By Daragh O'Leary
The impending return of Premier League football has had a huge impact on my work life and it is safe to say that I am daydreaming more than usual. My day dreaming has not been in vein, however. In fact it has given me inspiration for a blog post. My day-to-day research concerns developing ways of measuring and analysing what is referred to in the economics/business literature as scaling. This is a form of growth which is incredibly uncommon among businesses.
In contrast to a conventional growth trajectory, any increase in size, scaling must involve a repeated and proportional series of increases to an output (revenue) or an input (employment) – see more on this here. Meaning that for firms to scale, they must grow outputs by a sizeable amount and then repeat that same growth again. This sees them exhibit what Ott and Eisenhardt (2020) refer to as a hockey stick pattern of growth. This is a similar shape to the exponential curve we all unfortunately became so familiar with during the COVID-19 pandemic.
Amid my workday daydreaming, I began to wonder whether scaling has anything to offer the sports economics literature and sure enough, I think it may. I think we could use the criteria for a scaling trajectory as a proxy for how successful a manager will be at a club.
Take Erik Ten Hag for example. Most fans and pundits of the beautiful game would agree that his time at Manchester United has been a bit of a mixed bag and wouldn’t have been too surprised to see him replaced during the summer. Yes, there has been 2 domestic cups, but there’s also been an 8th place finish and some dismal signings. The points trajectory of Manchester United over this time period illustrates this.
The impending return of Premier League football has had a huge impact on my work life and it is safe to say that I am daydreaming more than usual. My day dreaming has not been in vein, however. In fact it has given me inspiration for a blog post. My day-to-day research concerns developing ways of measuring and analysing what is referred to in the economics/business literature as scaling. This is a form of growth which is incredibly uncommon among businesses.
In contrast to a conventional growth trajectory, any increase in size, scaling must involve a repeated and proportional series of increases to an output (revenue) or an input (employment) – see more on this here. Meaning that for firms to scale, they must grow outputs by a sizeable amount and then repeat that same growth again. This sees them exhibit what Ott and Eisenhardt (2020) refer to as a hockey stick pattern of growth. This is a similar shape to the exponential curve we all unfortunately became so familiar with during the COVID-19 pandemic.
Amid my workday daydreaming, I began to wonder whether scaling has anything to offer the sports economics literature and sure enough, I think it may. I think we could use the criteria for a scaling trajectory as a proxy for how successful a manager will be at a club.
Take Erik Ten Hag for example. Most fans and pundits of the beautiful game would agree that his time at Manchester United has been a bit of a mixed bag and wouldn’t have been too surprised to see him replaced during the summer. Yes, there has been 2 domestic cups, but there’s also been an 8th place finish and some dismal signings. The points trajectory of Manchester United over this time period illustrates this.
In his first season (2022/2023) Ten Hag took United to a 3rd place finish with 75 points. This was a 17 point gain on their previous season (2021/2022) where United finished 6th. However, the following season United only managed an 8th place finish with 60 points – a 15 point loss on their previous campaign. If you were to work out the average growth rate of United’s points tally over these three seasons it comes in at roughly +2%. This illustrates why average growth rates can be misleading.
An average growth rate of +2% over three years may sound like progress, but in reality we know that Manchester United have looked to identify replacements for Ten Hag during this time and some pundits are even predicting he may be out of a job by January. All this unrest about United’s progress gets hidden behind an average growth rate because it can’t effectively incorporate a positive period of change and a negative period of change into one final value. If the criteria for progress during this period was scaling rather than just growth, then Ten Hag would already be out of work. United’s trajectory during his time would not be considered scaling. Yes, there was growth, but the growth didn’t follow the repeated and proportional trajectory of scaling.
Managers which have exhibited this scaling trajectory in their first 5 years include Mikel Arteta at Arsenal (below in red) and Jurgen Klopp at Liverpool (below in orange). These managers didn’t just improve their teams in one season, they repeatedly improved their points tally each year.
An average growth rate of +2% over three years may sound like progress, but in reality we know that Manchester United have looked to identify replacements for Ten Hag during this time and some pundits are even predicting he may be out of a job by January. All this unrest about United’s progress gets hidden behind an average growth rate because it can’t effectively incorporate a positive period of change and a negative period of change into one final value. If the criteria for progress during this period was scaling rather than just growth, then Ten Hag would already be out of work. United’s trajectory during his time would not be considered scaling. Yes, there was growth, but the growth didn’t follow the repeated and proportional trajectory of scaling.
Managers which have exhibited this scaling trajectory in their first 5 years include Mikel Arteta at Arsenal (below in red) and Jurgen Klopp at Liverpool (below in orange). These managers didn’t just improve their teams in one season, they repeatedly improved their points tally each year.
In the case of Jurgen Klopp’s Liverpool, this trajectory would see Klopp call time on his tenure at Anfield having won every honour available to him. At the time of writing, Arteta has only won his Arsenal side an FA cup and 2 Community Shields, but this may change if Arteta is to stay as long at Arsenal as Klopp did at Liverpool. If it is the case that exhibiting a scaling trajectory is a good proxy for a manager’s future success, then hopefully Arsenal fans will have something to cheer about come May next year.
It should be noted that I have also included the trajectory for Pep Guardiola’s Manchester City above in sky blue to show that success can come from non-scaling trajectories as well. However, I think it’s worth mentioning that Pep’s Man City not fitting a scaling trajectory is more so to do with their quality relative to Arteta’s Arsenal and Klopp’s Liverpool rather than any inability of Guardiola to improve his team repeatedly. Pep simply inherited a team that had challenged or won the league in 2 out of their previous 3 seasons, so there was just less room for them to improve into. Arteta and Klopp on the other hand both took over fallen giants languishing in 8th place.
It should be noted that I have also included the trajectory for Pep Guardiola’s Manchester City above in sky blue to show that success can come from non-scaling trajectories as well. However, I think it’s worth mentioning that Pep’s Man City not fitting a scaling trajectory is more so to do with their quality relative to Arteta’s Arsenal and Klopp’s Liverpool rather than any inability of Guardiola to improve his team repeatedly. Pep simply inherited a team that had challenged or won the league in 2 out of their previous 3 seasons, so there was just less room for them to improve into. Arteta and Klopp on the other hand both took over fallen giants languishing in 8th place.
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