Was England right to not try?
England fielded a lesser squad today in their World Cup match with Belgium (so did Belgium). They also lost. Both teams were already assured of qualification to the knockout round. It was known in advance that the loser of the match (as it turns out, England) would face a more formidable team (Colombia) in the round of 16 but likely an easier team (Sweden or Switzerland) in the quarterfinals, should they get there.
So, it’s a simple problem. Suppose their objective was to maximize the probability of making the semi-finals (something they have not done since their sole World Cup victory in 1966). Did they make the ‘right’ decision?
Assumptions:
- The World Football Elo Ratings model accurately measures win probabilities for all World Cup teams
- (Implicitly) Those probabilities accurately account for winning on penalties (this is likely dubious).
Then it’s true that Japan is much easier to beat than Colombia. England should beat them roughly 80% of the time, compared to 51% of the time versus Colombia. However, in the next round, England would have either a 54% or 60% chance of beating Switzerland or Sweden, respectively, compared to a 24% chance of beating Brazil.
Of course, Brazil could lose to Mexico, and these scenarios are not all equally likely. If we do the mildly tedious calculations, then in the current situation (facing COL and SWE/SUI), England has a 29% chance of making the semi-finals. In the alternative world where they beat Belgium (and thus would face JPN and BRA/MEX), they have a 24% chance of making the semi-finals.
Was it the right decision? Who knows? Does it pass muster, on first glance? Yes.