# Adding risk to the equation

### Where Alex Morgan, Christen Press and the CAPM meet

**Editor’s Note: **Most of you probably already know Jared Young. He is a longtime contributor in the soccer analytics community, and in my eyes a bit of a legend. I always think of this ASA post from 2016 about goal kicks that used an early EPV(ish) framework to break into public view a previously held secret about the value of playing it short out of the back, but he’s contributed so much over the years and in several places that it’s hard to only recommend one article. While I’m reminiscing, I also loved his 2015 introduction of “Proactivity-Score,” a measure of a team’s playing style on both sides of the ball. And without a doubt his strong business insights show up in his soccer writing time and time again. He’s written for Stars & Stripes FC and Brotherly Game as well. Look him up. Anyhow, when Jared reached out with some thoughts to contribute to the “Absolute Unit" framework I jumped at the opportunity even though I thought I had a pretty clear roadmap of where I thought the remaining cycle would go. I’m delighted to share his first post with you today. Please bother him on twitter so he agrees to write more.

In the last post, I tried to pivot from projections to benchmarking, and a big part about benchmarking in the financial world is assessing risk.

In today’s post Jared talks about risk in the business world, and how we might map it over into soccer and I think you’ll enjoy it and find it a strong contribution to our meditation on front office theory thus far. Without further ado, Jared:

The Absolute Unit series is in the middle of faithfully outlining an approach to building a winning soccer organization. Maybe more accurately, it’s about how to build a winning soccer organization when you don’t have an owner than places endless bags of cash on your windowsill each transfer season. The thesis behind the approach borrows from the corporate world, which has built decades upon decades of financial tools to help companies make better decisions, optimizing their profits. Soccer clubs, at some level, are all money-making organizations and no doubt already use some of those tools to make decisions. However, the genius here is laying out how they might use those tools in constructing the actual roster, and even potentially recommending styles of play. Super clubs should take note too, as any edge is hard to come by, even when the coffers never run dry.

In a typical soccer club, the finance team runs some numbers that spits out an answer, and that answer is how much money a team can spend on the next roster. The GM takes that forward, and with the coach and other advisors, sorts through the available players and does their best to refresh the roster and improve for next season. The goal here is to ultimately take that money from the finance team and stretch it all the way through to each decision - to optimize those critically important dollars. This is challenging because the soccer world hasn’t historically invested in this kind of work, as it’s considered too difficult to measure the financial value of 22 players, with just one ball on a very large, infinitely high field. Yet in the corporate world this is exactly the work that is done ad nauseum. Heck, delivery drivers are routed by algorithms to avoid left turns as they slow down delivery times. Everything is measured and optimized, no matter the level of difficulty. Let’s borrow just a bit of that for player recruitment in soccer, shall we?

With that as backdrop, I’m grateful to take the baton for this relay and talk about risk. Risk is something that all sports fans are keenly aware of, whether its Cristian Pulisic’s soft tissues, or playing a high line with slow center backs. Taking risks is a part of stepping onto the field. So how then, might we think about these risks from a financial perspective? How might we factor them into the decision making?

Let’s create an example within the example this newsletter has developed. The GM has a goal of increasing goal difference by 27 goals, and they have a discreet budget to spend in this window. The scout and the analyst have brought forth two players they think can help and have dutifully calculated the benefit they can provide to the team in terms of goal difference. The brain trust has determined that player A will contribute 7 goals compared to last year’s squad. It just so happens that player B will also contribute 7 goals compared to last year’s squad.

From prior articles in this newsletter, we know that these projections were not easily derived. The tactical plan of the coaching staff and the players ability to fit the system is weighed. Relatively advanced algorithms have processed every touch of both players to determine just how much value they create each time they touch the ball. In the near future, off ball movements will also be factored into these calculations. All numbers crunched, the forecast predicts they will both improve the goal difference of this team by 7 goals.

Let’s take age off the table too. Let’s assume both players are veterans with a proven track record and enough time left to make a longer-term deal amenable. Age is certainly a critical factor when it comes to risk, but we can loosen this assumption later to see how it might best be factored in.

This journey with risk is windy one, with stops at MLS player volatility, Alex Morgan and Christen Press, Venture Capitalists and Pension Fund Managers, oat futures, and the digital rendering of Weston McKennie. We begin!

**Season to Season Player Volatility**

American Soccer Analysis has developed a metric that endeavors to attach a goal value to each action on the pitch. It’s called g+ and if you’re reading this newsletter you’ve likely heard of it. If you haven’t, let’s just sum it up to say it’s sufficient to measure a player’s potential to create goal difference for your club. Here’s a look at the distribution of players in terms of producing goal difference across a single season for Center Backs and Forwards looking over the last 8 MLS seasons.

I chose these two positions on purpose. It immediately becomes clear that Forwards have more impact on goal difference than Center Backs, on average. That’s not much of a surprise. What might raise an eyebrow is the differences in the widths of each distribution. Center backs don’t have a lot of variance, while Forwards are clearly more so. If you are trying to make a dramatic change to your goal difference, it will be more impactful to find a Forward, but not all players may be created equal.

Now let’s look at how individual players change their goal difference production from season to season.

At a player level Forwards are more volatile season to season. Center Backs are a pretty safe bet, but that Forward distribution you could argue is uniform, or potentially even bimodal, with some players consistent and another group wildly volatile.

These charts show that clubs need to understand the potential for each position on the pitch to contribute to goal difference, and that certain positions come with inherently more season to season volatility at the player level.

**Moving to a Real-Life Example**

Let’s assume we’re at the end of the summer of 2020, and the theoretical GM in this newsletter is looking at two players in the NWSL – Alex Morgan from the Orlando Pride and Christen Press at Utah Royals FC. Both players have expressed interest in a change, and the agents have reached out to the club of our GM.

Based on the history of these players, the GM and team have done the math and see that both players have produced 7 goals above replacement in their careers, assuming they’ll play 30 games next year. The GM has also done their homework and believes that NWSL player production will translate roughly equal to their league. Given these players are in the middle of their prime, it can be expected they’ll produce another 7 goals above replacement for the next few seasons.

Not so fast.

Looking at their career G+ data, the results show Alex Morgan has had a far more volatile career, and comes with inherently more risk. Christen Press is a rock of consistency, and her standard deviation is assumed to be 1.0 goals per season, while Morgan’s comes out to 3. Here’s a look at their expected goal difference distribution for next season based on American Soccer Analysis data.

Sure, both players might produce 7 goals next season, but there’s an 8 percent chance that Morgan will produce 2 or fewer goals next season, while there is almost no chance Press will produce fewer than 4. On the flip side, Press has never had a season as good as Morgan’s 2017 season from a G+ perspective. The upside is there for a really strong year.

And so now we’ve introduced the problem of accounting for risk in player recruitment. Not just in terms of injuries or age, but in the nature of the player.

How much risk a club might take is certainly something that the organization needs to discuss. Different entities are prone to different levels of risk. A Venture Capitalist lives in the world of high risk. A Pension Fund Manager will be more reluctant to take that level of risk and potentially lose someone else’s pension. The owners of a soccer club will have different tolerances for risk as well. One club might tell the GM, “Do try to get promoted, but if we get relegated you lose your job.” Another club might say “Take whatever risks you need to get promoted and don’t worry if we get relegated for trying.” Same goal but two very different statements about risk tolerance.

Risk comes with a price too. A Venture Capitalist needs to charge their Founders a significant premium for their investment given the uncertainty. Whereas the Pension Fund Manager is happy bringing in below market returns for the trade-off of ensuring the money won’t be lost.

Let’s now add a financial wrinkle to the example. Press can be acquired for a transfer fee of $X and a salary of $Y, while Morgan can be acquired for 10 percent less. The market clearly sees a little risk for the same average reward for Morgan compared to Press. But how should the GM think about this? Is 10% the right discount? Shouldn’t they just take the 7 goals for 10% less? Or is the certainty Press promises worth the extra money? But what about that Morgan upside? This might be a steal!

**Turning to the Financial World for Tools to Price Risk**

We’ve got the Venture Capitalist and the Pension Fund Manager. We’ve got Alex Morgan and Christen Press. Where shall the twain meet?

A commonly used tool that helps an investor determine if they are being paid fairly for the risk they are taking while adjusting for the time value of money is the Capital Asset Pricing Model (CAPM). If we can find a parallel between the finance world and the soccer world, this formula could be helpful to the GM when determining if they like or dislike that 10% reduced price for Alex Morgan.

The CAPM formula breaks down as follows:

**Expected return of an asset** = Risk free rate + Risk Sensitivity * (Expected return of the market – Risk free Rate)

The objective of the formula is to tell an investor the **expected return of an asset**. There’s a key nuance here to lay out, however. The word “expected” in this case doesn’t speak to an investor’s true expectation of the investment. It refers to what return the investor *needs* in order to receive fair compensation for the risk they are taking (see last week’s post). As an example, I happen to own a digital football card of Weston McKennie at Juventus. I might expect to make a 30% annual return on this digital card, for example, but a CAPM analysis might tell me what the fair return might be given the risky position I’ve taken in the crypto digital card market. If it’s less than 30%, I should feel good about my Weston McKennie card. If it’s greater than 30%, then I am not being fairly compensated.

The right side of the equation vocabulary is defined as follows:

**Market** – Going out of order, we need to define what the market is intended to represent. The “market” is a theoretical concept that stands for all investable assets. It’s impossible to actually measure “the market” given the ridiculous number of investable assets in the economy, which could include stocks, bonds, houses, silver, oat futures, digital football cards, and more. The market in this case is the summation of every single thing investable, which is impossibly hard to quantify and measure. It’s even harder to realistically invest in. The standard shortcut is to pick a popular index like the DOW, S&P 500 or the Vanguard Total World Stock Index.

**Risk-free rate** - In market terms, the risk-free rate represents the return an asset with zero risk is expected to produce - think 10-year government bonds or 30-year US T-Bills. If you chose to invest your money with absolute certainty you won’t lose it, this is the rate you should expect. In normal market conditions this rate is about 4 percent, but given today’s lower rates something between 1 to 2 percent is where it stands.

**Risk sensitivity** - - Also referred to as an asset’s “beta”, risk sensitivity requires historical data to measure. This is calculated as the relationship between changes to the assets value relative to changes in the value of the market. The formula helps to make this concept more real. To calculate the beta of the McKennie card take the standard deviation of the returns of the card and divide by the standard deviation of the returns of the market, and then multiply by the correlation of the returns between the two. A Beta of 1 indicates the asset’s risk is equal to the risk of the overall market. A result of more than 1 indicates that the investment has higher risk than the market. A result less than 1 indicates that the investment is less risky than the market.

**Expected Return of the Market** – The expected return is equal to the average return of the market. How far back one chooses to assess market returns is up to the formula’s user, but generally the longer the better.

When subtracting the risk-free rate from the expected return of the market we get what is referred to as the **Market Risk Premium**, which is the important concept to internalize. This is the expected increase in returns from entering the market at all – leaving that safety net of no risk. Once I start accepting an average level of risk in the market, I should expect the Market Risk Premium for my investment. This is essentially the mid-point of positive risk investments and corresponding returns.

That is the Capital Asset Pricing Model in a very quick nutshell. Back to Christen Press and Alex Morgan and this transfer situation - let’s see if there’s a parallel with the components of CAPM and investing in a soccer player.

**The Risk-Free Rate** – In the case of the Risk-Free Rate, the soccer world should consider the replacement player as the risk free investment. Replacement players are part theory, part reality. Theoretically replacement players are easy to find and always basically competent. If a replacement player turns out to be underperforming, the theory goes that another player can easily fill in and take up a spot on the roster. The reality of course is more nuanced, but for the purposes of this formula, a replacement player is substitutes well for the equally theoretical risk-free investment concept.

**The Market** – If a risk-free player is a replacement player, then the market consists of all players that are expected to product something above replacement output, and would likely require some kind of transfer fee or longer term deal to sign. Alex Morgan and Christen Press qualify as being part of the market. But signing Press and Morgan requires a GM to understand their contributions and risk profile in the context of all players.

**The risk sensitivity** – When it comes to measuring the inherent volatility of a player’s performance we probably don’t need to get into the world of covariances, because the market, in this case, is not typically growing or shrinking on a daily basis. What we really need to understand is whether or not a player’s performance changes more or less than the average player in the market pool. It might be as simple as taking the standard deviation of a player’s performance and dividing that by the average.

Here is where the clubs need to do their own homework – coming up with a way to measure a player’s risk can be a method that a club develops over time. It could be a source of a competitive advantage. Standard deviations and ratios could be one simple way, but there are certainly other options to explore.

**The Market Risk Premium** – Theoretically there is a market risk premium in the soccer world. Perhaps a few soccer clubs have tried to quantify it, but likely this premium is widely unknown. There are many factors that go into the market price of players, but risk is undoubtedly one of them. We know there is one that factors in injury risk, but it’s less clear if season to season output variations are also a factor. They matter a great deal in the financial world and they should also matter in the soccer world. A source of differentiation for a club could be to understand how the market prices risk and trade on that knowledge.

To fully understand how the market values risk, a historical database would need to be created, similar to the massive ones that the world of finance uses to measure the risk of assets. Only after collecting the history of player goal difference contributions, their volatility and ultimately the prices paid could a GM fully understand just how much risk is a factor financially.

It’s very possible that risk premiums changes by position. Risk might be valued very differently in the Forward market compared to the Center Back market. There is likely more tolerance for risk among forwards, while decidedly less for the center backs that live closer to the home goal.

In the end, what this formula offers is a simple way for a GM to both quantify risk and understand the cost of that risk. In the investment world, the CAPM teaches an investor how much they should discount an investment given the risk. In the world of soccer, a similar formula would indicate how much risk should discount the price of the player.

In the case of Press vs. Morgan, it’s clear that Morgan has had the more volatile career in terms G+ above replacement value. Both players have averaged roughly the same production, but in a world that solely focused on risk as a factor, Morgan should come at a discount relative to Press. We know that Morgan can be acquired for 10% less than Press, but perhaps the model developed by the GM suggests that this risk should actually be only a 5% discount. In this case, Morgan appears to be more of a bargain than Press. A club without this insight would be operating without a true understanding of the dynamic.

If a club is generally risk averse and wants to avoid relegation above all else, they will be looking for players that perform consistently. They may in turn be willing to pay more than what the market pays for consistency. Meanwhile a team might like the idea of paying less for more risky talent in an effort to more inexpensively build a team that has a chance to exceeds expectations.

The bottom line (tl;dr too late!) is that the GM needs to quantify the variability around their projection of goal difference. Once accomplished they can assess player risk within the concept of the risk appetite of the club. They can also factor this risk into the valuation of the player and might be able to find opportunities in the player pool that can provide a competitive advantage. The use of the Capital Asset Pricing Model offers a simple way for GMs to start thinking about how integrate risk into their decision making process.