The Early Bird Gets The Turd - Analysing Early Transfers

Let me transport you back in time...

A richer time, when discourse was filled with hope and optimism for the promise of a better future that was ultimately never fulfilled. A time when dinosaurs walked the earth.

A time when Jarrod Bowen cost 7.9m to own in FPL, and Manchester City vs Watford held the record for the highest-xG game in Premier League history.

New Year's Eve 2023.

I've taken you here to perform a real analysis of the value of early transfers! And I think I'll attempt to convince you why - in my opinion - much of what you think you think about them is (probably) wrong.

Fantasy Football Trout

@FF_Trout

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I have some thoughts on this (will share) and I'm interested in hearing where the consensus lies: For most teams, transferring Salah -> Bowen before price changes (and before LIV vs NEW, WHU vs BHA, and FA Cup matches) on 31st December was...

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#The Situation

As I lace my boots and prepare for a hard night of boozing, my FPL team looks like this:

Being addicted to FPL as I am, I can't help but delay my outing to run a few dozen fairly heavy stochastic solves across DGW scenarios for GW21 moves. With Salah off for AFCON, and Haaland returning to fitness in the next 2 GWs, several obvious candidate moves emerge:

Any of these moves can be combined with J.Alvarez -> Haaland in the case the Norwegian was confirmed fit for GW21.

Salah -> Bowen is, according to my solver (and therefore according to me), the best move. Bowen is expected to rise in price a couple of times before the GW21 deadline, and Salah to fall a couple of times, so a permanent team value swing of 0.2m is probably on the cards. I also notice in my solves that Salah -> Bowen almost always remains part of the optimal combination of present moves regardless of injuries (and many combinations of injuries) to relevant FPL assets (excluding, of course, Bowen himself).

Given what we know here, can we measure the justification for going early?

#The Approach

As far as I'm aware, there is no good framework for precisely estimating the EV (expected value) of an early transfer.

In the above formula, if $\textrm{EV}_{\textrm{Early Transfer}}$ evaluates to $>0$, the early transfer can be considered worthwhile. While true, this formula is not very useful, because the value of information is very difficult to quantify.

However, if we can put an upper bound ($\textrm{UB}$) on the value of information, we can produce a lower bound ($\textrm{LB}$) on the value of an early transfer:

Again, if $\textrm{LB}_{\textrm{Early Transfer}}$ evaluates to $>0$, the early transfer can be considered at least worthwhile. This formula is more useful, because we can often bound the value of information from above.

#The Value of Team Cost

To calculate the value of gaining team value, we can study how many more points we can expect to score with more team value, and measure the marginal value of added value:

Right now, the marginal value of added team value is about 0.3 points per GW for each additional 1m. This number has remained pretty static through the course of this season, so I think it's pretty reasonable to assume it will hold.

We expected to permanently gain at least 0.2m from making the Salah -> Bowen move early, and there are 18 GWs left of the season.

In total, we expect to gain at least $0.2 \times 0.3 \times 18 = \bold{1.08}$ points from the early transfer.

#The Upper Bound of the Value of Information

An upper bound for the value of the information we're losing by making the early transfer is the number of points lost in the worst-possible realisation of information at the GW21 deadline, multiplied by an upper bound for the probability of any information realisations at the GW21 deadline which exclude Salah -> Bowen from the optimal set of transfers.

#How often can we expect a bad realisation of information?

As I mentioned in my description of the situation, I notice that Salah -> Bowen appeared in plenty of plans containing injuries and combinations of injuries to relevant FPL assets.

Obviously, we don't want Bowen if he gets injured. So what is chance he does get injured?

Well,

So, Jarrod Bowen has been unexpectedly absent for 83 days of football in the last 6 seasons of football. The football season is about 9 months long, so that's about 5% of the time.

You could argue that the probability he misses GW21 is lower than 5%, because he is not currently injured and there is probably a 14-day rest between West Ham's FA Cup tie and their GW21 fixture. But we're after an upper bound here, so let's say it's not just not lower than 5%, but in fact 10%, since Bowen has played more minutes than usual in the last few months.

Besides Bowen, there are some combinations of injuries that exclude Bowen from the optimal plan. For example, if two important defenders get injured, or both GKs get injured. Again, let's be very generous here since we're after an upper bound, and again say there is a 10% chance of other injuries that would drive us away from the Salah -> Bowen path.

So, in total, the upper bound we'll use for the probability of a realisation of information bad enough to deter us from Bowen is about $1 - (1 - 10\%) \times (1 - 10\%) = \bold{19\%}$.

#What is the worst possible realisation of information?

The worst-case scenario is that we have to immediately revert the Salah -> Bowen move, with a hit. This will cost us 4 points, no more, no less.

So, a reasonable upper bound for the value of information lost is $4 \times 19\% = \bold{0.76}$ points.

#Summary

Let's go back to our equation for the lower bound of the value of the early transfer:

This suggests that on this day - New Year's Eve 2023 - the early transfer is not only justifiable, but probably the "correct" decision - if you agree with my definition of "EV-optimal" decision.

This analysis contains some flaws & limits:

• EV movement can occur before the GW21 deadline for reasons besides injuries, such as position changes or more marginal xMins changes. This is not accounted for.

• This applies to my team only. Planning to hold only one player from Liverpool, Brighton, and Newcastle in GW21 helps to minimise the risk of combinations of injuries that radically alter the optimal plan. That said, I think that a sufficient amount of the above analysis holds for almost any manager who considered moving early that I would find it difficult to call it an objectively "bad" move for any team.

#So, What Did I Do?

I didn't have time to think this out, so I decided instead to leave my bedroom and get a life.