If you’d like to skip the explanation and see the full list of StatScores and Win Shares, you can go to this Google Sheet.
The biggest off-season story in the NRL was the transfers of Cooper Cronk from Melbourne to Sydney and then Mitchell Pearce from Sydney to Newcastle. From the Roosters’ perspective, for two players likely on similar pay packets, how did the Roosters decide one was better than the other? Then I wondered if it were possible to work out a way of judging value for money in player trades. It’s big in baseball, so why not rugby league? This led me to develop StatScore and Win Shares as ways to numerically evaluate rugby league players.
If you’re wired for numbers, like I am, it can be hard to deal with people’s feelings and understanding why they think the things that they do. That’s why I’ve decided to quantify the feelings a team generates into five distinct indices: Power, Hope, Panic, Fortune and Disappointment.
Each index has two components. There’s a main mechanism for ranking the teams and some minor tie-breaking stats. The main mechanism typically uses Elo ratings to make an estimation of what we expect from a team, whether or not they are meeting that expectation and what that means for the season ahead. The tie-breakers are statistics used to award a few points here and there to help rank the teams should they have similar mechanism results.
Editor’s note: As much of last season’s material was influenced by The Arc, much of this season’s material owes a debt to SB Nation, including the idea of panic/hope indices.
The Greeks is the collective name given to a series of Elo rating models for tracking performance of rugby league teams and forecasting the outcomes of games. I usually refer to them as if the philosopher himself was making the prediction, even though the Greeks have mostly been dead for a couple thousand years and certainly would never have heard of rugby league or Arpad Elo.
The differences between each Greek are on the subtle side, with the intention of measuring different things. You may want to revisit primers from last year:
While the recent RLWC was on, I couldn’t help but notice that the RLIF had Scotland pegged as the world’s fourth best team. Scotland hadn’t won a game since 2014 and even that was against Ireland. Since then, they’d lost to Australia, England, Ireland, Wales and France. I also got frustrated because a fifteen second Google didn’t reveal how the rankings are actually calculated.
So I figured I could come up with a better system. I did and this is how the Pythago World Rankings (PWR) work.
The Collated Ladder takes in two inputs:
- The projected number of wins for each club from the Stocky
Put simply, the Collated Ladder is an average of these two numbers, with a 2:1 weighting towards the output of the Stocky, rounded to the nearest whole number.
The Ladder is then based on sorting each team by its Collated number of wins, then by its Pythagoras projection, which is a loose analogue for for-and-against (the greater the number of wins projected, the better the team’s for-and-against will be).
Why bother with this if both systems have limitations and inaccuracies? Aren’t we just compounding that?
The Stocky, which is short for stochastic simulation, is a Monte Carlo simulation of the season using Elo modelling to work out what the outcome of that season might be.
The basic premise of a Monte Carlo simulation is that if you have a few pieces of the puzzle, an idea of how they relate and then throw enough random numbers at it, you’ll get a pretty good idea of what the puzzle picture is.
Let’s say you have a circle inside a square with sides the same length as the circle’s diameter. Then throw a bunch of sand onto the square/circle combination and count how many grains of sand end up in the circle. If you know the length of the square’s side and the proportion of sand that ends up in the circle, you can work out a value for π.
(You want more detail? Fine: the side of the square can be used to calculate the area of the square, multiply that by the proportion of sand inside the circle will give you an estimate of the circle’s area, divide the circle’s area by square of half the square’s length and you will get an estimate of π).
The more grains of sand you throw at the square/circle, the closer the estimate will be to the actual answer.
In my previous primer on Elo ratings, I talked about different ways of calculating Elo ratings with a view of measuring form and/or class. This primer will look in a bit more depth at how I arrived at the specific numbers for the variables.
The main variables in an Elo model are:
- Starting ratings (discrete versus continuous)
- If continuous, then the reversion to mean discount of ratings
- Calculation method (margin vs result/WTA)
- K, weighting for each game
- h, homefield advantage
- p, margin factor
Some are derived from game data, others from optimisation. Let’s tackle them one by one.