Rounding Out Player Projections: The Complexity of "Opportunity"

Taking our projected player contribution abilities and combining them with opportunities to contribute to project actual contribution.

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.”

To (i) project future cash flows the basic steps we agreed on were:

  1. Obtain relevant and reliable accounting records of historical results, which are (1a) denominated in the unit of value that you care about (in our case “marginal goal difference contribution”).

  2. Adjust the historical results for noisy, non-recurring items to create “pro-forma historical results.”

  3. Take those pro-forma historical results and project them forward into the future in some kind of documented, evidenced-based manner based on the information publicly available.

  4. Layer in any proprietary information you may have related to the thing being valued.

  5. Apply individual judgments not already included above.

To catch us up, several weeks ago we laid out the structure of there being two overall phases to steps 3-5 above: first, we needed to project out a player’s contribution ability (measured in marginal expected goal difference per 90 minutes (or per 100 passes/possessions, etc), and second, we would need to project out the player’s opportunities to contribute (e.g. minutes to be played, or number of possessions to be included within). Over the last several weeks, we have somewhat painfully made our way through the first phase, and more specifically, the various “layers” that made up that phase, together a process of projecting a player’s contribution ability (or rate).

In this post, there’s a quick loose-end to tie off related to projecting “contribution rates” and then we’ll tackle the second phase: projecting a target player’s opportunities to contribute.

Closing Out Projected Player Contribution Rates (Abilities)

The last several projection deep dive posts have walked through the below layers and the steps to move from one layer to the next while we try to take the rate at which a player has contributed to team goal difference in the past, un-lever it for past team/league effects, grow it based on a player development curve, and then re-lever it based on our proprietary understanding of our own team’s game model and other factors specific to the team’s overall performance model that might interact with this more abstract concept of a player’s inherent contribution rate.

However, handwavy I was about the specifics of these layers, one way to think about them was that you could set up processes that rely on the objective data and its interaction with (either) static proprietary judgments you’d make around team effects and league effects and other factors, or periodically (but systematically) updated judgments. Said, another way you could theoretically set this part up on auto-pilot and have it feed insights to you for your recruitment team to consider and weigh against the other evidence. The other evidence is really the last layer to deal with here in this “contribution rate projection” phase.

And so this is just a reminder that qualitative information is information too. I’m not demanding an entire recruitment process be run on autopilot using a combination of data and logics laid out in poorly drawn Powerpoint slides in a newsletter. But in separating out this last layer of subjectivity from the more modelled outputs, we can also visually highlight this distinction for a key decision maker. The idea being, “look, here is our best estimate of the projected goal difference contribution per minute this player will bring the club during his time here. 85% of this estimate is suggested by our data models, and there’s a remaining 15% that comes from the following observations the scouting team has made that aren’t reflected in the models:_______________.” And again, it isn’t just qualitative vs quantitative outputs that are helpful to distinguish, but also past results from growth projections, team effects vs no team effects, etc. And I suggest a worthy visual depiction that breaks this into legible bits looks like this:

“Boss, we expect this player is going to contribute +0.12 goal difference per game during his time with us, which puts him in upper quartile of wide attacking players in the league. He’s currently contributing about half this amount with his current team (+0.6), but we expect him to improve over the contract term based on his age and current performances and our understanding of the development curve for wide players (+0.02). Further, our model thinks his game fits the manager’s game model tremendously better than it does his current club (+0.01), and lastly our scouts saw some real spark at the end of last season and they understand he’s had an inspired summer with his fitness trainer and is leaner than ever before. They tell us his off the ball runs open up space for his teammates in ways our data models cannot currently capture (+0.03)”

I think that’s a good model. If the decision maker feels that any more of those are more persuasive than the others, they can pull them part easily and challenge things. It drives conversation towards important matters since time is limited. The hard time-consuming stuff has been done upfront in the organizing of this process.

Projecting Opportunities

Months ago, when we were walking through the overall projections process outline, we talked about the difference between contribution rates and opportunities:

Basically, while the per 90 [minutes] or per 100 [possessions] metrics tell us something about a player’s ability, when we allocate budget dollars to a player contract, we’re paying for more than ability. If the player doesn’t ever step on the pitch then he cannot contribute to the team’s overall performance as measured in expected goal difference, and accordingly we should not allocate many budget resources to signing him.

There are a couple of important points. First, the above is the most obvious point, and it feels pedantic saying it let alone repeating it, but since this blog is nothing if not deliberate: any club who faces resource constraints and is charged with putting together a team to optimize its goal scoring and prevent goal conceding, must recruit with a mind not only towards player ability but towards his actual contribution, which involves using his ability while also being on the pitch in games. So just from an elementary perspective, if what we’ve worked towards the last couple months is a process for projecting that marginal goal contribution rate per 90, then we just need to multiply that times a projection of player minutes (opportunities), to arrive at this total marginal goal difference contribution number that we’ll check against baselines and allocate budget to etc.

The most obvious factor here is injury risk (and to a lesser degree suspension propensity or the potential for international callups). I imagine that when sorting on players with historically high goal contribution rates who are also available in the transfer window, it is not uncommon for a club to find players with unfortunate injury history towards the top of that list because consistently healthier players with similar outputs are snatched up quite quickly or never made available to begin with.

That gorgeous spacious house with the vaulted ceilings and magnificent curb appeal that’s been on the market for 4 months hasn’t sold for a reason, but eventually a buyer will come along who is willing to accept whatever flaws or risks lay await. Similarly, I think every single fan can remember at least one such signing their favorite club made that just didn’t pan out because of injuries, even injuries that were well known at the time. Clubs with constrained resources have to take risks, and they have to deal with what’s in front of them, so this is not surprising. Sometimes you have to place bets. I’m not here to offer some sort of epiphany about the importance of scouting for player health and injury history (this should be exceedingly obvious in 2020), nor am I here to introduce the concept of injury risk to clubs (lol). But since we’re building a framework that sprints furiously towards a last step of allocating budget resources to roster spots based on each player’s expected contribution towards a team-level goal difference objective, we can place this concept of injury risk into our framework in a tangible way, by specifically putting a name and a number on the injury risk, by allowing it to burden the player’s otherwise attractive goal contribution rate calculated in the earlier phase, and in doing so demanding it be acknowledge and accounted for. Injuries have real effects on team performance.

Everything Connected

The other point to make is that the projection of a player’s minutes in the team is an estimation that impacts not only how we account for that individual player’s contribution to the team, but both on an abstract and more practical level, all other players on the team as well. By specifically requiring the projection of a target players minutes as a part of the process, we are forced to think about the interconnections between the player and the rest of the team as we continue to maintain our sights on the overall team goal difference objective.

To put a finer point on it, assume injury risk doesn’t exist for a moment. If your current striker is contributing a goal every four games (0.25 G/xG/g+ whatever), and you sign a better striker who you project to contribute a goal every other game (0.5/game), quite obviously, and I apologize for making the point, you have not added 0.5 goals per game to your team, you have added something closer to 0.25 goals per game. There are only so many minutes. This is the type of mistake that is easy to make if you don’t think about your transfer business using an integrated stock-flow consistent framework (i.e. on the margin how many expected goals will this player contribute to the team through all of his touches?). And it gets harder. What happened to that player who was putting up 0.25 per game but is no longer starting? Has he been cut or transferred, or traded? Is he still with the team? If so, whose substitute minutes is he taking now? And what’s going on with the old substitute? These types of questions cascade down and around the roster naturally in ways that impact our projected overall team goal difference through many facets. This demands some sort of structure or framework to model. Again, if you just close your eyes and swing you might hit a home run, but you know the drill by now, and what I’d say about that. Place it within the system and account for it.

Not to cause existential math dread, but this cascade of changes to our projections around opportunities for individual players to contribute even loops back around into the player contribution rate projections. We may be through with [those older posts], but [those older posts ain’t through with us]. After all, if you’ll remember, when calculating these rates (abilities) there is some adjustment for team-effects which might or might not contemplate the teammates that will surround the target player and the impact those players will have on his contribution rate — and not simply “those players” or even “those players’ contribution rates” but those players’ contributions (their rate X their opportunities). As we change the amount and frequency of the nodes of interaction between these teammates, it gets complicated.

Reprise (Team Effects)

A point I failed to emphasize in the team-effects posts, which I’ll CYA for myself now, is that as expected possession models (EPVs) like "Goals Added” become more publicly available, and hopefully as they start to become the common unit of account for analysis, you’ll start to see them be pulled apart and analyzed more, as is the case with ASA’s investigation into “g+Boost.” John Muller went hunting and bagged the observation that while the idea of using machine learning to model the impact of a given player action to his team’s chances of scoring and conceding (and then adding all those up to determine how much a player contributes to his team overall based on his on the ball actions) is useful, there appear to be some players who consistently impact the g+ values of others in positive or negative ways. Famously, Darlington Nagbe in MLS has middling g+ values for a central midfielder (based on the model, his individual on-ball events don’t have significant impacts on his team’s chances of scoring goals), but he has consistently elite “g+ boost” values — that is to say, when he completes passes to teammates, those teammates in turn generate more g+ on their next action then they otherwise do when other teammates are passing to them in similar situations. Nagbe boosts his teammates ability to themselves increase the team’s overall chance of scoring (and not conceding) on possessions. Who really is “adding goals” and in what proportions to the other?

If your model of team effects does contemplate teammates in this way and perhaps it should, your projection of a target player’s contribution rate is exposed to changes in these team effects as the projected minutes of all the various players change, for instance when a new player joins the roster and starts stealing minutes off of others.

This is solvable though! Right? I think it’s solvable.

Gentle Suggestion for Projecting Opportunities

I don’t build models and my math is just OK, so someone else needs to solve this, but my recommendations for how to model projected opportunities include the following starting points:

  1. Perform an analysis of distributions of minutes for roster slots across all teams in your league as far back as you feel comfortable. This is almost a “minutes concentration” analysis at first. By position (use whatever yardsticks normally use for this), come up with the average minutes for the starting striker(s), the starting wide attacker(s), the starting central attacking midfielder, the starting central midfielder(s), the starting fullback/wingbacks(s), and the starting centerback(s), and punt goalkeepers into space - who cares for this exercise. And drag this down for all the depth pieces too (the backup striker, the backup wingers etc), until you end up with the sum total of all the minutes played distributed out to the "depth chart slots” on a roster.

  2. Perform this same analysis for your own club for as far back as you’d like, or for your current manager as far back as you’d like.

  3. Using some weighting of the above two (league average distributions and team average distributions), come up with the basic expectation for number of minutes in a season for each “roster spot” clunkily defined as the unit of account of a depth chart, these roster spots being agnostic as to who the actual players are. Through the process of averaging all of this data, the result should have “normal injuries” essentially baked into it (i.e. you’ll avoid just forgetting about the normal slippage of injury absence and suspension absence and substitution/rest absence).

  4. Assign the players on your roster (or the players you expect to be on the roster) to these spots based on what you expect to be the manager’s preferences (speak to him if you must :)). This will create natural differences between the minutes a player played last year and the minutes you’re expecting of him this year. Doing so will naturally hedge against the temptation to accidentally carry forward one-off impacts to a player’s health from season to season, and instead to base some critical decisions for the club on a more measured base of available minutes.

  5. Steps 1-3 can be automated, and step 4 requires judgment based on intimate knowledge of the current roster. Step 5 is to make certain discreet adjustments where absolutely necessary. For instance, players who you know are undergoing serious surgeries (ACL MCL etc) that will keep them out for large chunks of the season, go ahead and discreetly reduce their minutes and/or assign them lower depth slots on the average minutes distribution.

  6. To cast your gaze out multiple years (which I’d suggest you might need to fully value a player’s potential “contract,{ you would want to apply these steps with increasingly broad assumptions. Many current players may no longer be mappable at all to these slots beyond 1 year out, and you might be using placeholders players you would intend to sign. You might move players up and down a roster spot (and thus estimating more or less minutes respectively) based on their projected contribution rate growth that stems mostly from the development/growth layer we discussed previously.

  7. Once you build up this environment of distributed minutes/opportunities, you can play with the impact of swapping one player’s contribution rate in for another (a transfer!), measuring the marginal impact of that player’s contribution by multiplying his projected contribution rate(s) by his expected minutes, and then cascading the impact of this depth chart change to the rest of the team along similar lines.

  8. (Optional) To the extent your projected contribution rates are dependent upon the interaction between specific players during a game — this idea of a g+ boost— the modelling of the above Step 7 “swap out” might be quite complicated and iterative as each change in minutes/opportunities changes the opportunity for the various boost effects to play out. I don’t have the expertise to model this or even to articulate how this should work exactly, but hopefully this sparks something for someone out there.

If you attempt this feat and come out the other side successful, you will have successfully modelled out a projection of the marginal impact of a target player signing that is broken down both into his marginal goal contribution rate and his projected opportunities to contribute, together forming his projected total contribution to the team’s marginal goal difference. Moreover, by placing his addition into an otherwise coherent depth chart system, you’ve gleaned the “marginal” impact of this move to the team’s goal difference as a whole. You have contemplated his contributions plus the residual effect on the contributions of others based on his presence minus the contributions of whoever he replaced (or however this cascades down the depth chart) minus those other residual effects on the contributions of others, and so on to infinity.

Said another way, at this point you will have successfully projected the increase or decrease in your team’s marginal goal difference from signing the player. You have completed all 5 steps (and the many phases and layers within them) of projecting player performance.

Looking Ahead

If you read the opening pre-ambles of these posts rather than skipping them (not pointing fingers), you will know that now that you have this player projection in-hand, the next step will be to benchmark it against readily available alternatives in the market. There are several interesting choices that face us as to how exactly to accomplish this, and that feels like the next post, or one of the next few posts. As always, thanks for reading and sharing. Thank you for your patience.

If you’re trying to remember or imagine for the first time where exactly the posts go from here in bullet point form, it’s something like this:

  • Taking the projections and use some concept of a discount rate or required rate of return to benchmark the projections against those attached to other available player contracts

  • Putting it all together to calculate the “value” of a player contract as denominated in marginal goal difference.

  • Converting the “value” of a player contract denominated in “marginal goal difference” to the “value” of a player contract denominated in allocated budget resources.

  • Taking this “value” denominated in allocated budget resources and trying to clear a transaction on the actual transfer market. This involves negotiating a player wage and/or a transfer fee with his existing club, if applicable.

  • Taking everything we’ve walked through and pausing to consider the macro team-level vision of “Absolute Unit” as a functioning holistic player recruitment/transfer strategy/squad building system.

  • Taking the macro-vision of “Absolute Unit” at the team-level and extrapolating it out to all clubs operating in a global transfer market, to understand and abstract theory for what the transfer market is, how transactions clear, what transfer fees are and are not, and what we can learn from this as it relates to transfer fees in relation to player wages, transfer budgets, and marginal goal difference contribution.

  • We absolutely will spend a post or two on Major League Soccer specifically, which operates within such an unusual monetary situation compared to the rest of the global transfer network.

  • Assorted topics I meant to cover but skipped (e.g. plenty of applications of the team-performance model, or reactions to recent applications of this model or lack thereof).

Happy Holidays!

Appendix: The Opportunity of a Set Piece

I think way back in Step 2 of the Five Steps of projecting player performance, when we were stripping out noise from the underlying accounting records we got from step 1, we talked about set pieces:

Similarly, when a direct free kick is awarded 20-25 yards from goal, the player who stands over the ball, ready to shoot on goal or create an opportunity for a teammate via delivery into the box, has also himself not “shaken a defender” or “found space” or “received the ball,” nor does he “pick out a pass” or “get off a shot” on his subsequent dead ball attempt. For similar reasons as the above, these accounting records should be stricken or at the very least quarantined from the data as part of our Pro-forma adjustments in Step 2. We want the good stuff. The open play stuff.

You may already have a penalty kick taker or free kick taker on your team, or the target player might take on that role, but your team might find itself experiencing far fewer penalty kick or free kick opportunities than the target player’s current team. These things will need to be projected wholly separate from the target’s player ability to increase his team’s chances of scoring from open play. Same goes for corner kicks. In general, when forecasting a team’s performance and managing towards an objective of “goal difference,” the GM should project his team’s open play expected goal difference, including its ability to win or concede penalties, win or concede set pieces, and win or concede corners (each of these having an impact on the likelihood of scoring). And then separately it should project it’s teams marginal expected goal difference from penalties, set pieces, and corners over and above the expected amounts “won” in the open play forecast.

Well, theoretically now would be the time to add back in the effects of set pieces when appropriate. Basically we’ve quarantined the open play ability and the open play opportunities somehow, but if the target player we’re after is good at direct free kicks or corner kicks for instance, we should place him into the direct free kick taker role based on our expectation of him winning that role — or more precisely we should allocate to him some share of free kick attempts based on our judgment of whether or not he will actually take them, and then apply a separately observed/calculated/judged free kick ability rate to the number of opportunities we project he’ll experience over his contract term. I don’t want to belabor this point, just wanted to close the loop since we took dead ball stuff off the table earlier. You would add it back in based on its own separate “opportunity” projection. There.