Clarification on game counts for provisional ratings

There continue to be questions as to how the game counts for provisional ratings are determined when a rating is initialized using other ratings information. The Ratings Committee has approved the following explanation:

For US Chess players who have a provisional rating (normally those who have completed 25 or fewer games), the “based-on” value connected to their rating is not always the number of games they have played; it is the “adjusted” number of games which is usually larger than the actual number of games.

The only situation in which the adjusted number of games is the same as the actual number of games played is when the player’s initial rating was determined solely based on their age. In every other situation, i.e., when players’ initial ratings are derived from ratings converted from other systems (including other US Chess systems), the adjusted number of games is the sum of the actual number of games played and a value that reflects the information used to initialize a player’s rating. That value, which can never be larger than 10, depends upon the possibly multiple sources of converted ratings (the other US Chess online or over-the-board systems, FIDE, or CFC) to obtain an initialized rating, and the staleness of the converted rating.

However, after a first tournament, the adjusted number of games increases only by the actual number of games completed in subsequent events. The details of the calculation for the adjusted number of games can be found in section 2 of the US Chess rating system specifications:

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Some historical background may be useful.

Prior to the introduction of the blended ratings initialization process several years ago, most ratings initialized from other US Chess ratings information had an initial game count of 0 while ratings initialized from FIDE ratings had a game count of 5 or 10, based on the player’s FIDE rating.

Under blended ratings, any rating initialized from other ratings information (FIDE, CFC or US Chess) will have an adjusted game count between 1 and 10.

As a result, we are seeing more questions about why someone’s provisional rating game count is different from their number of competed games in that ratings system.

Whether this will reduce the number of questions raised about this issue is uncertain.

Links to this Forums topic have been added to several pages on MSA, including the MSA FAQ.

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Let’s say a player has their US Chess OTB regular rating initialized from the other ratings they have and the game count they get from that initialization is five. Usually a provisional rating based on 5 games is governed by the “special” rating formula but is it governed by the special rating formula in this case?

As long as the game count is 8 or lower, the special formula applies.

The Special Formula exists because the Standard Formula can get a bit funky when N’ (from whatever source) is small. The Standard Formula does one step in a Newton’s method procedure, where the first step can be a doozy when N’ is small.

Note that It’s possible to have N’<=8 when the player has more than 8 credited games if the rating is very low, but it can only be barely less than 8 even for R=100, and a possible overshoot isn’t a serious issue for someone with such a low rating.