Chess Tactics Server


Rating

This page is based on the FICS help page on Glicko Rating.

As you may have noticed, each tactician has a rating and an RD. RD stands for ratings deviation.

What RD represents

The Ratings Deviation is used to measure how much a tactician's current rating should be trusted. A high RD indicates that the tactician may not be competing frequently or that the tactician has not solved very many problems yet at the current rating level. A low RD indicates that the tactician's rating is fairly well established. This is described in more detail below under RD Interpretation.

How RD Affects Ratings Changes

In general, if your RD is high, then your rating will change a lot each time you solve a problem. As it gets smaller, the ratings change per problem will go down. However, the problem's RD will have the opposite effect, to a smaller extent: if his RD is high, then your ratings change will be somewhat smaller than it would be otherwise.

How RD is Updated

In this system, the RD will decrease somewhat each time you solve a problem, because when you solve more problems there is a stronger basis for concluding what your rating should be. However, if you go for a long time without solving any problem, your RD will increase to reflect the increased uncertainty in your rating due to the passage of time. Also, your RD will decrease more if the problem's rating is similar to yours, and decrease less your problem's rating is much different.

Mathematical Interpretation of RD

Direct from Mark Glickman:
Each tactician can be characterized as having a true (but unknown) rating that may be thought of as the tactician's average ability. We never get to know that value, partly because we only observe a finite number of problems, but also because that true rating changes over time as a tactician's ability changes. But we can estimate the unknown rating. Rather than restrict oneself to a single estimate of the true rating, we can describe our estimate as an interval of plausible values. The interval is wider if we are less sure about the tactician's unknown true rating, and the interval is narrower if we are more sure about the unknown rating. The RD quantifies the uncertainty in terms of probability:

The interval formed by current rating +/- RD contains your true rating with probability of about 0.67.
The interval formed by current rating +/- 2 * RD contains your true rating with probability of about 0.95.
The interval formed by current rating +/- 3 * RD contains your true rating with probability of about 0.997.

For those of you who know something about statistics, these are not confidence intervals, but are called central posterior intervals because the derivation came from a Bayesian analysis of the problem. These numbers are found from the cumulative distribution function of the normal distribution with mean = current rating, and standard deviation = RD. For example, CDF[ N[1600,50], 1550 ] = .159 approximately (that's shorthand Mathematica notation.)

Credits

The Glicko Ratings System was invented by Mark Glickman, Ph.D. who is currently at Boston University.