Game Theory: Rotate or Full-Strength Squad in the League Cup Round of 16

Building on my previous “Game theory” post about how it’s rational to play a weaker squad in the Champions League compared to the EPL, I wanted to walk through the logic of doing so in the League Cup Round of 16.

The general idea is the same: you rotate if immediate results in the league are more important to you, you play a full-strength squad if the cup is more important to you. This is mitigated by several factors:

  • Your odds of winning today’s match with a full strength squad vs. rotated squad
  • Your odds of winning the Cup
  • Your league position relative to where you want to be/can you risk losing points this weekend
  • Psychological benefits

So I wanted to walk through the logic for a couple of teams playing today to see what the rational choice would be.

Leicester City

Leicester City has been over-achieving in the league, with 19 points through 10 games as of today. You’d have to think they would have been ecstatic with a mid-table finish at the beginning of the season, so they’re over-achieving by any measure.  They can afford to drop points this weekend in the league.

Similarly, they’re playing a weaker opponent they’d be expected to beat in Hull City. Rotating the squad could make a significant difference there, but if they play a full strength squad they’d be significant favorites, even on the road.

Their odds of winning the cup aren’t great, but a lot of that depends on the draw and what Arsenal, Chelsea, and the two Manchester teams plan on doing.

The psychological benefits of making a run in a tournament like this, and potentially getting  a game at Wembley and winning a trophy could be huge for a team like Leicester.

Based on these factors, my “model’s” prediction would be a full-strength squad, or close to it.


Arsenal have to be considered heavy favorites over Sheffield Wednesday, but this is also likely true for a rotated squad. A team the size of Arsenal should be able to play their second best XI and beat Sheffield Wednesday.

As one of the top teams in England, Arsenal have to be considered one of the favorites to win the Cup. However, they’re probably co-favorites with Manchester City, Manchester United, and Chelsea (if Chelsea ever gets their act together…).

Arsenal’s league position is roughly where they want it,  tied with Manchester City at the top of the league. However, because they’re tied they don’t really have any room to spare and can’t afford to take any risks in the league if they want to mount a serious title challenge. And because they’re Arsenal, they may want to be extra careful to avoid tempting the fates.

Psychological benefits are minimal – a loss with a rotated squad to Sheffield Wednesday would get a couple snickers in the papers tomorrow, but no one would actually think badly of them if they lost. Similarly, they’ve won the FA Cup two years in a row so there’s no burning need to win a lesser trophy anytime soon.

Prediction: Arsenal rotates.


Chelsea is a tough case.1 They’re playing Stoke, so they should be favored fairly heavily. That being said, they’ve been playing well below form so maybe a full-strength squad doesn’t win today. You’d struggle to assign a win probability to them right now, so that’s tough. That being said, Stoke’s a good enough team that they should be able to beat Chelsea’s fully rotated squad.

Also, who knows what Chelsea’s odds are of winning the tournament? They beat Arsenal earlier in the season, but that looks more and more like a fluke with every game that passes. You’d have to think they’re not favored over either of the Manchester clubs right now, nor would they be favored over Arsenal. A win today likely just gets them a tough game next round and an exit by the semi-finals.

Chelsea’s league position is abysmal by their standards (15th through 10 games), and clearly they can’t afford to lose any more ground if they want to keep their chances alive for a 4th place finish. The league is clearly the priority right now.

Psychological benefits: these are tricky. They could use a win right now to maybe build some momentum, building #confidence in the locker room and among the fans. Mourinho is clearly trying to fix things on the fly (see Mike Goodman’s great piece on this ), and he could use some reps with some new tactical tweaks in a setting where there are no real consequences. Mourinho presumably could use a win to get some pressure off of him, especially given the rumors that he might be on his way out soon.

Prediction: tough to call, but the psychological benefits might outweigh other considerations.

  1. Spoiler alert, they played a full-strength squad

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