Rating formulas

WinTD provides three formulas for computing approximate ratings. These are called US Chess, FIDE and 2P. These are used either in computing (approximate) post tournament ratings or in maintaining a local rating system. Note that all of these are based upon the same "Elo" methods and are normed to give similar rating gaps based upon relative performance—they differ mainly in how quickly ratings are permitted to change when a result substantially differs from the expected one.

US Chess and FIDE use approximately the current rating formulas for those two bodies. These can only approximate the information for a number of reasons:

•US Chess rates tournaments in chronological order, and the rating that you have for players may not include tournaments played since the last database was produced.

•US Chess computes ratings for previously unrated players which depend (to some extent) on the birthdate of each player. WinTD doesn't collect that information. (You can input it for your purposes, but it isn't required).

•US Chess makes occasional adjustments to the rating formula, particularly regarding bonus points.

•FIDE uses somewhat different formulas depending upon the age of the participant and number of rated games previously played. Again, WinTD doesn't collect that information.

•FIDE doesn't rate games between unrateds. Note that the FIDE rating report is completely different from what we're discussing here—that only includes information for games that are FIDE-ratable.

2P stands for 2 Parameter. Unlike the US Chess and FIDE systems, which assign to a player a single number (their rating), the 2P system keeps two: a rating and a standard deviation. The standard deviation measures how precise the estimate of the rating is. For a player who has played only a few games, the standard deviation will be quite large (over 200). For a player who has played many games and has consistent results, the standard deviation will be much smaller, possibly as low as 50. However, players with low ratings (below 1000) will have a standard deviation which stays fairly high. This allows their ratings to move up very quickly once they start to perform better. The standard deviation usually goes down from one tournament to the next, but it can go up if a player's results are highly unlikely (in either direction) given her current rating. Again, this helps the rating track improving players better.

The standard deviation is used in several ways:

•If Player A plays Player B, and Player B has a very high standard deviation (that is, his rating is not very well established), the game is given less weight in updating A's rating than if B had a low standard deviation.

•If Player A has a high standard deviation, the change in his rating will be much larger for a given performance than if his rating were the same but his standard deviation were lower. (This is similar to the behavior of the US Chess system, where ratings of players with relatively few games change more than those of established players).

If you're creating your own local rating system, we would recommend using the 2P method.

Unrated Players

In order for the calculations to work, it is necessary to have "prior" estimates of the ratings for the players. In computing the 2P rating, WinTD will use the main rating field for a player with a main rating but no local rating. For previously unrated players, you have two ways to handle this:

•You can assign prior ratings yourself, based perhaps on age. We would recommend a standard deviation of 250 or 300. Edit>Change Common Info... allows you to set local ratings and standard deviations of all players that you select in the window.

•You can use an "average" rating that WinTD computes using the tournament information. To compute this, WinTD looks at games between unrated and rated players and determines a (single) rating for the unrateds which is compatible with their performance. When WinTD does the calculations, it will pop up the Rate Section dialog box.

You can accept or modify WinTD's estimate of the average strength of the unrateds. An alternative (and probably superior) way to handle this is to use a standard value for sections of a particular type, where the players would be a relatively standard age. US Chess' initialization is 50 x age (up to age 26) so a standard value of 500 for players who are roughly 10 years old would be similar to that.

Note that if a small percentage of the players (fewer than 1/3) is unrated, the computed ratings won't be very sensitive to the prior ratings assigned to the unrateds.

The Lowest Rating Allowed is typically 100 (which matches US Chess practice), but you can pick any number you want, even negative ones. In a population of players where quite a few are very inexperienced (and for instance have no real chance of checkmating an opponent) a number like -200 will spread the bottom end out as there will be a meaningful difference between -200 and +50.