Just curious. If an IM who does not have a USCF rating, joins the USCF and plays in a tournament. His FIDE rating is 2400. He plays 4 rounds against opponents averaging 1900. He wins all the games. What will his provisional rating be?
That is insufficient information to duplicate what happens in the ratings formula (in this case the special formula.)
If what you are getting at is whether the IM’s rating will be 2300, the answer is no. We no longer use the old provisional formula. My guess is that it would be above 2450, perhaps above 2470. See glicko.net/ratings/rating.system.pdf
The FIDE rating converts to 2468, based on 10. The “average” rating of the opponents isn’t a sufficient statistic, even if the “special” (old provisional) rating formula is used, which it wouldn’t be in this case anyway. If, for instance, we treated this as 2468/5, then 1900W, 1900W, 1900W, 1900W wouldn’t change the rating at all (you can’t lose rating points for a win).
However, since it’s treated as b/10, the regular formula applies with a K of 800/(10+4)=57.1. With four wins over 1900’s, his expected score would be 3.995 so the only gain would be due to rounding up, so 2469/14. OTOH, with 1500W, 1800W, 2000W, 2300W, his expected score is 3.87 (courtesy of the one game against an opponent who isn’t completely overmatched), so he would pick up 8 points (since he has a high K factor due to the low game count) to end at 2476/14.
Good catch, Tom, I forgot that the initial estimate would be /10, dictating use of the regular formula instead of the special formula.
However, the time control is also relevant information here, because a high rated player in a dual-rated event has a much lower K.
Interesting, thanks for the information.