Brief Thoughts on Marginal Utility, Marginal Cost, Certainty and Roster Construction

Robert Cianflone

One of the things that actually writing this out instead of idly ruminating has done is made a couple of connections to other concepts.

Diminishing Marginal Returns

Every footballer is measured by the number of goals either, prevented or scored, that they contribute to the team (yes, I know there are interaction and partnership effects--I don't know of any models, proprietary or otherwise that can disambiguate this). In economics, one of the first things that students are taught is that the cost of marginal improvements (that is, how much it costs to add one additional unit of production) rises as production rises. Producing each extra unit usually costs more than the last one once you're far enough along the marginal cost curve.

If we're talking about the top-end of football roster construction, I suspect we can safely assume that adding extra goals has an increasing marginal cost, i.e. it costs more money to move to from n+1 goals to n+2 goals than it would from n to n+1.


One of the things that’s tough about measuring footballers is that, as alluded to above, in a fluid game with eleven contributors on each side it’s tough to separate who’s driving the play. It’s made even harder that some players play so many of the available minutes; it’s hard to tell how valuable, say, Xavi is because he’s on the pitch so frequently that it’s hard to get a decent sample of what his teammates look like without his influence, and those samples are normally against markedly inferior opposition. He doesn’t score a ton of goals, just runs a lot and completes a lot of passes. He wins possession back and keeps possession extremely well, but how much is that worth, in terms of goals? Clearly it’s a lot—his influence on the game is undeniable when he’s playing. How much though? Even if we developed a model for touches or passes weighted on the location of the field, like Gabe Desjardins did, there’s still a lot of uncertainty.

Strikers, on the other hand, come with less uncertainty—they either put the ball in the net or they don’t. It’s not no uncertainty, just less. Edinson Cavani has a very strong history of production in both goals and the underlying numbers that normally indicate future goals are coming—barring catastrophic injury, we can be pretty sure he’s going to continue putting up excellent numbers for at least three more years.

Risk Premium

More certainty means less risk on the return of the asset, which usually resolves as a higher price. That makes sense—there’s less expectation of a bust, so they buyer needs to hold less in reserve in case of that eventuality.

Combine the certainty of Cavani’s production over the last few years and his position (the easiest to evaluate with certainty) and that’s going to drive his price up. Not only is the ability to score goals rare, it’s relatively easily discernible—the combination of scarcity and certainty makes the price of strikers what it is in comparison to other positions, I think.

Team Construction

So once we’ve accepted that each player is worth some number of goals over the course of the season within a fairly large margin of error, we can identify which players we think are relatively weak at their positions. Using this framework, the approach is fairly obvious—identify the position at which marginal goal upgrades are cheapest, and upgrades are most available.

David Silva, Sergio Aguero, Vincent Kompany, and Yaya are probably all in the top-15 in the world at their respective positions. Upgrades are very expensive when they’re available at all—how many players in the world are clear upgrades on each? I can only think of a few at each position (and only Thiago Silva for Kompany).

To that end, premium players at the positions those players play don’t make a whole lot of sense as targets for City. Going into this offseason, I probably would have wanted upgrades at RAMF, CDM, LB, and CAMF (assuming that Silva is drifting in from the left). Soriano and Begiristain actually did a pretty good job in upgrading those positions or acquiring useful depth, although the prices paid for some of that depth were too high (Fernandinho, Navas) for my taste. That said, because of their record of production, their certainty of production going forward is higher than it would be for younger prospects and players, which means a price increase.

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