Opportunity Cost and Probability In FPL Decision Making

In this article, the brilliant  Wee Rogue on twitter – pens a guest piece for us as part of our Analysis series.

So far, this has included a top piece on Team Analysis by Tom Campbell, and Tom’s work on Talisman Theory and Overmanagement

As an exercise which, at its core, centres on the optimal allocation of scarce resources and the ability to identify efficiencies ahead of the market to establish a comparative advantage, FPL is well suited for discussion in the language of Economics.

As FPL managers we seek to ‘produce’ points, and the scarce resources we have with which to achieve this could be Money Available, Free Transfers, slots in our team, Captaincy or ‘Chips’.

Wherever there is scarcity, there is choice.

Wherever there is choice, there is Opportunity Cost.

Defined as “the value of the next best opportunity foregone” (or “the cost of the next best thing”, as my High-School Economics teacher put it), Opportunity Cost is a fundamental Economic concept which is helpful in the making and evaluating of decisions.

Tom also wrote about the qualitative side of Opportunity Cost in his Overmanagement piece, which you can find here.

Impact On Decision Making

To illustrate some examples, a simple look at Cost vs Points per Match for the 18/19 season shows a naturally occurring Pareto Efficiency Frontier (red line); this resembles an Economic ‘Production Possibility Frontier’ and shows the limits of your production (points) capability relative to your investment.

If you want to score more points, you need to spend more money; if you need to spend less money, you need to accept fewer points.

The two Liverpool full-backs (green dots) represent outlying efficiencies, which should be taken advantage of.

They are beyond the bounds of what is typically possible elsewhere in the market.

However, this requires using two out of three Liverpool slots and so the Opportunity Cost of picking both might be having only one remaining Liverpool slot available for an attacker. It might be difficult to spend your money on the remaining premium players without sacrificing more efficiency than is optimal.

The blue dots represent an inefficient use of resource; elsewhere you can either spend less for the same return, or achieve a higher return for the same spend. However, due to the rules of the game, some of these players will be required to fill our squads.

The Opportunity Cost of, for example, choosing all five DEFs which are on (or above) the Efficient Frontier is that you may have spent too much of your budget to then be able to afford the optimal attacking players.

Often in FPL, our decisions might come down to whom we are most willing to live without – choosing “the hill on which we are prepared to die” – this is equivalent to recognising those choices where the Opportunity Cost is smallest.

Probability and Expected Value

Whether we are conscious of it or not, it is my belief that we are all using quantifiable probabilistic determinations to help with all of our decisions in FPL.

Consider these two common examples:

  • I think player A has a better chance of outscoring player B, so I bench player B.
  • I think player C will outscore player D by more than 4pts in the next few weeks, so I transfer in player C for a hit.

Implicit in each of these is the idea that we have evaluated (at least) two things: the value of the choice we eventually make and the value of the main alternative – the Opportunity Cost.

Having a solid, objective idea of what we are passing up when making a decision is a great place to start.

In Probability Theory, when you analyse the range of possible outcomes for an uncertain event and assign probabilities to each in order to find the most likely ‘average’ outcome, you create an Expected Value (EV).

In the FPL Community, there are plenty of resources which do exactly that, using probability modelling (via Bookie Odds or otherwise) to create EV projections for upcoming FPL Points.

Random Chance & Variability of Outcomes

EVs can be extremely helpful.

I personally use them for all of my FPL decision-making, but even they conceal the rather wide distribution of possible outcomes that could occur in any given match.

Take for example Mohammed Salah in 18/19: he put up season-long averages of 0.6 xG90 (Expected Goals per 90 Mins) & 0.3 xA90 (…Assists).

Therefore, for an average fixture, he would have the following Probability Distributions for Goals, Assists & their corresponding FPL points:

We can see that despite Salah’s known prowess, the single most likely outcome is that he registers zero goals or assists (i.e. he “blanks”), with a ca. 40% chance. The flip-side of this is that there’s a 60% chance that he registers at least one return and it turns out there’s more than a 20% chance that he gets a double-return or better.

Looking at the Cumulative Distribution Function for his expected FPL Points from Goals & Assists only, showing the probability that he scores ‘this many points or less’, we see there is a >50% chance that he scores three or less attacking points in an average match.

That would mean that transferring Salah in for a four-point hit for a playing midfielder with no attacking threat (think Dale Stephens’), would pretty much be a coin-toss as to whether it pays off over a single Gameweek.

This all helps to illustrate the high-stakes gambles we are forced to make with premium players, weighing the Opportunity Costs of, for example, sacrificing quality in the rest of our squads to hold multiple Premium assets, or when ‘Captaining’ a particular player over another.

The bulk of the likelihood is that they either do nothing or achieve a modest return, but there is a very long tail of non-zero possibilities for huge hauls, ‘Black Swan’ events, which are very hard to predict with accuracy.

I relate this to the adage of advising against ‘sideways moves’, where we transfer broadly equivalent (fit-and-available) players for one-another: the often overlooked Opportunity Cost of using some of your scarce resource in this way – a Free Transfer, or even a Points ‘Hit’ – is that you forego the points of the departing player, whose chance of an explosive return is unlikely to be very different to his replacement’s.

Conclusion

In future articles we might explore how these concepts can be applied to the Evaluation of our Decisions: helping us Learn from Mistakes & separate Luck from Skill to avoid some of the pitfalls we can so easily fall prey to.

For now, though, hopefully this article has served as a good introduction to how applying some concepts from the fields of Economics & Probability Theory can help us to make better decisions through increasing our understanding of the value in the options we are passing up – the Opportunity Cost.

(caveat: this articles condenses complex concepts into bitesize chunks – there is obviously far more depth and detail to the concept, with reams of academic and practical theory that informs what is reported here)