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Incentives in Olympic women’s hockey: the last group matches

Is there an incentive to lose in the final group play matches here?

In the wake of four badminton pairs having been disqualified from the Olympics for trying to lose their game, the way the Olympic women’s hockey competition is shaping up is quite interesting.

At time of writing, there was the last match-ups in group A, and Argentina vs Australia in group B, left to play. Australia qualifies first if they win; Argentina qualifies first otherwise (including tie). New Zealand will qualify second either way (if AUS/ARG draw then NZL is second on goal difference). Whoever of Argentina and Australia doesn’t progress gets eliminated, so no weird incentives there.

For group A, I’ll explain the scenarios from the view of each country but it’s easiest to start with a table. Current standings in group A are: NED 12, GBR 9, CHN 7, KOR 3, BEL 2, JPN 1. In each cell, the first country qualifies as top of the group. The China–Japan game is before the Netherlands–Great Britain game.

  NED win tie GBR win
CHN win NED
CHN
NED
CHN*
GBR
NED
tie NED
GBR
NED
GBR
GBR
NED
JPN win NED
GBR
NED
GBR
GBR
NED

* China qualifies ahead of Great Britain as the winner of the match between them.

China must win, not tie, in order to stand any hope of qualifying. Japan, on the other hand, has no self-interested incentive to win. So China’s got more to play for than Japan, so they should win, unless Japan for some reason cares about whether China or Britain qualifies. (Anyway, Japan’s currently bottom of the pool, so it’d be a gigantic upset if they won.)

The Netherlands will qualify for a semi-final no matter what, so you might say less is at stake for them.  They’re playing to qualify top rather than second (a tie will do), which I’ll address later.

Great Britain, on the other hand, has everything to play for. If China wins against Japan, then a tie won’t cut it for Britain: they must win to advance to the semi-final. If China ties or loses, then Britain and the Netherlands are just playing to qualify first rather than second.

So for the Netherlands, and for Britain if China ties or loses (unlikely), the two are playing to determine the ranking between them. In theory, they should both want to win, since qualifying first means they’ll face the runner-up of group B rather than the winner, i.e. get the easier game.

In practice, they might trust other things about their potential match-ups over the group play results. The group A runner-up faces whoever wins of Argentina and Australia. (This is the last group match, so Netherlands and Great Britain won’t know which one it is when they play.) So, if Netherlands and Great Britain would prefer to face Argentina or Australia than New Zealand, there’s an incentive to lose.

What might they prioritise? If it’s Australia, they might note that New Zealand beat Australia in group play (Australia will still qualify first on total points), or that New Zealand currently ranks ahead one place ahead of Australia in the FIH World Rankings. That might then be an incentive to lose. But remember, they don’t know if it’ll be Australia or Argentina. If it’s Argentina, they’re almost certain to prefer not to face them, given that Argentina are reigning world champions, second in the FIH rankings, and beat New Zealand in group play.

Let’s assume, for the sake of the argument, that Australia is a preferable (i.e. weaker) opponent to New Zealand. There are two things to take into account: the probability that Argentina (or Australia) will win, and the margins by which Argentina is less preferable (stronger) and Australia more preferable to New Zealand. Argentina is probably more likely to win, and the ARG>NZL margin is probably bigger than the NZL>AUS margin. Both of these factors make it better for Great Britain and the Netherlands to win their match against each other to book a guaranteed place against New Zealand.

So in the women’s hockey competition, even if we ignore the group rankings themselves and look elsewhere to weigh up opponents (an approach which I rejected in my post on badminton), none of the remaining matches seem to give any team an incentive to lose.  Sorry the result of the analysis wasn’t more exciting, but at least we know the games will be!

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