Sir Alex Ferguson is arguably one of the greatest managers in British association football history. He was even knighted and inducted into the Order of the British Empire for his “contributions to British football”. His contributions to Manchester United’s success is undeniable, but the question is, just how much better was he compared to the rest of the league? How much better was he compared to David Moyes?

Ferguson’s successors have spent a lot of money already, and it’s not even two seasons since his retirement yet. Moyes spent 28 odd million on Fellani, nearly 30 million on Mata, and extended Rooney at £300 thousand a week. United has already purchased quite a few actual solid stars for Luis van Gaal already, and we haven’t reached the winter transfer window yet!

With an infinite budget, any manager can win the Premier League. Yet Sir Alex Ferguson never really splurged and “bought the league”. He had an absurd record, 13 league wins in 20 seasons, yet they were constantly outspent by their rivals. In the early years of the Premier League, Blackburn and Liverpool were the big spenders. More recently, it is Chelsea and Manchester City. United were never a penny pinching team, but they were for the most part not the biggest spenders.

Moyes and Giggs cannot replicate Ferguson’s success despite significantly higher spending. Van Gaal spent even more, and although it is very early in the season, his odds of winning the league do not look good at all. This got me thinking, could we evaluate Sir Alex’s performance from a monetary standpoint? Or in other words, if we put some other manager like Moyes in his place for the last 20 years, and demand that Moyes replicate Ferguson’s achievement, how much money would he need?

Hypothesis

Sir Alex Ferguson was the best manager in England from a performance vs. perceived talent standpoint. Or in other words, Ferguson’s teams performed better than what the rest of the league perceived their talent level to be.

What does the data tell us?

So first of all, I will be looking at wage data. A player’s wages are a decent approximation of how much the league as a whole thinks he is worth in performance (of course, there are some other factors like marketability, personal risk, home grown status, etc.)

The idea is, say for instance multiple teams are competing for the same player’s services, and the player would most likely choose to sign with the team offering the highest wages. Thus the wages the player is offered is effectively what the team perceives his value to be.

On a micro level, a player’s wages is a poor indicator of his perceived value. Individuals might be overpaid or underpaid, but as a whole, the luck tends to even out. So for instance, the industry might perceive an 80k a week player to be better than a 100k a week player, the higher paid player might be overpaid, or maybe the lower paid player might be underpaid. But as a whole, you would struggle to find people who would disagree with the fact that a team paid 1 million a week is not as good as a team paid 2 million a week.

The wages that the 25 men on a Premier League roster are paid is a decent enough estimation on how much the industry thinks they are worth in performance. If we were to plot the wage data and points, we can see a decent correlation between the two, and although individual teams may seriously over or under perform what their wages tell us to expect of them, on a large scale, the wages are a decent predictor of performance.

My first step is to account for wage inflation. I normalized all the salary data to 2012-2013 levels. I did this by finding the league average total wage bill, and my comparing the average between seasons, we can see how much the wages inflated by. For instance, in 2011-2012, the league average was £81.3 million, and in 2012-2013 the league average was £89.1, this marks a 9.6% increased. 1 million bought a lot more back in 2000 than it did in 2013, and we have to account for inflation before we can compare numbers.

This graph shows the inflation that has occurred in the Premier League since the turn of century. Average payroll tripled since the 2000-2001 season, and of course, United’s wages have gone up accordingly along with the league average.

After doing this, we can plot the numbers on a graph, with wage bill as the independent variable, and points as the dependent variable. We can see that for the most part, most seasons fit in quite nicely. We can see that the graph results in a curve, since the law of diminishing returns mean that it is more difficult to improve a team the better the team already is (you are only allowed a 25 man roster with 11 men on the pitch at any given time after all).

From thus graph we can establish the curve of best fit as:

Where y is the number of points, and x is the annual payroll of a club.

What does this curve mean? For a league average club, x represents the amount of money this club spends on payroll, Y represents the expected amount of points this team is expected to earn. The curve of best fit represents how many points a hypothetical “league average” team can expect to get with the amount that they spend on wages.

Or in other words, if we abstract a club into a “black box” that takes in money, spends money on players, and outputs points, the above equation is an abstraction on how well a team spends its money. Obviously clubs sometimes over or underperform their predicted finish, but to consistently over perform? Let’s look at the graph again, this time with Manchester United’s data points in orange.

Every single one of Manchester United’s seasons this millennium has outperformed the league average. Really demonstrating that Manchester United outperformed the perceived talent level.

Analysis

Sir Alex Ferguson outperformed his expected performance every season at Manchester United since the 2000-2001 season (the earliest season which I have reliable wage data). In fact, his performance is almost absurd, no other club has so consistently outperformed the expectations.

I cannot stress enough just how special Sir Alex’s performance was. Remember, traditionally we say that sporting performance is determined by two components, luck and skill. Or if we were to convert it to a very crude approximation, it would look something like this:

Everyone has a level of innate skill and resources, but there is also a huge luck component involved. Usually, we say that truly stunning athletic performance has to have quite a bit of both, an athlete has to be both skilled and lucky. For instance, statisticians explain the Sports Illustrated cover curse as a function of luck. Usually athletes get on the cover of Sports Illustrated because they performed really well, people say that they are “cursed” after they get on the cover, since they perform worse after getting on the cover. The curse is a simple result of luck. To perform at a stunning level, you need to be both skilled, and lucky. Your skill stays, your luck doesn’t, and thus athletes featured on the cover of Sports Illustrated usually regress back to their usual performance after getting on the cover.

If Sir Alex performed amazingly for 1 season, I would say that it was probably a product of good luck. But Ferguson’s Manchester United outperformed their payroll consistently every single season. This cannot be luck, other teams sometime outperform their payroll, and sometime they underperform. From the beginning of the Premier League to 2012-2013, the players changed, the coaching staff changed, the ownership changed, Ferguson was the only constant.

I’m probably telling you something you already know, that Sir Alex Ferguson is a very good manager. After all, he was inducted into the Order of the British Empire due to his management prowess. But the question is, just how good was he? How much better was Ferguson compared to the “league average manager”?

We can take United’s inflation adjusted payroll, and plug it into the formula to determine how many points United can expect to obtain every season. Subtracting the number of points United actually got from the number of points United can expect to get can give us an idea on just how good Ferguson was. Using the curve of best fit, we can figure out how many points United could have expected with their payroll. The results are below:

In other words, if a mediocre manager replaced Sir Alex, from 2000-2001 to 2012-2013, he can expect nearly 124 points less, and average of approximately 9.5 points a season.

But how much money was Ferguson worth? Can we put a dollar value on his over performance? All we need to do is plug in the amount of points United earned every season to the curve of best fit, and from that we can get the expected payroll that United should have needed to perform that well. Subtract the two figures, and we can get the amount of money that Alex Ferguson was “worth” to Manchester United.

And there you have it. Sir Alex Ferguson saved Manchester United nearly £1 billion. Of course, the recent transfer window showed us that for Louis van Gaal to perform nearly as well, Manchester United would be forced to spend a lot more than they spent under Ferguson. No other manager in the Premier League ever approached Sir Alex’s spending efficiency, and I doubt those heights will ever be reached again.