Some sports adjacent financial analysis

To follow on from my previous post, I thought I'd turn my attention from United's on-pitch performance to their financial situation.  Whilst this is obviously only tangentially football related, the business of football itself is sadly more relevant than ever to both sporting success and institutional achievement. This was also a useful exercise in learning to carry out some basic financial analysis functions in R including time series analysis, financial analysis and forecasting. 

To begin with, I performed a time-series analysis of United's quarterly revenues from 2015 to 2022. This can be seen below. 

For anyone unfamiliar (including myself until recently!), time series analysis is a statistical technique used to identify patterns and trends in data over time.  This can include analysis of both trends (long term movements) and seasonality (year-in-year movements). To break this down further the above charts show the following:

Data -  This is the original time series data in its stock form. 

Trend - This chart attempts to indicate the general direction of the data over time.

Seasonal - This chart indicates the seasonality of the data, indicating any spikes in certain quarters.  

Remainder - This chart highlights irregularity that is not explained by the previous two charts. 

The bars are called 'forecast intervals', these indicate the confidence intervals for each chart. In R, the default value for this is 95%. 

Now the necessary explanation is out the way, we can move towards the analysis segment.  On the whole, it appears that despite variation in the club's fortunes over the years, overall revenues have remained somewhat flat.  This mostly likely reflects the club's already strong market position alongside the locked-in revenues mostly derived from the premier league's TV deal.  There is however a large degree of quarterly variation within this. Performing a T-test on the trend data creates a value of 280.44, which is highly suggestive of variation over time. Nonetheless, despite this, the fact that the relative peaks and troughs have remained flat suggests this is more due to seasonality or the club's accounting practices.  

Turning to the seasonality data, performing a spectral density analysis reveals a frequency bandwith of 0.0385 and is suggestive of what appears to be a highly predictable pattern.  This may appear obvious when the homogeneity of the seasonality graph is considered but nonetheless, United's quarterly revenue appears to be extremely regular. 

Finally, the remainder, which examines the irregularity or the 'random' element of the data is not strongly conclusive. The Ljung-Box test generates a value of 2.825 whilst the p-value is 0.092. In essence, this suggests that there is some chance that this pattern is random, but equally does not prevent its existence as a legitimate pattern. The p-value above suggests that the chance of this is essentially 9.2%. This is above the preferred typical confidence level but nor is it fatal. 

We can use the time series analysis alongside the tools described above to draw a number of conclusions about United's business and revenues:

1. Commercial revenues are largely flat.

2. The data is highly seasonal and varies across the year. This is perhaps not surprising for a business that is highly active during the football season itself. 

3. Whilst there is a chance that this variation is purely random, the data would suggest that this is unlikely.

There is perhaps one caveat that ought to be applied, a significant part of the data set intersect with the COVID-19 pandemic, which depressed revenues through the elimination of gate receipts and any corollary sales.  It has been estimated that each missed game cost United around £5 million.