# EPL 2013/2014: Football Pythagorean So Far

Posted by Martin Eastwood January 20, 2014 2 Comments 1907 views

Between work, life, kids etc it’s been a while since I posted much on my blog here but I managed to grab a little free time so I thought I’d add a post about how my football Pythagorean was looking for the English Premier League so far this season.

Football Pythagorean

In case you haven’t seen it before, my football Pythagorean is an adaptation of the baseball Pythagorean that allows you to quickly estimate how many points a team would be expected to achieve on average based on the number of goals they have scored and conceded. It’s a pretty simple little equation but it is surprisingly accurate!

The Season So Far

Figure One below shows the difference between the actual points each Premier League team has achieved this season and how much my Pythagorean predicts they should have on average. For teams in green the difference is positive so they actually have more points than expected while those in read have gained less points than would be expected based on the number of goals they have scored and conceded (click the image to see it in full size).

Figure One: EPL Pythagorean Results So Far

The stand out team here is obviously Tottenham, who have somehow managed to end up with eleven points more than would be expected based on their goals. Spurs’ Pythagorean has looked pretty big for a while now so I suppose you could look at this two ways – either they have developed an extremely effective and efficient system or they have been lucky to get as may points as they have. I’ll let you decide on the answer to that one…

Interestingly, Manchester City are pretty close to their expected points total despite their enormous goal difference. One reason for this is that my football Pythagorean is not linear so as you score more goals they become less valuable to help account for high scoring matches, such as most of City’s home games this season! This helps prevent over-prediction of expected points for teams scoring heavily – having a good goal difference is obviously helpful but whether you win by one goal or five goals you still only get three points from the match.

As it stands though Manchester City are in second place behind Arsenal who have acquired six points more than expected, meaning that typically we would not expect Arsenal to be top based on their results so far this season.

How Will The Season End?

As well as looking at how teams are doing so far, we can also extrapolate the results and predict how the teams will end up at the end of the season (Table One). This is a very simplistic prediction, for example it does not take into account strength of schedules, but it is fairly accurate – the r squared value for Pythagorean predicted points versus actual points across multiple leagues worldwide was 0.938 with an average error of less than four points – so it should give a reasonable estimate of how the Premier League will finish next May.

Team Points
1 Manchester City 84.50
2 Arsenal 83.59
3 Chelsea 80.99
4 Liverpool 73.75
5 Everton 72.20
6 Tottenham Hotspur 65.89
7 Manchester United 62.56
8 Newcastle United 59.32
9 Southampton 54.42
10 Aston Villa 41.52
11 Hull City 40.97
12 West Bromwich Albion 40.74
13 Swansea City 39.66
14 Stoke City 36.85
15 Norwich City 35.78
16 West Ham United 33.91
17 Sunderland 32.28
18 Crystal Palace 31.30
19 Fulham 30.65
20 Cardiff City 29.29

Table One: Pythagorean Predicting Final Standings For the English Premier League 2013/2014

Martin is football fan and data scientist. In his spare time he likes to combine the two and write about the mathematical analysis of football.

1. - January 20, 2014

Hi Martin

Great to see you posting again. It’s an interesting and easy to understand post. Furthermore your model is easy to use for other league forecasts. If interested I’ve done so for the Danish Superliga in these two posts:

http://super-analyse.blogspot.dk/2013/06/pythagorean-expectation-in-football.html

As a side comment: Isn’t the R^2 between EP and actual final points less than 0.938 after 22 rounds? (I have a value of 0.7 after 22 rounds calculated from last season in Denmark)

Sorry for linking, but just wanted to let you know that you inspired me to do the same to danish football so you could see it if interested

• - January 21, 2014

Hi Rasmus

Thanks for the links, it’s great to see my Pythagorean equation getting used elsewhere

Yes you are correct the r2 value I quoted was for the end of the season. Perhaps I should have made that clearer in my last post? It’s good to see that you found the same results as me and that the predicted points stabilises pretty fast in Danish football too.

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• #### Martin Eastwood

Good idea, will post a follow up when I get chance …

• #### marko

teams of 12 players with requirement that one play …

• #### Martin Eastwood

Cool, look forward to reading it :-) …

• #### Peter

Hi Martin, I have given it a go (through Excel, …

• #### Martin Eastwood

It was all taken from my PostgreSQL database so yo …