | 72,00 | 2 |
| Ipswich Town | 38,50 | 2 |
| Norwich City | 48,50 | 2 |
| Queens Park Rangers | 73,50 | 2 |
| Reading | 52,50 | 2 |
| Watford | 60,00 | 2 |
| Barnsley | 73,00 | 1 |
| Blackpool | 49,00 | 1 |
| Burnley | 58,00 | 1 |
| Sheffield United | 70,00 | 1 |
| Swansea City | 43,00 | 1 |
The seasonal card distribution clearly differ from team to team as we see from the averages, and a boxplot of the two extreme observations makes it clear that there are differences between (at least) some of the teams.
