Game Theory: The Case for Villa Selling off Youth Players

My previous game theory posts (“The Logic of Not Caring About the Champions League” and “EPL’s Treatment of Europe is a Tragedy (of the Commons“) were well-received, so I thought I’d put together another one related to a topic on my mind that may get a fair amount of attention when transfer rumor season starts. Aston Villa is currently involved in a serious relegation fight, that has seen their odds of relegation increase to almost 70%.  The heat map below shows how their odds of getting relegated have increased over the season, especially in the last couple of weeks.
Heat Map Aston Villas Finishes

I’ve run some analyses to see exactly where Villa’s best opportunities for growth are, and they all point to Jack Grealish being the biggest opportunity for them. The average gain in his position is a  very solid 5 points, and the maximum gain is an astounding 20 points. Grealish may be a future Aston Villa and England star, but my model think he’s holding them back significantly today. But how do we know if it’s time to sell?

The immediate calculation is fairly easy and straightforward:

EV(Keep Grealish) = Pr(Staying in the EPL)* (Total Revenue from being in the EPL)  + Pr(Relegated)* (Total Revenue from the Championship)  – (Money spent improving the squad)

EV(Sell Grealish) = Pr(Staying in the EPL) * (Total Revenue from being in the EPL) + Pr(Relegated)* (Total Revenue from the Championship) + (Money gained from Selling Grealish) – (Money spent replacing him)

Then all you’d have to do is compare the two numbers: If EV(Keep) > EV(Sell), then you keep him. If EV(Sell) > EV(Keep), you sell him. Assuming net transfer spend in both situations is the same, the equation comes entirely down to what Aston Villa believes their chances of staying in the EPL is with/without him. If you believe my model, the chances improve significantly with the right replacement (many of whom are in Aston Villa’s buying range at first glance), therefore EV(sell) is much greater than EV(keep), meaning that it’s time to sell him.

This all assumes a one-shot game, which may be a reasonable assumption if you believe next year will be a similar fight to stay in the Premier League. I’ll post the longer version in my next post, but this illustrates the expected value calculations that teams go through on these decisions. Single-minded forsakers of relegation may have to go against club ethos and sell a young star so they can achieve their primary goal of maintaining Premier League status.

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