Game Theory in Rugby Could Overturn Conventional Play Strategy

Game Theory in Rugby Could Overturn Conventional Play Strategy

In many rugby games the difficult decision of what to do with a penalty arises.  There are a number of options as to what can be done in the event of a penalty including: slotting the ball if it’s on the touchline, going for a scrum, or kicking the ball into touch for a lineout.  Some of these options can post more points on the board for the team, but come with higher risk.  Therefore, this situation becomes an important decision that the captain must make for the team.

While this situation may seem to give birth to a tough decision for the captain, the statistics of the 2019 World Cup that ended last weekend may have provided some insight for a clear answer to the problem. Thanks to the release of Opta “chalkboards” that record most of the actions that occur during any given game, statistics for conversion percentages and expected returns have been released. 

The statistics show that Tier 1 teams have only allowed opponents to score on 9.8% of lineouts and 12.5% of scrums behind the 22-meter-line.  As a result, on average one scrum will earn 0.91 points and one lineup will earn 0.72 points.  The stats are almost identical for Tier 2 teams as well.  These results mean that a kick only needs a 30% conversion rate for the kick to be the best option that will yield the highest expected score per attempt.  This is an interesting point because only 5 kicks out of 460 have fallen below the 30% threshold.

If we were to look at this situation through the lens of a game theorist, it would be evident that kicking is the dominant strategy when given a penalty.  The kick will yield the highest expected return for the team, and give them the best shot at winning regardless of the opponent’s actions.  The strategy to kick on every penalty is good in theory, but would also take away any threat of a different play and certainly would not please fans looking for action.  So while teams should account for mathematical expected returns when choosing plays, they must also account for the predictability of their play calling.

Therefore, game theory can be an important piece of making tough decisions in a high-stakes games.  It can help players understand which decisions are most likely to create a winning outcome; however, following game theory blindly is not the answer either, as it would create a predictable team offense that is more vulnerable to the opponent’s defense.