Gratis ratings notes

Gratis is a system for estimating players' strength from tournament data using a statistical 
package developed by David Bofinger.

For each player yopu will find three numerical values (followed by the corresponding dan/kyu
levels). The two outer numbers give a range within which Gratis estimates the player's actual
rating lies; the middle number is the most likely rating within that range. The value 4.91
indicates slightly weaker than average five dan; 2.5 is on the borderline between 2 dan and 3 dan;
4.0 is an exactly average 4 dan; -3.61 is a strong 5 kyu; 0 is an average 1 kyu; 3d+ is in the top 
third of 3 dans; 1d is in the middle third of 1 dans; 4k- is in the bottom third of 4
kyus; 12k is a 12 kyu of any kind (+/- are not used below 10 kyu).
 
Note that the indicated ratings may not necessarily correspond to ratings given by AGAGoR,
as they are based on different methodologies. This will be most eveident in kyu-level ratings.
AGAGoR is an Elo-type system in which a change is a player's rating is made on the basis of 
results in an individual tournament, which has the advantage of simplicity; Gratis uses a more
sophisticated but more computer-intensive algorithm which recomputes over the whole archive of 
tournament records. 

Both ratings should be taken as indicative only, they reflect tournament play
up to to a certain point in time, an do not necessarily reflect current strength or strength under
other conditions such as club- or internet- games. Ratings based on a very small number of games
should not be trusted at all (and in Gratis will be reflected in a large range being shown).