Proposed new World ranking system announced for comment

[<<] [>>] by Jonathan Kirby
10th February 2011 (CqE Official News)

The WCF's Ranking Review Committee has been looking at changing the way the AC world rankings are calculated to address various issues, the biggest one being the lag effect of the current system which means that your grade can go down when you win a game or up when you lose. We are likely to recommend that the "Dynamic Grading" system (DG) be adopted.

Rankings calculated with DG can be found on Chris Williams' rankings website: butedock.demon.co.uk/cgs/rank.php (select Dynamic Grade).

We have written an article explaining the new system and the various insights we had on the way to creating it, which is available at: oxfordcroquet.com/tech/nel-dg/

It is intended to be a complete enough technical description for anyone else to understand the mathematical issues we had to consider. However, I hope that it is also possible to get the general idea from that article.

Comments would be very much appreciated. We will probably write a report with a recommendation to the WCF around the end of March or early April, so it would be helpful to get any comments or suggestions by then.

Jonathan
Chairman, WCF Ranking Review Committee

I'll try to give a quick overview of what DG does.

If you look at the DG ranking list, you will see two important numbers for each player: the grade, and the pdt (performance deviation trend).

The grade is simple - it is the system's best guess at how good the player is, in terms of their recent (and predicted future) form. When you win a game, your grade goes up, and when you lose it goes down. The rest of the system is all about how much it goes up or down. Just like the existing systems, if you beat someone with a high grade then you get more points than if you beat someone with a lower grade. So if you beat Robert Fulford, expect a bumper reward, but if you beat a novice who has just started playing ranking games and is at the bottom of the rankings, don't expect it to affect your grade much. On the other hand, if you lose to your local novice then expect to see a bigger effect.

So far the system is simpler than the existing one, where it is possible to win a game and for your grade to go down instead of up. So what is pdt? Roughly it measures how well you have played to your grade over the last 37 games (or how much you have deviated from your grade). So pdt = +100 means you have played about 100 points ahead of your grade, and pdt = -50 means 50 points under. Note, this is how well you played compared to your grade at the time of each game, not how well you played compared with your current grade. The current grade is still the system's best guess at how good you are now. The other thing to bear in mind is that pdt only very approximately measures how many points ahead or behind your grade you have played. That is not exactly how it is calculated, but just a rule of thumb.

A player with a very high pdt looks like they may be a rapid improver, so the system adjusts by making their rewards (or losses) for winning or losing games bigger. That way, the system catches up with rapid improvers faster. Also, rapid sliders drop down the rankings faster. But players who are very steady at their grade (pdt close to 0) have smaller rewards and smaller losses for their games. The DG system works better than the existing ranking system for the various tests we have thrown at it.

Why 37 games and not 10, or 36, or 38? And why are the cut-offs for a steady player or a rapid improver exactly what they are. The answer is simple: experiment shows these numbers work best for the tests we did.