I'm a Manchester United fan, and after what was a disappointing 2017/2018 season I was amazed at how much money a team can spend on payroll without anything to show for. I decided to dig up some data and try to find the relationship between a team's payroll and its season performance.
When we plot data for the previous four seasons of the English Premier League (2013-14 through 2016-17), a simple eye test suggests that there is a positive relationship between team payroll and points at the end of the season. There are two very distinct clusters: the first, with the usual suspects on the upper-right corner of the graph (Manchester United, Manchester City, Liverpool, Chelsea and Arsenal) with high payrolls and high amount of points in the table, and a second, with everybody else, led by Tottenham and Everton.
The clear outlier in this sample is the 2015-16 Leicester City, a team that won the league with a payroll of GBP 48.2 million. In comparison, Manchester United averaged a payroll of GBP 206.7 million, finishing 7th, 4th, 5th and 6th.
To make a more formal determination of the relationship between the two variables, I ran a simple univariate OLS regression (log-log) using a sample of 67 observations. This should've raised a flag for football fans who are paying attention: the league has 20 teams, and four seasons worth of data should yield 80 observations. The problem is that three teams get relegated every season, and our source, which was originally focused on the teams that participated in the most recent season (2016-17), did not provide payroll data for those teams that were not a part of that one season. Because of this, the teams that were present on all fours seasons are over-represented in our sample. Payroll data is adjusted for inflation, so payroll data in our estimation is for 2015 prices.
The results show that with a 1% increase in payroll we could expect a 0.35% increase in points in the table, but payroll only explains ~60% of the variability in team performance. So yes, we can expect a higher standing on the table from teams with a higher payroll, but there is still 40% of the variation that can be attributed to other variables, like team chemistry, fitness, games played in the year (there are multiple competitions happening simultaneously), managers, etc. Even if you were able to gather data for all of that, it would still be hard to explain why Leicester City over-performed by 35.25 points in the 2015/2016 season (based on a level-log estimation). A certain share of the variability is likely to be ultimately attributed to luck.
It also puts in question the quality of the spending. Our work shows that higher spending is associated with a higher standing in the table, but if a team spends those high salaries on acquiring players that are as good as myself and my buddies who play on a questionable Saturday league, then obviously, the team is likely to finish below what the model would predict. Regarding Manchester United's performance in recent times and how short they fall with respect to what they are expected given their payroll spending, I think some of it can be attributed to poor spending.
There is a growing body of statistical research being devoted to sports. In baseball, the field of SABRmetrics is becoming more and more relevant for decision-making both inside and outside of the field. My beloved Yankees had the third highest payroll last year, and came one game shy of reaching the world series. For this year, pre-season expectations were set considerably high, but the payroll dropped. Some of their prospects and young players are under their rookie (and inexpensive) contracts but they also shed some expensive players. Twenty games into the season they are a disappointing .550 team (.562 at the end of 2017). If we assume that this theory of mine translates from football to baseball, then we could've expected this drop. There's a lot of games remaining in the season, but one can only hope that the Yankees have their bases covered with respect to the 40% that our model is not explaining, or that the team's front office is willing to buy the Leicester City players from 2015/2016 before heading to the playoffs.