Road to Rugby World Cup 2019: Rugby scores decomposition

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With the Rugby World Cup 2019 Japan starting on 20th September, I thought I’d take a look at the tournament from a few different statistical angles. For this post I’ll be looking at the problem: given a rugby score, how can we decompose it into possible combinations of tries, conversions, penalties and dropped goals?

Context

I have a dataframe of results for almost all professional and international rugby union scores since the 2012/13 season, more than 10,000 matches. This is nice in terms of ‘breadth’ of the sample – however in terms of depth it’s a bit lacking! For each result I only have home/away team and home/away score, for example:

27/07/2019  New Zealand  South Africa  16  16

I was curious: is it possible to decompose the results into valid combinations of scoring methods? Then, perhaps as a second stage, estimate the probability of occurrence of each combination for a given score? The first question I will be looking at in this post, and the second will be next up in the series!

I’ve never seen a match of rugby before! What are the scoring methods you’re referring to?

TRY (5 points): awarded when an attacking player grounds the ball in the area at the end of the pitch (“in-goal area”).

CONVERSION (2 points): the team who has scored a try immediately gets to kick at goal for another 2 points before kick-off restart.

PENALTY GOAL (3 points): when an infringement is made, a penalty may be awarded to the other team who may then choose to take a penalty kick at goal.

DROP GOAL (3 points): a player may, at any time in play, drop-kick the ball over and between the posts.

PENALTY TRY (7 points): if a foul has stopped the attacking team from scoring then a penalty try is awarded, worth a full 7 points. Note: these happen fairly rarely so I include this just for completeness but don’t refer to penalty tries hereon.

I took the videos above from World Rugby Laws of the Game which is a great resource if you want to learn more about the laws of the game.

Grouping the Elementary Scoring Methods

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