Survival analysis of relegation in the Premier League

Getting to the Premier League is the ultimate goal of every single English team not currently in the top flight. The financial implications are simply huge. According to Deloitte’s Sports Business Group, the Championship playoff final is the most lucrative soccer match in the world, with a financial boost of at least 215M$ over the next three seasons for the winner (and at least 381M$ if the team can avoid relegation in it’s first season). Yes, you read that right. Winning the Championship playoff final is worth more than winning the Champions League final.

With that being said, if getting to the Premier League is lucrative, staying there is even better. It is also harder. When new teams come into the league, they are expected to struggle. They simply don’t have the same level of talent or the budget to really compete. In the last 21 Premier League seasons, 42.9% of teams were relegated within their first season, and 60.3% within two seasons. A problem new teams face is that they can’t score goals consistently enough. The forwards that did the job in the Championship generally don’t have what it takes in the Premier League. This leads us to my question: is buying a new forward a good way to ensure survival in the Premier League for newly promoted teams?

To answer this question, I collected data dating back to the 1997-1998 Premier League season. For each season, I looked at which teams were promoted, how long they survived in the Premier League (in seasons) and whether or not they bought a new starting striker to help their offense when they got promoted ( I considered that a team bought a new starting striker if they brought in a player that featured at least 25 times for them in the season.

I then compared all those teams using the Kaplan-Meier estimator. For those unaware (pretty much everybody I assume), the estimator is used to approximate the survival function, which is the probability that a certain event will occur before a certain time. Survival analysis is used across many fields, most notably medicine, to for instance compare groups of patients after different treatments, or predict how long a patient will survive a certain disease.

Given the fact that I know as much about medicine than a monkey that knows nothing about medicine, I will stick to soccer here. To answer my question, I compared two survival curves, one for teams that bought a new striker and one for teams that did not. Here are the results.

In blue is the survival curve for teams that did buy a new starting striker, in red the curve for teams that didn’t. What the curves say is that teams with a new striker have an estimated 72.5% chance (survival probability axis) of still being in the league after one season, compared to only 40.8% for teams that did not. After two years, those percentages are at 67% and 17%. Huge difference!

The p-value of 0.0027 comes from the log-rank test, comparing the survival distribution of the two samples. Here, we see that the p-value is very small, meaning that the two curves are significantly different, and therefore buying a new striker does help increase the chance of survival in the Premier League.

Now, you are probably thinking what I was thinking. Of course, teams with a new striker have better chances of surviving. Spending money just helps, right? I fitted a Cox model, useful to look at the individual impact of a variable on the survival curve. I looked precisely at two variables (having a new striker, and how much teams spent the summer they arrived in the league), and how exactly they affect chances of relegation. Here are the results.

VariableHazard RatioP-value
New striker0.4960.021
Transfer spendings (M$)0.9980.098

The hazard ratio (HR) represents a baseline comparison for every variable. A hazard ratio of 1 means that the explicative variable has no impact on the dependent variable. Here, the first HR means that having a new striker reduces the risks of relegation by 50.4% (1 – 0.496).

We also see that every million spent on transfers decreases chances of relegation by about 0.2%. However, we see that this value is not statistically significant (higher than 0.05), meaning that spending more money in a first Premier League season does not significantly help increase the stay of a team in the British top flight.

I want to reinstate something here. Spending more money IN A FIRST SEASON does not significantly help avoiding relegation. Over time, obviously, spending more will help achieve success in the Premier League (Im guessing, I did not actually look at those figures).

Surviving in the Premier League is hard. It does seem however that bringing in a new striker has been, through the years, a very effective way of ensuring the stay in the top flight lasts longer.

2 thoughts on “Survival analysis of relegation in the Premier League

Add yours

    1. Aston Villa and Sheffield United both bought new strikers. Norwich didn’t, and look where they are right now! Seemingly, the trend will continue this year!


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