The holy grail of statistical analysis in any sport is to have one metric that fits all.
Not only does it fit all, but it can accurately evaluate a player’s quality. Existing examples of this from other sports include “Wins Above Replacement” (WAR) in baseball or “Player Efficiency Rating” (PER) in basketball. To date, however, no such metric exists in rugby. I wanted to change that, and so I created the “Expected Wins Contributed” (xWC) metric.
Expected Wins Contributed
To understand how xWC was devised, we must first understand a few concepts. The first of which is the key performance indicator (KPI). Just using wins as a measure of success for your sports team can be misleading. For example, Ireland’s recent win against France could easily have been recorded as a loss if Sexton had missed his drop goal. Or even if Anthony Belleau had successfully kicked his penalty. Because of this, sports teams like to measure their success by looking at the statistics that highly correlate to winning. These statistics are called KPIs.
The 4 KPIs I used for this analysis were:
- Tackle percentage,
- Metres made,
- Line breaks and
If we look at tackle percentage specifically, we can make a scatter plot with data from last year’s Six Nations. The plot shows the clear correlation between percentage of tackles made and games won.
The R-squared* for this is 0.7228, indicating a strong correlation.
* – R-squared is a statistical measure of how close data is to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression. The higher the number between 0 and 1 the more significant the correlation. Similarly, a negative number suggests a negative correlation.
We can now perform a regression analysis, which is finding the equation of the line of best fit. From this analysis, we can calculate that a simple model for predicting a team’s win is [0.3664 * Tackle percentage – 30.05]. The “- 30.05” essentially accounts for the y-intercept of the graph.
Of course, tackling isn’t everything, so we can improve our model by including the same values for all the other KPIs and taking an average. We end up with this table for what I’ll call expected wins.
As you can see, when rounding to the nearest whole number, the model correctly predicted that Ireland and France would get 3 wins each and suggests that Wales were slightly unlucky and should have possibly stolen a win off England.
But can it be applied to individual players?
Yes, but there are some important limitations to recognise before we do so. This model doesn’t consider the strength of opposition and, as such, a lot of English players will have inflated numbers this week. Also, by the nature of the metrics involved, backs are more likely to put up bigger numbers than forwards. That being said, it can still be a useful and interesting metric for the casual fan, so without further ado, here are the top players from the first weekend.
I would agree that xWC provides a fair representation of England’s key players in the match on Sunday. Do you?
I’m sure you’ll tell me in the comments.
Author: Peter Matthews
I’m from just north of Edinburgh, Scotland and I am currently studying Mathematics with Statistics. I love blending my two passions of maths and sports – mainly rugby, cricket and football (soccer) – by looking at stats and patterns in the game.