"Benchmarking" via a "Required Rate of Return"
Leaving the numerator and going down below
Previously On “Absolute Unit”
We were lifting the financial valuation framework over to player recruitment in a football club. At a high level, the financial world estimates the “value” of an asset as (i) the projected future cash flows it generates, which are then discounted, to price it relative to the amount, risk, and timing of similar assets' cash flows using (ii) the concept of a “required rate of return.”
We completed our initial pass of (i) project future cash flows with the last post. Briefly to summarize, we talked about:
For footballing purposes, this meant taking event data and scouting data and compiling it into historical player performance reports denominated in “marginal goal difference contribution”).
Adjusting the historical results for noisy, non-recurring items to create “pro-forma historical results.
For football purposes, this meant stripping out finishing rates and other mean-reversion sensitive activities from our observed player performances, as well as certain discreet events like set-pieces and other examples where sample size is a problem in the historical observations.
For footballing purposes, this meant building models to take the historical player performances and project them forward. First, this meant projecting a player’s “ability” (or rate of contribution), and secondly his opportunities to contribute.
To project a player’s rate of contribution based on his historical performance, we needed to build models to better understand the impacts of outside effects (beyond his natural ability to contribute) that might remain embedded in the historical results. This demanded that we better understand league effects, team effects, etc, so as to have a process for stripping them out of the historical player performance observations. It also meant building models to estimate natural development and growth of player abilities based on age and other factors.
Layering in any proprietary information you may have related to the thing being valued.
For footballing purposes, this meant first modelling the impact of our own team-specific factors to a player’s estimated future contributions, which we explored via a Team Performance Model and discussed the Manager’s Game Model as one component of the Team Performance Model. It also meant, modelling a player’s opportunities to contribute, whether it be the minutes we expect him to play or the number of possession sequences we expect him to be involved in, or more specifically the various moments/opportunities to link with other specific individuals, each of whom may have an impact on his contributions to goal difference just as he has an impact on their own contributions. This was a thought exercise that put in fresh light just how complex and dynamic modelling the sport of soccer is (and perhaps something for someone much smarter than me to return to later). At any rate, with a projection of a player’s rate of contribution in one hand and opportunities to contribute in the other, we could multiply them together to get a good basis for a player performance projection over whatever contract period we are considering offering the player.
Apply individual judgments not already included above.
This last step is included as a catch-all and as a reminder that while the above steps often talk about starting with event data and then layers of models to help us project a future contribution in terms of marginal expected goal difference, qualitative information also plays a part and should be layered in and specifically called out distinctly for decision makers to differentiate. In fact, you could in theory apply each and everyone of these steps or concepts to a scouting process without the event-based data but you would be doing so perhaps intuitively and at your own peril.
The Aesthetics of Rates of Return
Now that our process for projecting player contributions is in place (or our meditation on this process published), it’s time to move onto (ii) benchmarking these projections against readily available alternatives. So the rest of this post reprises our analogy of basic corporate finance principles which uses the concept of a “discount rate” to properly price the present value of projected cash flows to arrive at the value of an asset. Then next week, I’ve got an exciting guest post on the way that I think you’ll enjoy from a brilliant writer and soccer thinker.
Back to required rates of return, in a previous post I had written about the basics of how this works, but I think for today’s reading, it would be useful to reaffirm the corporate finance basics and then do some prep-work for the conversion over to soccer, since there are some aesthetics in the financial world that we can perhaps unwind and discard, after having considered them.
The idea of investing, whether it be an individual saving for retirement, or a mutual fund picking and choosing among assets to grow its customer’s savings, or a corporation choosing between various capital projects in pursuit of positive net present value opportunities is to take some pot of cash (often the amount of this cash is certain) and give it up (an outflow), exchanging it instead for the prospect of receiving cash in the future (inflows) in amounts that have varying levels of uncertainty attached to them. No rational person in a normal circumstance would willingly exchange a certain amount of cash now for the uncertain prospect of receiving that same amount of cash or less some time in the future, so we can simplify this to say people invest now with the express purpose of receiving a return on their investment (not just the same amount back). Otherwise, they’d just hang on to it, put it in the bank, or under the mattress, or just like use it to buy stuff they want or need to live.
Because the purpose of exchanging certain cash now for uncertain cash in the future is to generate or return more cash overall, the aesthetics of investment is very much articulated in this idea of “returns.” And because of basic finance/math conventions, these returns are denominated in and spoken of in the form of annual percentages or rates (e.g., an annual growth rate of 8% or an annual rate of return of 8%).
Similarly, if the language of investment is anchored in this idea of rates of return, the language of financing is too. Sometimes you need to buy something but you don’t have the cash on hand. When you borrow, a lender may extend to you a certain amount of cash upfront in exchange for a higher payment he expects to receive in the future, or in exchange for a stream of cash flows he expects you to pay over the duration of the loan. He expects you to pay him back, but he can’t know for sure. He is accepting “credit risk” (and the opportunity cost of growing this money elsewhere) and in exchange he wants a return. He will quote you an interest rate that captures this credit risks and communicates the annual cost to you, over and above your commitment to eventually pay the borrowed amount back. When you’re financing something, your interest rate is essentially the lender’s rate of return.
A required rate of return just means the rate of return that a rational actor would require to expect from a given investment option given the level of risk of that opportunity and the other opportunities available to him. Said another way, the required rate of return is the going rate in the market for an asset (or investment opportunity) with similar risk, or it is the going rate of interest for lending to someone with a given credit profile.
The mystery guest writer will dive a little deeper into how these rates are determined at a component level next week. Clear you calendars.
Back to the overall “Discounted Cash Flow Model”
So again, if I’m staring at an investment, and I’ve projected its cash flows out and estimated the risk of those cash flows, and I’m trying to determine what price I’m willing to pay now for those cash flows in the future (i.e. I’m using the discounted cash flow model to calculate the value of an asset), then the required rate of return that I will hold that projected stream of cash flows responsible for (via the price I pay) will be the “market rate” of return for assets (things producing similar cash flows) with similar risk profiles.
Said another way, if the investment is expected to return us an annual growth rate of 8%, it really matters if similar investment alternatives out there (yielding cash flows with a similar risk profile) are returning a compounded annual growth rate of 9%. If they are, then we really don’t want to pay the same price for our inferior investment opportunity only returning 8%. In this example, when we’re doing pricing, we’re going to discount our cash flow projections at 9% even though they themselves are projected to return 8%, and the resulting math (some present value equations that ultimately boil down to 8% being less than 9%) tells us to pay a lower amount upfront for the investment. By paying a lower amount for the investment now for that same stack of uncertain future cash flows in the future, we have effectively lifted the total expected return of the investment opportunity back up to the market rate of 9%. The “discount rate” or the “required rate of return” we used was 9%. The market clears transactions via changes in the price of the assets being exchanged (such that the expected returns match the going market rates of returns). Theoretically, just as there is no stream of expected cash flows so strong so as to be “priceless,” there is also no stream of expected cash flows so weak that one cannot find a buyer at any price.
This aesthetic of an annual percentage rate of return is incredibly useful as a short hand in finance. This is because investing and finance is basically about moving money forward and backward through time. The convention of using years (i.e. “annual” rates) as the unit of time just fits .. *gestures broadly* .. you know — the way people organize their lives and budget cycles. To benchmark an investment, something that returns money over time, it’s helpful to think in terms of rates of return like this. If rational people act at the margin, then this sort of language helps the corporate finance world better shape these margins.
Benchmarks in Soccer
But soccer is not about moving money through time. Competitive soccer is about trying to score goals and not concede goals in order to win games, and this blog/newsletter is focused on analogizing to corporate finance in a way that helps us frame up front office theory to better facilitate a GM or Sporting Director to organize his organization’s processes and decisions in a structured efficient (and effective, ugh) manner. This mental model was supposed to help us recognize that our very difficult task in soccer (predicting the future and then acting on it) has a cousin in corporate finance, and the cousin is older and pretty sophisticated, even if he sometimes does get drunk and do some stupid shit (swear I wrote this line before the meme stock short squeezes). We could learn from him. A big piece of the gambit of the blog has been to replace the currency unit of account that powers the corporate financial world with the soccer unit of account of goal difference.
When we map this corporate finance concept back to soccer, having just spent months working through a framework to build player projections that are denominated in “marginal expected goal difference,” we just need to remember that just like an investor faced with a multitude of investment alternatives, a sporting director needs to “act at the margin” and benchmark a given player’s contribution projections against a relevant baseline tied to what players are available out there to roster. If the financial world uses this language of “required rates of return,” perhaps the GM wants to just stick with “marginal expected goal difference,” and think in terms of “marginal expected goal difference above average” or “marginal expected goal difference above replacement level” “Average what?” and “Replacement what?” are fine questions to tackle soon enough.
Also, with an eye to the future, we know in our hearts that because all clubs are resource-constrained in one way or another, we will ultimately need to optimize our benchmarked goal difference projections at the team level by allocating our club’s approved budget resources properly. We might be projecting our player performances out in the future and denominating them in goal difference, but ultimately a GM doesn’t pay a player in “goal difference.” He doesn’t pay a transfer fee with goals either. He pays using money that has been allocated to his operating budget by the board. In this way, try as we might, we will ultimately fail to escape the reality of these finance principles entirely in the soccer world. But for now, as we work towards completing the “soccer via corporate finance” analogy and before we get to this step of considering the budget, I think it’s best to map “discount rates” over to some soccer equivalent contemplation of replacement player baseline contributions, and then for a sporting director to imagine and manage multiple years of impacts to team goal difference when he considers signing or releasing or trading (etc) a soccer player to his club.
Positions are kind of a lie right? I mean formations are a lie or something. Ultimately what a player is asked to do by the manager — how he fits into the team’s game model — cannot accurately be summed up in a simple “left sided attacker” or “right sided fullback". We all know this, but I… I really don’t have the time to slug it out at the moment, nor do I have the solution at hand. When it comes down to it, from what we can tell in the data, not all the player roles in a standard starting eleven directly impact the team’s marginal goal difference via their on ball actions equally. Said another way, when we look at EPV models (g+ for example), the most impactful players in raw terms are the players who make themselves available and receive the ball close to goal, and when you include the interrupting actions that end opponents’ possessions, the defenders who disrupt those very situations, zeroing out opponent possession values also pop. In raw goal difference units, EPV models just sort of shrug at the central midfielders operating in the most neutral parts of the pitch, at least relative to the other positions. For this reason, until there is a better alternative — and people are working on it to be sure (ideas for clustering player roles/styles), I think we’re just sort of stuck in this basic framework of comparing the EPV values of players within position silos. This is probably not too disruptive of a concept as player recruitment teams surely speak in terms of basic football positions also.
If a finance analyst is trying to determine the correct discount rate (benchmark) for a given investment and it’s projected stream of cash flows, he’s essentially trying to compare it to the correct population of similar investments, sort of like a recruitment team would compare a right sided fullback to other right-sided fullbacks, however blunt that is. So for now, let’s stick with this “position” construct and benchmark accordingly.
The other question we need to answer soon enough is how to determine where the actual baseline is, whether it’s an average player at a position, or a replacement level player at a position, and what about the fact that soccer is played everywhere, that there are countless leagues of varying qualities? I don’t know. We’ll tackle it. Steady as she goes.
Thanks for sticking with this. The posts are not as regular as they used to be, and I apologize for that. I’m unable to pop these out as quickly as I did earlier in the year; however in my mind, the roadmap of where this thing goes from here is pretty clear even if it is treacherous. There are some really exciting things to cover too as we make our way through the full cycle of the valuation process and onto some macro ideas. I am committed to continuing the journey and I appreciate you reading and sharing.