Luke Shaw, Wayne Rooney, and evaluating player contracts and transfers through the Marginal Point Theory

Fans love to see the inner workings of their team. NFL fans look forward to the draft, NBA and NHL fans endlessly discuss the salary cap, while MLB fans relentless discuss the statistics and contracts of their favorite players. Soccer fans have the big transfers to look forward to, and today, I’ll take a quick look and discuss the concept of the marginal point, evaluating player contracts, and why buying Luke Shaw is a much better decision than extending the contract of Wayne Rooney for Manchester United.

Of course, the concept discussed here applies to leagues without a salary cap or league balancing measures, where the title is decided based on points alone (no playoffs), and where the bottom teams get relegated. I will discuss variations of the marginal point theory that involve salary caps, drafts, playoffs, and no relegation at the end.

Introduction and Explanation

In economics, there is a classic idea called the Marginal Utility Theory. The marginal utility of a good or service refers to the value in the consumption of a good or service. According to economists, the marginal utility of a good or service is most closely linked to the quantity of a good or service, and that a change in quantity would inevitably change the marginal utility of a single unit.

Imagine a burger restaurant. When there are more grills than employees, the productivity increases in scale pretty linearly. If one employee with one grill can make 50 burgers an hour, 2 can make 100, 3 can make 150, and so on. The marginal utility of an employee here is 50 burgers an hour. Eventually, you will reach a point where the marginal utility of each employee would decrease. When there are more employees than grills, each extra employee can only help others make burgers, and so the productivity increase of each additional employee slowly goes down. Finally, you will reach a point where the additional employee provides no more value. At this point, the marginal utility of each additional employee is 0.

How this relates to Football

Let’s come and apply this theory to football, and consider the following question: how much is a point worth? Or in other words, what is the marginal utility of a single point? It’s hard to say isn’t it? The value of the point heavily depends on the ownership group, the team itself, and how much the team management values winning. For instance, if a team’s owners do not care about winning, in theory every point above relegation is worthless (and of course, if the team’s owners don’t care at all, well points are effectively worth nothing). Assuming that a team wants to win the league title, and that the team does not want to get relegated, we can determine the marginal value of an individual point probably looks something like this:graph1

Economists refer to graphs that plot the value of an individual point as the marginal value curve, this graph right here is an approximate marginal value curve of a point in the Premier League, or another 20 team league.

How important is a point for a title contender? The Premier League title this season was decided by 2 points. Had Liverpool gained an extra 3 more points, they could been crowned champions. In optimal situations, where there is an actual competition for the title, the value of the individual point is highest at the top and at the bottom. The closer you are to first place, the higher that value for each individual point is. Of course, there is a point to be made that each extra point after winning the title is wasted, but since we are talking about actual athletes whose performance is inconsistent here, a team in an actual competitive league should never stop improving. This graph applies to competitive leagues like the Barclays Premier League. Of course, the value is skewed in leagues where there is little actual competition for the title, like the Greek Super League, where Olympiacos ended up winning the league by 17 points.

Applying this theory in evaluating player contracts and transfers

In theory, the marginal value of each point is how much a team should pay to improve itself by one point. The difference between the first and second place team is huge. The first place team wins the trophy, the second place team doesn’t. But the difference between 8th and 9th? We just end up calling them mid-table teams, and usually, there is little difference between them in regards to attendance and revenue.

When the front office team and the board are making personnel decisions, the most important factor to consider is the marginal utility of a point in their position. Imagine two teams, one team is in second place, the other is in 10th place. There is a big name striker on the market right now, and both teams have poor strikers. The value of the striker is much higher to the second place team than the 10th place team. In an ideal world, the second place team should be willing to pay much more for the striker than the 10th place team, as they derive much more value from his services.

Consider Manchester United. They went from champions with 89 points in the 2012 – 2013 season, to 7th with 64 points in the 2013 – 2014 season. Let A be the value of all the arrived players, D be the value of all the departed players, F to be the value of Sir Alex Ferguson, and M to be the value of David Moyes. We can then describe the change of talent (∆T) between the two seasons (disregarding injuries and luck) as:

formula1Equating the change in talent with the change in points, assuming that the level of play in the league did not change, we get:


Using this simple model, we can say that the change in talent between the 2012 – 2013 Manchester United team and the 2013 – 2014 Manchester United team to be worth 25 points. This is without compensating for the change in the overall level of play in the league, and injuries. Remember, every time a better foreign player gets brought into the Premier League to replace a player who previously played in the league, the total amount of talent in the league as a whole increases, and vice versa for when a player leaves and is replaced by a worse player. I personally tend to write off luck and biased officiating, as I believe over the course of a season, it should even out. Over the course of a full season, I would usually equate points with talent (with a small margin of error). Yes, this does not consider many factors such as team chemistry, but it is completely unrealistic for a fan to delve into and quantify those factors.

When it comes to evaluating transfers, it is important to look at a player’s replacement. The new talent of each team would be:


Because each Premier League team’s squad is 25 players, with each arrival, there must be a departure. The arriving and departing players do not have to play the same position, but that would require us to compensate for the playing time between each player and that would lead to us discussing the managerial skill of the manager, which is far out of the scope of this article. The important thing to remember is that in the Premier League, each new arriving player must mean that another player is departing.

Unfortunately, unlike baseball, we cannot quantitatively evaluate the talent of individual footballers. However, it should still be possible for us to have a rough idea of the relative talent difference between different players, and we can use that as a rough estimate. I tend to compare players with a hypothetical “replacement level”, league average player with average skills making an average salary.

Assuming that David Moyes is a league average manager, and that Manchester United’s true talent level with a league average manager is 64 points, we can put Wayne Rooney’s new contract and Luke Shaw’s transfer into perspective.

Wayne Rooney is a starter for Manchester United. How much worse would Manchester United do if they played a potted plant or simply started every game with 10 men instead? How much more is he worth over a random replacement level player? I’ll venture a guess and say that over the course of a full season, he is worth 5 points over a replacement level guy at the same position. Feel free to replace this number with your own number, and follow along.

Now considering that Manchester United’s current talent level is 64 points, we can say that the exact same team with Wayne Rooney replaced by some random free agent or transfer of a lesser talent at his position will get 59 points.

We can divide player contracts into different categories or archetypes, for instance the young prospect, the benchwarmer, the old player looking for a last contract, etc. With a new 300 thousand pound, five and a half season contract, Wayne Rooney can be considered to be the big star looking for the big contract.

As a player, Rooney would undoubtable decline throughout the life of his contract. Forwards usually peak in their late 20s, and decline by their 30s. By the end of his contract, it is inevitable that Wayne Rooney would be considered to be too old and massively overpaid.

Unless Manchester United can bring in a large batch of players raising the overall talent level of the team as a whole back to a position where they can contend for the, I would consider Wayne Rooney’s contract to be very poor. He is paid 300 thousand a week to raise the team from 59 to 64 points. At this range, the value of each individual point is very low, and thus I would consider Wayne Rooney’s contract to be pretty bad. Wayne Rooney’s performance can only go down from here, so unless Manchester United can add a lot of talent and be ready to compete next season, Wayne Rooney’s contract can only go down from its current value. In 3 seasons, he might not even be close to the player he currently is, by which point he might just be league average, or possibly worse. If Manchester United takes a few seasons to rebuild we can say that Rooney’s talent has been “wasted” on bringing an 8th place team to 7th, which in the grand scheme of things, is not important.

However, if hypothetically Chelsea obtained Rooney and offered him the same contract, to replace a replacement level player on their team, I would say that it was a great contract. With 5 more points Chelsea would win the Premier League title, and since the marginal value of each point is at the highest for title contending teams, I would say that if this was Chelsea, Rooney’s contract would be a great idea. When evaluating the value for an established player the most important factor to consider is always the marginal utility of a point for the team at its current position. Established players in their prime simply do not become better. They either stay the same, or they decline.

Luke Shaw on the other hand, is a completely different case. Luke Shaw represents a completely different type of player- he is a young player who already plays well and is still developing. Prospects represent risk. Buying prospects is an inherently risky act in of itself – you are buying him for who he might become in the future, not who he is now. Signing young players to long term deals is even riskier. Younger players can only improve, the question is, by how much.

Whether the Luke Shaw deal is a good one depends on his contract which we currently know nothing about.  Assuming that Manchester United can keep him for a long period of time, because he is young, unless he suffers from a career destroying injury, 27 million pounds is a great deal. Either Luke Shaw stays at Manchester United for a long period of time (at 10 years it comes down to 2.7 million per year), or Manchester United can sell during his prime for much more. Unless Luke Shaw is horribly overpaid, I can see him working out for Manchester United.

When it comes to young players with high ceilings, I tend to say that a long contract is nearly always better, for young players who are already playing well at a young age, I would say that a long contract is even better. For a wealthy club, a prospect who busts and does not live up to his potential is not a big deal, he is simply an overpaid player, and which team doesn’t have a few of those? But superstars are inherently limited in number, young players with superstar potential should be signed to as long of a contract as possible that he would possibly agree to.

As for judging player contracts and transfers for established players, the most important thing to consider is the marginal utility of the player. Whether it was an overpay or a steal is completely dependent on the current and expected position of the team. For instance, buying Fernandinho for 35 million pounds can be seen as a poor move for most teams, but for Manchester City? They won the league didn’t they? Or as the MasterCard Ad would say: Fernandinho, 35 million. Negredo, 22 million. Jovetic, 22 million. Winning the title? Priceless.

For younger player however, the marginal utility is not important.  They will not naturally decline, they can only get better – at the very least, and the team can sell the young player. You cannot sell an aging, rapidly declining former star with a big contract. In a worst case scenario, a former superstar could very well end up as a bench warmer, not only would he provide no value to your team, he would be a waste of a roster spot.

Additional factors

A few factors significantly skew the marginal utility curve. Namely, the biggest factors include a playoff system, salary cap, draft, and no relegation. Let’s look at the factors one by one.

Playoffs are the greatest “equalizer” when it comes to talent. Major League Soccer, A-League, and Liga MX are a few prominent leagues with a playoff system to determine the champion. It is almost impossible for a major “upset” to happen during the regular season, a better team would slowly pull away from a worse team over the large sample size of the regular season. But in a single elimination playoff? Anything can happen, luck arguably plays a bigger role than skill in determining the champion. The goal of a team in a league in a playoff system should be to get into the playoffs, once your there, all you can hope for is good luck really. Thus, in a league with a playoff system, what happens is that the marginal utility curve “slides” to the right.  In the Liga MX, with 18 teams and 8 teams qualify for the playoffs, the marginal utility curve looks like this:


Once you reach the playoffs, the value of additional talent should decrease, if a single game playoff is mostly luck dependent anyways, adding additional talent to the team is does not proportionally increase the odds of actually winning the title.

If there is no relegation, for instance in leagues like the MLS and A-league, there is little value in a bottom team signing a big star. If a bottom team is to improve, they should make multiple improvements at once, going directly from the bottom to title contenders. Toronto FC has the right idea, after struggling at the bottom of the MLS for multiple seasons, they went all out this seasons, and bought the biggest splash this offseason, signing Jermain Defoe and Michael Bradley. The marginal utility curve in a league that doesn’t have relegation looks like this:


If the league has a draft, points for bottom teams actually have negative value. After all, what’s the difference between last place and second last place? Sign a big star, and a last place team might move up a bit on the table. But by improving, the team is making their draft position worse, which effectively hampers their ability to get the next big star. The utility curve in a league with a draft effectively looks like this:



Today I talked a bit about evaluating contracts and transfers through looking at the marginal utility of the player. However I glossed over actually giving players a proper, more in-depth valuation. Check back in a few days, when next time I will discuss how to evaluate players by looking at the relationship between goals scored, goals conceded, and points.

Tags: Analysis Contracts Transfers

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