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STATS DROP: Round 7, 2023
Interesting looking garbage, NRL club numbers to plummet in Australia's largest city, Adam Renyolds, Bernardo O'Higgins, Form Elo, Pythagorean expectation, 2nd order wins, WARG and TPR
Welcome to Stats Drop, a weekly inundation of rugby league numbers.
One idea I’ve had for a while is to plot running metres for forwards against the minutes played. My hunch was that there was a non-linear trend that could be analysed and tell us something about the nature of fatigue and forward utilisation.
Last week, while mulling over whether Taumalolo needed more minutes or not, I went to work placing 10,000+ data points into bins of minutes, cross-analysing season by season, applying third order polynomial regressions and using calculus on the resulting trendlines to work out the rates of change. None of that, not even the calculus, is an exaggeration.
And the result? It’s all garbage. It’s interesting looking but still garbage. Sometimes, going in-depth on numerical analysis takes you down some dead-ends. The current iteration of Wins Above Reserve Grade is the third and a half-th player rating system I’ve worked on. There were Poseidon offensive and defensive ratings, which turned out to be total noise.
I produced those Taumalolo charts several times using slightly different bin widths and they all look completely different, which is not good. The curves are over-fitted for the data, which means that the derivatives reflect more statistical noise than actual signal. Doing simpler regressions without doing multiple degrees of polynomials would just mean the trend is a straight line, the derivatives of which wouldn’t tell us anything interesting (in fact, would be zero above the first derivative) and certainly don’t allow for jerk off jokes1. Never mind needing a hundred game sample size per player to do anything meaningful.
It is a trivial result that you will get more metres from forwards the longer they spend on the field. Even if the rate of accumulation can be said to be non-linear, if the details cannot be accurately and precisely derived, then there’s no insight to be gleaned about how production changes during a game.
While I think the fundamental idea is still sound, it could only potentially work with in-game data, rather than whole of game datapoints. There are still potential limitations even so, e.g. whether the sample size is large enough, whether data can be sampled frequently enough with enough game state context applied, and these may prevent this idea from coming to fruition but I could see it being handy that if you see the middles start producing at a rate below a certain threshold, you know it’s time to make a change.2 It’ll be over to someone else to test that idea out and the good news is I can stop thinking about this and move on to other, more productive areas of life.
Why bother telling this story then? When it comes to quantitative analysis, it never hurts to ask yourself how thoroughly tested the ideas are, what limitations may exist due to the nature of statistics3 and data collection, whether the author has their correlation, cause and effect in the right order, and use that to inform your reading. Some people won’t tell you what they're up to, so it’s up to you to work out how much weight to give the output of their mathematical black boxes.
I will do my best to explain How It All Works, what’s going on and why I think that it means and what the limitations are. These posts will have the same explanations under each chart each week because every post is someone’s first and I hope the context is more insightful than the equally interesting looking, equally garbage output that is ranking players by a fraction of a WARG.
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Official ABS forecasts indicate that by 2032, the NRL will go from having nine teams in Australia’s largest city to just one. It’s unbelievable that not only has the administration not responded to this impending cataclysm, they have no plan for addressing this. Unless action is taken, rugby league will lose its pre-eminent place in the heartlands. It’s not too late to consider relocations or mergers to save these clubs.
Adam Reynolds is clearing the lowest goal conversion rate in his career, dating back to 2012. So far in 2023, Reynolds is kicking at 73.0%. The NRL average of all players since 2013 is 73.6%. His next worst season was 2018 at 75.0% and his best was an astonishing 90.1% in 2013, scoring an even 100 goals. That the Broncos have only scored 17% of their tries in the middle, which is sixth least in the league, might be a factor.
Ambrós Bearnárd Ó hUiginn (“Ambrosio O'Higgins”, sa bhéarla), an Irish Catholic, was Viceroy of Peru from 1796 to 1801. His illegitimate son, Bernardo O’Higgins, became el liberatador de Chile, and later Supreme Dictator, successfully defeating Royalist forces and proclaiming Chilean independence in 1818.
Form Elo Ratings
Elo ratings are a way of quantitatively assessing teams, developing predictions for the outcomes of games and then re-rating teams based on their performance, home ground advantage and the strength of their opposition. Form Elo ratings are optimised for head-to-head tipping and tend to reflect the relative strengths of each team at that particular point in time, although there are many factors that affect a team’s rating.
Pythagorean expectation estimates a team’s number of wins based on their for and against with a reasonable degree of accuracy. Where there is a deviation between a team’s actual record and their Pythagorean expectation, we can ascribe that to good fortune, when a team wins more than they are expected to, or bad fortune, when a team wins less than they are expected to.
There’s always one or two teams each year that win more than their Pythagorean expectation and one or two that grossly underperform and it’s difficult to tell in advance which is which, but over the long run, Pythagoras remains undefeated and always demands his tribute.
Win Percentage Comparison
The black dots are each team’s actual win-loss record to this point in the season. The coloured dots represent what the stats say about your team’s underlying performance, i.e. how many games they should be winning. Wins and losses are binary and can be prone to good and bad luck in a way that other stats that correlate to wins are not, so we have other metrics to help see through the noise to good teams, rather than just good results.
Pythagorean expectation (gold) relies on points scored and conceded. 2nd order wins (silver) relies on metres and breaks gained and conceded turned into SCWP. Elo ratings (maroon) rely on the margin of victory and strength of opponent. Each metric has strengths and weaknesses.
Dots should tend to gravitate towards each other. If a team’s dots are close together, that means their actual results are closely in line with their underlying metrics and represents a “true” or “fair” depiction of how good the team is. If a team’s coloured dots are clustered away from their actual record, then we should expect the actual to move towards the cluster over time.
If the black dot is well above gold, that team is suffering from good fortune and may mean regress to more typical luck in the future (vice versa also holds). The silver dots will tend to hover around .500, so if gold is between silver and .500, the team could have an issue with executing efficiently.
This table compares the SCWP produced and conceded by each team (a product their metres and breaks gained and conceded) against the actual points the team scores and concedes to measure which teams are most efficiently taking advantage of their opportunities.
Production the amount of valuable work done by a team as measured in counting statistics that correlate with winning. These statistics are converted to a single unit called Taylors. Taylor Player Ratings (TPR) are a rate metric that compares an individual player’s production, time-adjusted, to that of the average player at their position, with a rating of .100 being average (minimum 5 games played). Wins Above Reserve Grade (WARG) is a volume metric that converts player’s production over a nominal replacement level into an equivalent number of wins they contribute to their team. While these metrics generally conform to the eye test, they do a poor job of assessing defensive qualities and evaluating some specific positions (e.g. hookers, centres).
Queensland In Focus
(As the kind of genius who worked out how to apply calculus to rugby league stats, I also successfully worked out how to combine several images into one, which saves space and means I can post all 4 Queensland NRL clubs each week, although it’s probably going to get a reformat because this was an ass pain to assemble)
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The third time derivate of position is “jerk” and while double-checking that, I found out the fourth, fifth and sixth derivates are called “snap”, “crackle” and “pop“ respectively. Physics is phun.
The other thing that works really well is looking at them and seeing if they look tired. That possibly may be a more efficient allocation of resources for NRL clubs.
If someone tells you its 3.31, the real value is more likely to be 3±1.